ALBERT

Description:    In this paper, we consider families of operators { x r } r Î L in a tracial C*-probability space ( A , j ) , whose joint *-distribution is invariant under free complexification and the action of the hyperoctahedral quantum groups { H n + } n Î \mathbb N . We prove a strong form of Haagerup’s inequality for the non-self-adjoint operator algebra B generated by { x r } r Î L , which generalizes the strong Haagerup inequalities for *-free R-diagonal families obtained by Kemp–Speicher (J Funct Anal 251:141–173, 2007 ). As an application of our result, we show that B always has the metric approximation property (MAP). We also apply our techniques to study the reduced C*-algebra of the free unitary quantum group U n + . We show that the non-self-adjoint subalgebra B n generated by the matrix elements of the fundamental corepresentation of U n + has the MAP. Additionally, we prove a strong Haagerup inequality for B n , which improves on the estimates given by Vergnioux’s property RD (Vergnioux in J Oper Theory 57:303–324, 2007 ). Content Type Journal Article Pages 1-33 DOI 10.1007/s00220-012-1447-6 Authors Michael Brannan, Department of Mathematics and Statistics, Queen’s University, 99 University Avenue, Kingston, ON K7L 3N6, Canada Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    To any locally finite representation of a given double crossed sum (product) Lie algebra (group), we associate a stable anti Yetter-Drinfeld (SAYD) module over the bicrossed product Hopf algebra which arises from the semidualization procedure. We prove a van Est isomorphism between the relative Lie algebra cohomology of the total Lie algebra and the Hopf cyclic cohomology of the corresponding Hopf algebra with coefficients in the associated SAYD module. Content Type Journal Article Pages 1-21 DOI 10.1007/s00220-012-1452-9 Authors Bahram Rangipour, Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB, Canada Serkan Sütlü, Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB, Canada Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    If X  =  X ( t , ξ ) is the solution to the stochastic porous media equation in O Ì R d , 1 £ d £ 3, modelling the self-organized criticality (Barbu et al. in Commun Math Phys 285:901–923, 2009 ) and X c is the critical state, then it is proved that ó õ ¥ 0   m ( O \ O t 0 ) dt 〈 ¥ ,\mathbb P - a . s . and lim t ® ¥   ó õ O   | X ( t ) - X c | d x = l 〈 ¥ , \mathbb P - a . s . Here, m is the Lebesgue measure and O t c is the critical region { x Î O ; X ( t , x )= X c ( x )} and X c ( ξ ) ≤ X (0, ξ ) a.e. x Î O . If the stochastic Gaussian perturbation has only finitely many modes (but is still function-valued), lim t ® ¥   ó õ K   | X ( t ) - X c | d x = 0 exponentially fast for all compact K Ì O with probability one, if the noise is sufficiently strong. We also recover that in the deterministic case ℓ  = 0. Content Type Journal Article Pages 1-17 DOI 10.1007/s00220-012-1429-8 Authors Viorel Barbu, Octav Mayer Institute of Mathematics of Romanian Academy, 700500 Iaşi, Romania Michael Röckner, Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    In higher dimensional quantum field theory, irreducible representations of the Poincaré group are associated with particles. Their counterpart in two-dimensional massless models are “waves” introduced by Buchholz. In this paper we show that waves do not interact in two-dimensional Möbius covariant theories and in- and out-asymptotic fields coincide. We identify the set of the collision states of waves with the subspace generated by the chiral components of the Möbius covariant net from the vacuum. It is also shown that Bisognano-Wichmann property, dilation covariance and asymptotic completeness (with respect to waves) imply Möbius symmetry. Under natural assumptions, we observe that the maps which give asymptotic fields in Poincaré covariant theory are conditional expectations between appropriate algebras. We show that a two-dimensional massless theory is asymptotically complete and noninteracting if and only if it is a chiral Möbius covariant theory. Content Type Journal Article Pages 1-23 DOI 10.1007/s00220-012-1439-6 Authors Yoh Tanimoto, Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 1, 00133 Roma, Italy Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    Associated to any (pseudo)-Riemannian manifold M of dimension n is an n  + 1-dimensional noncommutative differential structure (Ω 1 , d) on the manifold, with the extra dimension encoding the classical Laplacian as a noncommutative ‘vector field’. We use the classical connection, Ricci tensor and Hodge Laplacian to construct (Ω 2 , d) and a natural noncommutative torsion free connection ( Ñ , s ) on Ω 1 . We show that its generalised braiding s : W 1 Ä W 1 ® W 1 Ä W 1 obeys the quantum Yang-Baxter or braid relations only when the original M is flat, i.e. their failure is governed by the Riemann curvature, and that σ 2  = id only when M is Einstein. We show that if M has a conformal Killing vector field τ then the cross product algebra C ( M )\rtimes t \mathbb R viewed as a noncommutative analogue of M ×\mathbb R has a natural n  + 2-dimensional calculus extending Ω 1 and a natural spacetime Laplacian now directly defined by the extra dimension. The case M =\mathbb R 3 recovers the Majid-Ruegg bicrossproduct flat spacetime model and the wave-operator used in its variable speed of light prediction, but now as an example of a general construction. As an application we construct the wave operator on a noncommutative Schwarzschild black hole and take a first look at its features. It appears that the infinite classical redshift/time dilation factor at the event horizon is made finite. Content Type Journal Article Pages 1-41 DOI 10.1007/s00220-012-1416-0 Authors Shahn Majid, Queen Mary, University of London, School of Mathematics, Mile End Rd., London, E1 4NS UK Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We propose the operatorial Baxter’s TQ-relations in a general form of the operatorial Bäcklund flow describing the nesting process for the inhomogeneous rational gl ( K | M ) quantum (super)spin chains with twisted periodic boundary conditions. The full set of Q-operators and T-operators on all levels of nesting is explicitly defined. The results are based on a generalization of the identities among the group characters and their group co-derivatives with respect to the twist matrix, found by one of the authors Kazakov and Vieira (JHEP 0810:050, 2008 ). Our formalism, based on this new “master” identity, allows a systematic and rather straightforward derivation of the whole set of nested Bethe ansatz equations for the spectrum of quantum integrable spin chains, starting from the R-matrix. Content Type Journal Article Pages 1-28 DOI 10.1007/s00220-012-1428-9 Authors Vladimir Kazakov, Ecole Normale Superieure, LPT, 75231 Paris Cedex-5, France Sebastien Leurent, Ecole Normale Superieure, LPT, 75231 Paris Cedex-5, France Zengo Tsuboi, Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Am Mühlenberg 1, 14476 Potsdam, Germany Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We find and investigate the structure of solutions to the Ginzburg Landau equation for a high temperature superconductor with tetragonal symmetry. This is done near an isolated, rotationally symmetric d-wave vortex state with its core at the origin defined on all of \mathbb R 2 . We prove that the solution’s s-wave component nucleates near the vortex core for temperatures just below the d-wave critical temperature. We further show that this causes the rotational symmetry to break and that the solution develops a fourfold symmetry with respect to a rotation by an angle of \frac p 2 . Content Type Journal Article Pages 1-30 DOI 10.1007/s00220-012-1430-2 Authors Minkyun Kim, CGGVeritas, 10300 Town Park Drive, Houston, Texas 77072, USA Daniel Phillips, Department of Mathematics, Purdue University, West Lafayette, IN 47907-2067, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    Let T =\mathbb R d . Let a function QT 2 ® \mathbb C satisfy Q ( s , t )= Q ( t , s )   and | Q ( s , t ) | =1 . A generalized statistics is described by creation operators ¶ t f and annihilation operators ∂ t , t Î T , which satisfy the Q -commutation relations: ¶ s ¶ f t = Q ( s , t ) ¶ f t ¶ s + d ( s , t ) , ¶ s ¶ t = Q ( t , s ) ¶ t ¶ s , ¶ f s ¶ f t = Q ( t , s ) ¶ f t ¶ f s . From the point of view of physics, the most important case of a generalized statistics is the anyon statistics, for which Q ( s , t ) is equal to q if s  〈  t , and to - q   if s  〉  t . Here q Î \mathbb C , | q | = 1. We start the paper with a detailed discussion of a Q -Fock space and operators ( ¶ t f , ¶ t ) t Î T in it, which satisfy the Q -commutation relations. Next, we consider a noncommutative stochastic process (white noise) w ( t )= ¶ t f + ¶ t + l ¶ t f ¶ t , t Î T . Here l Î \mathbb R is a fixed parameter. The case λ = 0 corresponds to a Q -analog of Brownian motion, while λ ≠ 0 corresponds to a (centered) Q -Poisson process. We study Q -Hermite ( Q -Charlier respectively) polynomials of infinitely many noncommutatative variables ( w ( t )) t Î T . The main aim of the paper is to explain the notion of independence for a generalized statistics, and to derive corresponding Lévy processes. To this end, we recursively define Q -cumulants of a field ( x ( t )) t Î T . This allows us to define a Q -Lévy process as a field ( x ( t )) t Î T whose values at different points of T are Q -independent and which possesses a stationarity of increments (in a certain sense). We present an explicit construction of a Q -Lévy process, and derive a Nualart–Schoutens-type chaotic decomposition for such a process. Content Type Journal Article Pages 1-35 DOI 10.1007/s00220-012-1437-8 Authors Marek Bożejko, Instytut Matematyczny, Uniwersytet Wrocławski, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland Eugene Lytvynov, Department of Mathematics, Swansea University, Singleton Park, Swansea, SA2 8PP UK Janusz Wysoczański, Instytut Matematyczny, Uniwersytet Wrocławski, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We describe the general form of bijective comparability preserving transformations of the Hilbert space effect algebra, thus improving several known characterizations of ortho-order automorphisms. Content Type Journal Article Pages 1-10 DOI 10.1007/s00220-012-1434-y Authors Peter Šemrl, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We give an explicit formula for the number of nodal domains of certain eigenfunctions on a flat torus. We apply this to an isospectral but not isometric family of pairs of flat four-dimensional tori constructed by Conway and Sloane, and we show that corresponding eigenfunctions have the same number of nodal domains. This disproves a conjecture by Brüning, Gnutzmann, and Smilansky. Content Type Journal Article Pages 1-23 DOI 10.1007/s00220-012-1432-0 Authors Jochen Brüning, Institut für Mathematik, Humboldt–Universität, Rudower Chaussee 25, 12489 Berlin, Germany David Fajman, Max Planck Institut for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, 14476 Golm, Germany Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    Vortices in supersymmetric gauge field theory are important constructs in a basic conceptual phenomenon commonly referred to as the dual Meissner effect which is responsible for color confinement. Based on a direct minimization approach, we present a series of sharp existence and uniqueness theorems for the solutions of some non-Abelian vortex equations governing color-charged multiply distributed flux tubes, which provide an essential mechanism for linear confinement. Over a doubly periodic domain, existence results are obtained under explicitly stated necessary and sufficient conditions that relate the size of the domain, the vortex numbers, and the underlying physical coupling parameters of the models. Over the full plane, existence results are valid for arbitrary vortex numbers and coupling parameters. In all cases, solutions are unique. Content Type Journal Article Pages 1-34 DOI 10.1007/s00220-012-1433-z Authors Elliott H. Lieb, Departments of Physics and Mathematics, Princeton University, Princeton, New Jersey 08540, USA Yisong Yang, Department of Mathematics, Polytechnic Institute of New York University, Brooklyn, New York, 11201 USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    In this paper we study inverse boundary value problems with partial data for the magnetic Schrödinger operator. In the case of an infinite slab in \mathbb R n , n ≥ 3, we establish that the magnetic field and the electric potential can be determined uniquely, when the Dirichlet and Neumann data are given either on the different boundary hyperplanes of the slab or on the same hyperplane. This is a generalization of the results of Li and Uhlmann (Inverse Probl Imaging 4(3):449–462, 2010 ), obtained for the Schrödinger operator without magnetic potentials. In the case of a bounded domain in \mathbb R n , n  ≥ 3, extending the results of Ammari and Uhlmann (Indiana Univ Math J 53(1):169–183, 2004 ), we show the unique determination of the magnetic field and electric potential from the Dirichlet and Neumann data, given on two arbitrary open subsets of the boundary, provided that the magnetic and electric potentials are known in a neighborhood of the boundary. Generalizing the results of Isakov (Inverse Probl Imaging 1(1):95–105, 2007 ), we also obtain uniqueness results for the magnetic Schrödinger operator, when the Dirichlet and Neumann data are known on the same part of the boundary, assuming that the inaccessible part of the boundary is a part of a hyperplane. Content Type Journal Article Pages 1-40 DOI 10.1007/s00220-012-1431-1 Authors Katsiaryna Krupchyk, Department of Mathematics and Statistics, University of Helsinki, P. O. Box 68, 00014 Helsinki, Finland Matti Lassas, Department of Mathematics and Statistics, University of Helsinki, P. O. Box 68, 00014 Helsinki, Finland Gunther Uhlmann, Department of Mathematics, University of Washington, Seattle, WA 98195-4350, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    The spectral action for a non-compact commutative spectral triple is computed covariantly in a gauge perturbation up to order 2 in full generality. In the ultraviolet regime, p →∞, the action decays as 1/ p 4 in any even dimension. Content Type Journal Article Pages 1-19 DOI 10.1007/s00220-012-1587-8 Authors B. Iochum, UMR 7332, Unité Mixte de Recherche du CNRS, Aix-Marseille Université, Luminy Case 907, 13288 Marseille Cedex 9, France C. Levy, Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark D. Vassilevich, CMCC, Universidade Federal do ABC, Santo André, S.P., Brazil Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    From a non-constant holomorphic map on a connected Riemann surface we construct an étale second countable locally compact Hausdorff groupoid whose associated groupoid C* -algebra admits a one-parameter group of automorphisms with the property that its KMS states correspond to conformal measures in the sense of Sullivan. In this way certain quadratic polynomials give rise to quantum statistical models with a phase transition arising from spontaneous symmetry breaking. Content Type Journal Article Pages 1-26 DOI 10.1007/s00220-012-1591-z Authors Klaus Thomsen, Institut for Matematiske FAG, Ny Munkegade, 8000 Aarhus C, Denmark Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We determine and study the ground states of a focusing Schrödinger equation in dimension one with a power nonlinearity | ψ | 2 μ ψ and a strong inhomogeneity represented by a singular point perturbation, the so-called (attractive) δ ′ interaction, located at the origin. The time-dependent problem turns out to be globally well posed in the subcritical regime, and locally well posed in the supercritical and critical regime in the appropriate energy space. The set of the (nonlinear) ground states is completely determined. For any value of the nonlinearity power, it exhibits a symmetry breaking bifurcation structure as a function of the frequency (i.e., the nonlinear eigenvalue) ω. More precisely, there exists a critical value ω* of the nonlinear eigenvalue ω, such that: if ω 0 〈  ω 〈  ω*, then there is a single ground state and it is an odd function; if ω 〉  ω* then there exist two non-symmetric ground states. We prove that before bifurcation (i.e., for ω 〈  ω*) and for any subcritical power, every ground state is orbitally stable. After bifurcation (ω = ω *  + 0), ground states are stable if  μ does not exceed a value m * that lies between 2 and 2.5, and become unstable for  μ 〉 μ *. Finally, for  μ 〉  2 and w 〉〉 w * , all ground states are unstable. The branch of odd ground states for ω 〈  ω* can be continued at any ω 〉  ω*, obtaining a family of orbitally unstable stationary states. Existence of ground states is proved by variational techniques, and the stability properties of stationary states are investigated by means of the Grillakis-Shatah-Strauss framework, where some non-standard techniques have to be used to establish the needed properties of linearization operators. Content Type Journal Article Pages 1-43 DOI 10.1007/s00220-012-1597-6 Authors Riccardo Adami, Dipartimento di Scienze Matematiche, Politecnico di Torino, C.so Duca degli Abruzzi 24, 10129 Torino, Italy Diego Noja, Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, v. R. Cozzi 53, 20125 Milano, Italy. Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    This paper is devoted to the study of the classification and stability of Mach configurations. In the Mach reflection of a shock wave by a rigid wall the flow behind the reflected shock front can be supersonic or subsonic. Correspondingly, the Mach configuration can be classified as E-E type and E-H type. In this paper we proved the stability of E-H type Mach configurations provided the reflected shock is weak. The result is the complement of the stability of E-E type Mach configurations in our earlier work. The stability of E-H Mach configurations is reduced to a generalized Tricomi problem of a nonlinear mixed type equation. The linearization of this problem is a generalized Tricomi problem of a linear Lavrentiev-Bitsadze’s mixed type equation. In order to prove the existence of such a problem we first use the equation in the hyperbolic region and a condition on the reflected shock to establish a relation of the unknown function and its normal derivative on the sonic line. Then the generalized Tricomi problem is reduced to a nonlocal boundary value problem in the elliptic region. Careful analysis gives necessary estimates and the solvability of the linearized problem. It leads to the existence of the solution to the corresponding nonlinear problem, which implies the required stability of E-H Mach configurations. Content Type Journal Article Pages 1-40 DOI 10.1007/s00220-012-1570-4 Authors Shuxing Chen, Institute of Mathematics, Fudan University, Shanghai, 200433 P.R. China Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We consider the vanishing-viscosity limit for the Navier-Stokes equations with certain slip-without-friction boundary conditions in a bounded domain with non-flat boundary. In particular, we are able to show convergence in strong norms for a solution starting with initial data belonging to the special subclass of data with vanishing vorticity on the boundary. The proof is obtained by smoothing the initial data and by a perturbation argument with quite precise estimates for the equations of the vorticity and for that of the curl of the vorticity. Content Type Journal Article Pages 1-28 DOI 10.1007/s00220-012-1581-1 Authors Luigi Carlo Berselli, Dipartimento di Matematica Applicata “U. Dini”, Università degli Studi di Pisa, Via F. Buonarroti 1/c, 56127 Pisa, Italy Stefano Spirito, Dipartimento di Matematica, Università dell’Aquila, via Vetoio 1, 67010 Coppito (AQ), Italy Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description: Erratum to: Faithful Squashed Entanglement Content Type Journal Article Category Erratum Pages 1-2 DOI 10.1007/s00220-012-1584-y Authors Fernando G. S. L. Brandão, Departamento de Física, Universidade Federal de Minas Gerais, Belo Horizonte, Caixa Postal 702, 30123-970 MG, Brazil Matthias Christandl, Institute for Theoretical Physics, ETH Zurich, Wolfgang-Pauli-Strasse 27, 8057 Zurich, Switzerland Jon Yard, Center for Nonlinear Studies (CNLS), Computer, Computational and Statistical Sciences (CCS-3), Los Alamos National Laboratory, Los Alamos, NM 87545, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We investigate the hydrodynamic limit for weakly asymmetric simple exclusion processes in crystal lattices. We construct a suitable scaling limit by using a discrete harmonic map. As we shall observe, the quasi-linear parabolic equation in the limit is defined on a flat torus and depends on both the local structure of the crystal lattice and the discrete harmonic map. We formulate the local ergodic theorem on the crystal lattice by introducing the notion of local function bundle, which is a family of local functions on the configuration space. The ideas and methods are taken from the discrete geometric analysis to these problems. Results we obtain are extensions of ones by Kipnis, Olla and Varadhan to crystal lattices. Content Type Journal Article Pages 1-39 DOI 10.1007/s00220-012-1574-0 Authors Ryokichi Tanaka, Department of Mathematics, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto, 606-8502 Japan Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We establish some scaling limits for a model of planar aggregation. The model is described by the composition of a sequence of independent and identically distributed random conformal maps, each corresponding to the addition of one particle. We study the limit of small particle size and rapid aggregation. The process of growing clusters converges, in the sense of Carathéodory, to an inflating disc. A more refined analysis reveals, within the cluster, a tree structure of branching fingers, whose radial component increases deterministically with time. The arguments of any finite sample of fingers, tracked inwards, perform coalescing Brownian motions. The arguments of any finite sample of gaps between the fingers, tracked outwards, also perform coalescing Brownian motions. These properties are closely related to the evolution of harmonic measure on the boundary of the cluster, which is shown to converge to the Brownian web. Content Type Journal Article Pages 1-33 DOI 10.1007/s00220-012-1552-6 Authors James Norris, Statistical Laboratory, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 0WB UK Amanda Turner, Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF UK Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We prove that the quotient of the group algebra of the braid group introduced by Funar (Commun Math Phys 173:513–558, 1995 ) collapses in characteristic distinct from 2. In characteristic 2 we define several quotients of it, which are connected to the classical Hecke and Birman-Wenzl-Murakami quotients, but which admit in addition a symmetry of order 3. We also establish conditions on the possible Markov traces factorizing through it. Content Type Journal Article Pages 1-36 DOI 10.1007/s00220-012-1519-7 Authors Marc Cabanes, Institut de Mathématiques de Jussieu, Université Paris 7, 175 rue du Chevaleret, 75013 Paris, France Ivan Marin, Institut de Mathématiques de Jussieu, Université Paris 7, 175 rue du Chevaleret, 75013 Paris, France Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We prove that, given a certain isometric action of a two-dimensional Abelian group A on a quaternionic Kähler manifold M which preserves a submanifold N ⊂ M , the quotient M ′ =  N / A has a natural Kähler structure. We verify that the assumptions on the group action and on the submanifold N ⊂ M are satisfied for a large class of examples obtained from the supergravity c-map. In particular, we find that all quaternionic Kähler manifolds M in the image of the c-map admit an integrable complex structure compatible with the quaternionic structure, such that N ⊂ M is a complex submanifold. Finally, we discuss how the existence of the Kähler structure on M ′ is required by the consistency of spontaneous N = 2 to N = 1 supersymmetry breaking. Content Type Journal Article Pages 1-30 DOI 10.1007/s00220-012-1541-9 Authors V. Cortés, Department Mathematik, Universität Hamburg, Bundesstraße 55, 20146 Hamburg, Germany J. Louis, Zentrum für Mathematische Physik, Universität Hamburg, Bundesstraße 55, 20146 Hamburg, Germany P. Smyth, Institut de Théorie des Phénomènes Physiques, EPFL, 1015 Lausanne, Switzerland H. Triendl, Institut de Physique Théorique, CEA Saclay, Orme des Merisiers, 91191 Gif-sur-Yvette, France Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We define matrix models that converge to the generating functions of a wide variety of loop models with fugacity taken in sets with an accumulation point. The latter can also be seen as moments of a non-commutative law on a subfactor planar algebra. We apply this construction to compute the generating functions of the Potts model on a random planar map. Content Type Journal Article Pages 1-53 DOI 10.1007/s00220-012-1573-1 Authors A. Guionnet, UMPA, CNRS UMR 5669, ENS Lyon, 46 allée d’Italie, 69007 Lyon, France V. F. R. Jones, Department of Mathematics, UC Berkeley, Berkeley, CA 94720, USA D. Shlyakhtenko, Department of Mathematics, UCLA, Los Angeles, CA 90095, USA P. Zinn-Justin, UPMC Univ Paris 6, CNRS UMR 7589, LPTHE, 75252 Paris Cedex, France Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We consider a system of particles confined in a box L Ì \mathbb R d interacting via a tempered and stable pair potential. We prove the validity of the cluster expansion for the canonical partition function in the high temperature - low density regime. The convergence is uniform in the volume and in the thermodynamic limit it reproduces Mayer’s virial expansion providing an alternative and more direct derivation which avoids the deep combinatorial issues present in the original proof. Content Type Journal Article Pages 1-18 DOI 10.1007/s00220-012-1576-y Authors Elena Pulvirenti, Dipartimento di Matematica, Università di Roma 3, Rome, 00146 Italy Dimitrios Tsagkarogiannis, Department of Applied Mathematics, University of Crete, Heraklion Crete, 71409 Greece Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    The Ising model is widely regarded as the most studied model of spin-systems in statistical physics. The focus of this paper is its dynamic (stochastic) version, the Glauber dynamics, introduced in 1963 and by now the most popular means of sampling the Ising measure. Intensive study throughout the last three decades has yielded a rigorous understanding of the spectral-gap of the dynamics on \mathbb Z 2 everywhere except at criticality. While the critical behavior of the Ising model has long been the focus for physicists, mathematicians have only recently developed an understanding of its critical geometry with the advent of SLE, CLE and new tools to study conformally invariant systems. A rich interplay exists between the static and dynamic models. At the static phase-transition for Ising, the dynamics is conjectured to undergo a critical slowdown : At high temperature the inverse-gap is O (1), at the critical β c it is polynomial in the side-length and at low temperature it is exponential. A seminal series of papers verified this on \mathbb Z 2 except at β = β c where the behavior remained a challenging open problem. Here we establish the first rigorous polynomial upper bound for the critical mixing, thus confirming the critical slowdown for the Ising model in \mathbb Z 2 . Namely, we show that on a finite box with arbitrary (e.g. fixed, free, periodic) boundary conditions, the inverse-gap at β  =  β c is polynomial in the side-length. The proof harnesses recent understanding of the scaling limit of the critical Fortuin-Kasteleyn representation of the Ising model together with classical tools from the analysis of Markov chains. Content Type Journal Article Pages 1-22 DOI 10.1007/s00220-012-1460-9 Authors Eyal Lubetzky, Microsoft Research, One Microsoft Way, Redmond, WA 98052-6399, USA Allan Sly, Department of Statistics, UC Berkeley, Berkeley, CA 94720, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    In our recent paper “The variational Poisson cohomology” ( 2011 ) we computed the dimension of the variational Poisson cohomology H · K ( V ) for any quasiconstant coefficient ℓ × ℓ matrix differential operator K of order N with invertible leading coefficient, provided that V is a normal algebra of differential functions over a linearly closed differential field. In the present paper we show that, for K skewadjoint, the \mathbb Z -graded Lie superalgebra H · K ( V ) is isomorphic to the finite dimensional Lie superalgebra ~ H   ( N l , S ) . We also prove that the subalgebra of “essential” variational Poisson cohomology, consisting of classes vanishing on the Casimirs of K , is zero. This vanishing result has applications to the theory of bi-Hamiltonian structures and their deformations. At the end of the paper we consider also the translation invariant case. Content Type Journal Article Pages 1-28 DOI 10.1007/s00220-012-1461-8 Authors Alberto De Sole, Dipartimento di Matematica, Università di Roma “La Sapienza”, 00185 Roma, Italy Victor G. Kac, Department of Mathematics, M.I.T., Cambridge, MA 02139, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    A convenient framework to treat massless two-dimensional scattering theories has been established by Buchholz. In this framework, we show that the asymptotic algebra and the scattering matrix completely characterize the given theory under asymptotic completeness and standard assumptions. Then we obtain several families of interacting wedge-local nets by a purely von Neumann algebraic procedure. One particular case of them coincides with the deformation of chiral CFT by Buchholz-Lechner-Summers. In another case, we manage to determine completely the strictly local elements. Finally, using Longo-Witten endomorphisms on the U (1)-current net and the free fermion net, a large family of wedge-local nets is constructed. Content Type Journal Article Pages 1-27 DOI 10.1007/s00220-012-1462-7 Authors Yoh Tanimoto, Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 00133 Roma, Italy Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    Long time existence and uniqueness of solutions to the Yang-Mills heat equation is proven over a compact 3-manifold with smooth boundary. The initial data is taken to be a Lie algebra valued connection form in the Sobolev space H 1 . Three kinds of boundary conditions are explored, Dirichlet type, Neumann type and Marini boundary conditions. The last is a nonlinear boundary condition, specified by setting the normal component of the curvature to zero on the boundary. The Yang-Mills heat equation is a weakly parabolic nonlinear equation. We use gauge symmetry breaking to convert it to a parabolic equation and then gauge transform the solution of the parabolic equation back to a solution of the original equation. Apriori estimates are developed by first establishing a gauge invariant version of the Gaffney-Friedrichs inequality. A gauge invariant regularization procedure for solutions is also established. Uniqueness holds upon imposition of boundary conditions on only two of the three components of the connection form because of weak parabolicity. This work is motivated by possible applications to quantum field theory. Content Type Journal Article Pages 1-59 DOI 10.1007/s00220-012-1558-0 Authors Nelia Charalambous, Department of Mathematics, Instituto Technológico Autónomo de México, México, Mexico Leonard Gross, Department of Mathematics, Cornell University, Ithaca, NY 14853-4201, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We present a rigorous scheme that makes it possible to compute eigenvalues of the Laplace operator on hyperbolic surfaces within a given precision. The method is based on an adaptation of the method of particular solutions to the case of locally symmetric spaces and on explicit estimates for the approximation of eigenfunctions on hyperbolic surfaces by certain basis functions. It can be applied to check whether or not there is an eigenvalue in an ε -neighborhood of a given number λ 〉 0. This makes it possible to find all the eigenvalues in a specified interval, up to a given precision with rigorous error estimates. The method converges exponentially fast with the number of basis functions used. Combining the knowledge of the eigenvalues with the Selberg trace formula we are able to compute values and derivatives of the spectral zeta function again with error bounds. As an example we calculate the spectral determinant and the Casimir energy of the Bolza surface and other surfaces. Content Type Journal Article Pages 1-43 DOI 10.1007/s00220-012-1557-1 Authors Alexander Strohmaier, Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU UK. Ville Uski, Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU UK. Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We determine the density of eigenvalues of the scattering matrix of the Schrödinger operator with a short range potential in the high energy asymptotic regime. We give an explicit formula for this density in terms of the X-ray transform of the potential. Content Type Journal Article Pages 1-12 DOI 10.1007/s00220-012-1551-7 Authors Daniel Bulger, Department of Mathematics, King’s College London, Strand, London, WC2R 2LS UK Alexander Pushnitski, Department of Mathematics, King’s College London, Strand, London, WC2R 2LS UK Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We consider a purely massive local relativistic quantum theory specified by a family of von Neumann algebras indexed by the space-time regions. We assume that, affiliated with the algebras associated to wedge regions, there are operators which create only single particle states from the vacuum (so-called polarization-free generators) and are well-behaved under the space-time translations. Strengthening a result of Borchers, Buchholz and Schroer, we show that then the theory is unitarily equivalent to that of a free field for the corresponding particle type. We admit particles with any spin and localization of the charge in space-like cones, thereby covering the case of string-localized covariant quantum fields. Content Type Journal Article Pages 1-20 DOI 10.1007/s00220-012-1546-4 Authors Jens Mund, Departamento de Física, Universidade Federal de Juiz de Fora, 36036-900 Juiz de Fora, MG, Brazil Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We prove the simplicity and analyticity of the eigenvalues of the cubic oscillator Hamiltonian, ll H ( b )= - \frac d 2 dx 2 + x 2 + i Ö   b   x 3 , for β in the cut plane C c := C \ R - . Moreover, we prove that the spectrum consists of the perturbative eigenvalues { E n ( β )} n  ≥ 0 labeled by the constant number n of nodes of the corresponding eigenfunctions. In addition, for all b Î C c , E n ( b ) can be computed as the Stieltjes-Padé sum of its perturbation series at β  = 0. This also gives an alternative proof of the fact that the spectrum of H ( β ) is real when β is a positive number. This way, the main results on the repulsive PT-symmetric and on the attractive quartic oscillators are extended to the cubic case. Content Type Journal Article Pages 1-22 DOI 10.1007/s00220-012-1559-z Authors Vincenzo Grecchi, Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato, 40126 Bologna, Italy André Martinez, Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato, 40126 Bologna, Italy Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We study the representation theory of a conformal net A on S 1 from a K-theoretical point of view using its universal C*-algebra C * ( A ) . We prove that if A satisfies the split property then, for every representation π of A with finite statistical dimension, p ( C * ( A )) is weakly closed and hence a finite direct sum of type I ∞ factors. We define the more manageable locally normal universal C*-algebra C ln * ( A ) as the quotient of C * ( A ) by its largest ideal vanishing in all locally normal representations and we investigate its structure. In particular, if A is completely rational with n sectors, then C ln * ( A ) is a direct sum of n type I ∞ factors. Its ideal \mathfrak K A of compact operators has nontrivial K-theory, and we prove that the DHR endomorphisms of C * ( A ) with finite statistical dimension act on \mathfrak K A , giving rise to an action of the fusion semiring of DHR sectors on K 0 (\mathfrak K A ) . Moreover, we show that this action corresponds to the regular representation of the associated fusion algebra. Content Type Journal Article Pages 1-26 DOI 10.1007/s00220-012-1561-5 Authors Sebastiano Carpi, Dipartimento di Economia, Università di Chieti-Pescara “G. d’Annunzio”, Viale Pindaro, 42, 65127 Pescara, Italy Roberto Conti, Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sezione di Matematica, Sapienza Università di Roma, Via A. Scarpa, 16, 00161 Roma, Italy Robin Hillier, Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 1, 00133 Roma, Italy Mihály Weiner, Mathematical Institute, Department of Analysis, Budapest University of Technology & Economics (BME), Müegyetem rk. 3-9, 1111 Budapest, Hungary Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    The existence of self-similar solutions with fat tails for Smoluchowski’s coagulation equation has so far only been established for the solvable kernels and the diagonal one. In this paper we prove the existence of such self-similar solutions for continuous kernels K that are homogeneous of degree g Î ( - ¥ ,1) and satisfy K ( x , y ) ≤ C ( x γ + y γ ). More precisely, for any r Î ( g ,1) we establish the existence of a continuous weak nonnegative self-similar profile with decay x - (1+ r ) as x → ∞. For the proof we consider the time-dependent problem in self-similar variables with the aim to use a variant of Tykonov’s fixed point theorem to establish the existence of a stationary profile. This requires to identify a weakly compact subset that is invariant under the evolution. In our case we define a set of nonnegative measures which encodes the desired decay behaviour in an integrated form. The main difficulty is to establish the invariance of the lower bound under the evolution. Our key idea is to choose as a test function in the time dependent problem the solution of the associated backward dual problem. Content Type Journal Article Pages 1-28 DOI 10.1007/s00220-012-1553-5 Authors B. Niethammer, Institute of Applied Mathematics, University of Bonn, Endenicher Allee 60, 53115 Bonn, Germany J. J. L. Velázquez, Institute of Applied Mathematics, University of Bonn, Endenicher Allee 60, 53115 Bonn, Germany Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    In this work we study the spectral zeta function associated with the Laplace operator acting on scalar functions defined on a warped product of manifolds of the type I  × f N , where I is an interval of the real line and N is a compact, d -dimensional Riemannian manifold either with or without boundary. Starting from an integral representation of the spectral zeta function, we find its analytic continuation by exploiting the WKB asymptotic expansion of the eigenfunctions of the Laplace operator on M for which a detailed analysis is presented. We apply the obtained results to the explicit computation of the zeta regularized functional determinant and the coefficients of the heat kernel asymptotic expansion. Content Type Journal Article Pages 1-31 DOI 10.1007/s00220-012-1555-3 Authors Guglielmo Fucci, Department of Mathematics, East Carolina University, Greenville, NC 27858, USA Klaus Kirsten, Department of Mathematics, Baylor University, Waco, TX 76798, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    Quantum systems whose classical counterpart have ergodic dynamics are quantum ergodic in the sense that almost all eigenstates are uniformly distributed in phase space. In contrast, when the classical dynamics is integrable, there is concentration of eigenfunctions on invariant structures in phase space. In this paper we study eigenfunction statistics for the Laplacian perturbed by a delta-potential (also known as a point scatterer) on a flat torus, a popular model used to study the transition between integrability and chaos in quantum mechanics. The eigenfunctions of this operator consist of eigenfunctions of the Laplacian which vanish at the scatterer, and new, or perturbed, eigenfunctions. We show that almost all of the perturbed eigenfunctions are uniformly distributed in configuration space. Content Type Journal Article Pages 1-20 DOI 10.1007/s00220-012-1556-2 Authors Zeév Rudnick, Raymond and Beverly Sackler School of Mathematical Sciences, Tel Aviv University, Tel Aviv, 69978 Israel Henrik Ueberschär, Raymond and Beverly Sackler School of Mathematical Sciences, Tel Aviv University, Tel Aviv, 69978 Israel Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We consider the Pauli-Fierz Hamiltonian with dynamical nuclei and investigate the transitions between the resonant electronic energy levels under the assumption that there are no free photons in the beginning. Coupling the limits of small fine structure constant and of heavy nuclei allows us to prove the validity of the Born-Oppenheimer approximation at leading order and to provide a simple formula for the rate of spontaneous decay. Content Type Journal Article Pages 1-40 DOI 10.1007/s00220-012-1547-3 Authors Stefan Teufel, Mathematisches Institut der Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany Jakob Wachsmuth, Mathematisches Institut der Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    It is shown that quantum fields for massive particles with braid group statistics (Plektons) in three-dimensional space-time cannot be free, in a quite elementary sense: They must exhibit elastic two-particle scattering into every solid angle, and at every energy. This also implies that for such particles there cannot be any operators localized in wedge regions which create only single particle states from the vacuum and which are well-behaved under the space-time translations (so-called temperate polarization- free generators). These results considerably strengthen an earlier “NoGo-theorem for ’free’ relativistic Anyons”. As a by-product we extend a fact which is well-known in quantum field theory to the case of topological charges (i.e., charges localized in space-like cones) in d ≥ 4, namely: If there is no elastic two-particle scattering into some arbitrarily small open solid angle element, then the 2-particle S-matrix is trivial. Content Type Journal Article Pages 1-24 DOI 10.1007/s00220-012-1560-6 Authors Jacques Bros, Institut de Physique Théorique, CEA, Saclay, France Jens Mund, Departamento de Física, Universidade Federal de Juiz de Fora, 36036-900 Juiz de Fora, MG, Brazil Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    This paper studies the existence of invariant smooth Lagrangian graphs for Tonelli Hamiltonian systems with symmetries. In particular, we consider Tonelli Hamiltonians with n independent but not necessarily involutive constants of motion and obtain two theorems reminiscent of the Liouville-Arnol′d theorem. Moreover, we also obtain results on the structure of the configuration spaces of such systems that are reminiscent of results on the configuration space of completely integrable Tonelli Hamiltonians. Content Type Journal Article Pages 1-25 DOI 10.1007/s00220-012-1536-6 Authors Leo T. Butler, Department of Mathematics, Central Michigan University, Mt. Pleasant, MI 48859, USA Alfonso Sorrentino, Dipartimento di Matematica, Università degli Studi “Roma Tre”, Largo S. Leonardo Murialdo 1, 00146 Rome, Italy Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We prove that an integrated version of the Gurau colored tensor model supplemented with the usual Bosonic propagator on U (1) 4 is renormalizable to all orders in perturbation theory. The model is of the type expected for quantization of space-time in 4 D Euclidean gravity and is the first example of a renormalizable model of this kind. Its vertex and propagator are four-stranded like in 4 D group field theories, but without gauge averaging on the strands. Surprisingly perhaps, the model is of the f 6 rather than of the f 4 type, since two different f 6 -type interactions are log-divergent, i.e. marginal in the renormalization group sense. The renormalization proof relies on a multiscale analysis. It identifies all divergent graphs through a power counting theorem. These divergent graphs have internal and external structure of a particular kind called melonic. Melonic graphs dominate the 1/N expansion of colored tensor models and generalize the planar ribbon graphs of matrix models. A new locality principle is established for this category of graphs which allows to renormalize their divergences through counterterms of the form of the bare Lagrangian interactions. The model also has an unexpected anomalous log-divergent ( ó õ f 2 ) 2 term, which can be interpreted as the generation of a scalar matter field out of pure gravity. Content Type Journal Article Pages 1-41 DOI 10.1007/s00220-012-1549-1 Authors Joseph Ben Geloun, Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, ON N2L 2Y5, Canada Vincent Rivasseau, Laboratoire de Physique Théorique, CNRS UMR 8627, Université Paris-Sud XI, 91405 Orsay, France Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    In this work we study certain invariant measures that can be associated to the time averaged observation of a broad class of dissipative semigroups via the notion of a generalized Banach limit. Consider an arbitrary complete separable metric space X which is acted on by any continuous semigroup { S ( t )} t ≥ 0 . Suppose that { S ( t )} t ≥ 0 possesses a global attractor A . We show that, for any generalized Banach limit LIM T → ∞ and any probability distribution of initial conditions \mathfrak m 0 , that there exists an invariant probability measure \mathfrak m , whose support is contained in A , such that ó õ X   j ( x ) d \mathfrak m ( x ) = \underset t ® ¥ LIM \frac1 T ó õ T 0   ó õ X   j ( S ( t ) x ) d \mathfrak m 0 ( x ) d t , for all observables φ living in a suitable function space of continuous mappings on X . This work is based on the framework of Foias et al. (Encyclopedia of mathematics and its applications, vol 83. Cambridge University Press, Cambridge, 2001 ); it generalizes and simplifies the proofs of more recent works (Wang in Disc Cont Dyn Syst 23(1–2):521–540, 2009 ; Lukaszewicz et al. in J Dyn Diff Eq 23(2):225–250, 2011 ). In particular our results rely on the novel use of a general but elementary topological observation, valid in any metric space, which concerns the growth of continuous functions in the neighborhood of compact sets. In the case when { S ( t )} t ≥ 0 does not possess a compact absorbing set, this lemma allows us to sidestep the use of weak compactness arguments which require the imposition of cumbersome weak continuity conditions and thus restricts the phase space X to the case of a reflexive Banach space. Two examples of concrete dynamical systems where the semigroup is known to be non-compact are examined in detail. We first consider the Navier-Stokes equations with memory in the diffusion terms. This is the so called Jeffery’s model which describes certain classes of viscoelastic fluids. We then consider a family of neutral delay differential equations, that is equations with delays in the time derivative terms. These systems may arise in the study of wave propagation problems coming from certain first order hyperbolic partial differential equations; for example for the study of line transmission problems. For the second example the phase space is X = C ([ - t ,0],\mathbb R n ) , for some delay τ 〉 0, so that X is not reflexive in this case. Content Type Journal Article Pages 1-39 DOI 10.1007/s00220-012-1515-y Authors Mickaël D. Chekroun, Department of Atmospheric Sciences and Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90095-1565, USA Nathan E. Glatt-Holtz, Department of Mathematics and The Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, IN 47405, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    It is shown that for each finite number N of Dirac measures d s n supported at points s n Î \mathbb R 3 with given amplitudes a n Î \mathbb R \{0} there exists a unique real-valued function u Î C 0, 1 (\mathbb R 3 ) , vanishing at infinity, which distributionally solves the quasi-linear elliptic partial differential equation of divergence form - Ñ ·( Ñ u / Ö   1 - | Ñ u | 2   ) = 4 p N å n =1   a n d s n . Moreover, u Î C w (\mathbb R 3 \{ s n } n =1 N ) . The result can be interpreted in at least two ways: (a) for any number N of point charges of arbitrary magnitude and sign at prescribed locations s n in three-dimensional Euclidean space there exists a unique electrostatic field which satisfies the Maxwell-Born-Infeld field equations smoothly away from the point charges and vanishes as | s | → ∞; (b) for any number N of integral mean curvatures assigned to locations s n Î \mathbb R 3 Ì \mathbb R 1, 3 there exists a unique asymptotically flat, almost everywhere space-like maximal slice with point defects of Minkowski spacetime \mathbb R 1, 3 , having lightcone singularities over the s n but being smooth otherwise, and whose height function vanishes as | s | → ∞. No struts between the point singularities ever occur. Content Type Journal Article Pages 1-15 DOI 10.1007/s00220-012-1502-3 Authors Michael K.-H. Kiessling, Department of Mathematics, Rutgers, The State University of New Jersey, 110 Frelinghuysen Rd., Piscataway, NJ 08854, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We continue the analysis of the set of locally normal KMS states w.r.t. the translation group for a local conformal net A of von Neumann algebras on \mathbb R . In the first part we have proved the uniqueness of the KMS state on every completely rational net. In this second part, we exhibit several (non-rational) conformal nets which admit continuously many primary KMS states. We give a complete classification of the KMS states on the U (1)-current net and on the Virasoro net Vir 1 with the central charge c  = 1, whilst for the Virasoro net Vir c with c 〉 1 we exhibit a (possibly incomplete) list of continuously many primary KMS states. To this end, we provide a variation of the Araki-Haag-Kastler-Takesaki theorem within the locally normal system framework: if there is an inclusion of split nets A Ì B and A is the fixed point of B w.r.t. a compact gauge group, then any locally normal, primary KMS state on A extends to a locally normal, primary state on B , KMS w.r.t. a perturbed translation. Concerning the non-local case, we show that the free Fermi model admits a unique KMS state. Content Type Journal Article Pages 1-32 DOI 10.1007/s00220-012-1514-z Authors Paolo Camassa, Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 1, 00133 Roma, Italy Roberto Longo, Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 1, 00133 Roma, Italy Yoh Tanimoto, Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 1, 00133 Roma, Italy Mihály Weiner, Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 1, 00133 Roma, Italy Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    In this article we present an approach to describing the geometry and curvature of the configuration spaces of a class of simple idealized planar linkages. This is based on determining the curvature of such configuration spaces canonically embedded into Euclidean space, and then the behaviour of the dynamics of such linkages can be understood via the associated geodesic flow. Our objective is to present a method which, in principle, can be applied to many different examples. Content Type Journal Article Pages 1-20 DOI 10.1007/s00220-012-1521-0 Authors M. L. S. Magalhães, Centro de Matemática, Universidade do Porto, Porto, 4169-007 Portugal M. Pollicott, Department of Mathematics, Warwick University, Coventry, CV4 7AL UK Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    In this paper, we investigate the formation of singularities and the existence of peaked traveling-wave solutions for a modified Camassa-Holm equation with cubic nonlinearity. The equation is known to be integrable, and is shown to admit a single peaked soliton and multi-peakon solutions, of a different character than those of the Camassa-Holm equation. Singularities of the solutions can occur only in the form of wave-breaking, and a new wave-breaking mechanism for solutions with certain initial profiles is described in detail. Content Type Journal Article Pages 1-29 DOI 10.1007/s00220-012-1566-0 Authors Guilong Gui, Department of Mathematics, Jiangsu University, Zhenjiang, 212013 P.R. China Yue Liu, Department of Mathematics, University of Texas, Arlington, TX 76019-0408, USA Peter J. Olver, School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA Changzheng Qu, Department of Mathematics, Ningbo University, Ningbo, 315211 P.R. China Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We study a quantum version of the SU(2) Hopf fibration S 7 ® S 4 and its associated twistor geometry. Our quantum sphere S 7 q arises as the unit sphere inside a q -deformed quaternion space \mathbb H 2 q . The resulting four-sphere S 4 q is a quantum analogue of the quaternionic projective space \mathbb HP 1 . The quantum fibration is endowed with compatible non-universal differential calculi. By investigating the quantum symmetries of the fibration, we obtain the geometry of the corresponding twistor space \mathbb CP 3 q and use it to study a system of anti-self-duality equations on S 4 q , for which we find an ‘instanton’ solution coming from the natural projection defining the tautological bundle over S 4 q . Content Type Journal Article Pages 1-42 DOI 10.1007/s00220-012-1565-1 Authors Simon Brain, Unité de Recherche en Mathématiques, Université du Luxembourg (Campus Kirchberg), 6 Rue Richard Coudenhove–Kalergi, 1359 Luxembourg, Grand Duchy of Luxembourg Giovanni Landi, Dipartimento di Matematica, Università di Trieste, Via A. Valerio 12/1, 34127 Trieste, Italy Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    This paper analyzes the action δ of a Lie algebra X by derivations on a C*–algebra A . This action satisfies an “almost inner” property which ensures affiliation of the generators of the derivations δ with A , and is expressed in terms of corresponding pseudo–resolvents. In particular, for an abelian Lie algebra X acting on a primitive C*–algebra A , it is shown that there is a central extension of X which determines algebraic relations of the underlying pseudo–resolvents. If the Lie action δ is ergodic, i . e . the only elements of A on which all the derivations in δ X vanish are multiples of the identity, then this extension is given by a (non–degenerate) symplectic form σ on X . Moreover, the algebra generated by the pseudo–resolvents coincides with the resolvent algebra based on the symplectic space ( X , σ ). Thus the resolvent algebra of the canonical commutation relations, which was recently introduced in physically motivated analyses of quantum systems, appears also naturally in the representation theory of Lie algebras of derivations acting on C*–algebras. Content Type Journal Article Pages 1-13 DOI 10.1007/s00220-012-1567-z Authors Detlev Buchholz, Institut für Theoretische Physik and Courant Centre, “Higher Order Structures in Mathematics”, Universität Göttingen, 37077 Göttingen, Germany Hendrik Grundling, Department of Mathematics, University of New South Wales, Sydney, NSW 2052, Australia Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We study the motion of a heavy tracer particle weakly coupled to a dense ideal Bose gas exhibiting Bose-Einstein condensation. In the so-called mean-field limit, the dynamics of this system approaches one determined by nonlinear Hamiltonian evolution equations describing a process of emission of Cerenkov radiation of sound waves into the Bose-Einstein condensate along the particle’s trajectory. The emission of Cerenkov radiation results in a friction force with memory acting on the tracer particle and causing it to decelerate until it comes to rest. “A moving body will come to rest as soon as the force pushing it no longer acts on it in the manner necessary for its propulsion.” —— Aristotle Content Type Journal Article Pages 1-44 DOI 10.1007/s00220-012-1564-2 Authors Jürg Fröhlich, Institute for Theoretical Physics, ETH Zurich, 8093 Zürich, Switzerland Zhou Gang, Institute for Theoretical Physics, ETH Zurich, 8093 Zürich, Switzerland Avy Soffer, Department of Mathematics, Rutgers University, New Jersey, 08854 USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    Double Lie algebroids were discovered by Kirill Mackenzie from the study of double Lie groupoids and were defined in terms of rather complicated conditions making use of duality theory for Lie algebroids and double vector bundles. In this paper we establish a simple alternative characterization of double Lie algebroids in a supermanifold language. Namely, we show that a double Lie algebroid in Mackenzie’s sense is equivalent to a double vector bundle endowed with a pair of commuting homological vector fields of appropriate weights. Our approach helps to simplify and elucidate Mackenzie’s original definition; we show how it fits into a bigger picture of equivalent structures on ‘neighbor’ double vector bundles. It also opens ways for extending the theory to multiple Lie algebroids, which we introduce here. Content Type Journal Article Pages 1-32 DOI 10.1007/s00220-012-1568-y Authors Theodore Th. Voronov, School of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL UK Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We study the existence of dislocations in an anisotropic Swift-Hohenberg equation. We find dislocations as traveling or standing waves connecting roll patterns with different wavenumbers in an infinite strip. The proof is based on a bifurcation analysis. Spatial dynamics and center-manifold reduction yield a reduced, coupled-mode system of differential equations. Existence of traveling dislocations is then established by showing that this reduced system possesses robust heteroclinic orbits. Content Type Journal Article Pages 1-25 DOI 10.1007/s00220-012-1569-x Authors Mariana Haragus, Université de Franche-Comté, Laboratoire de Mathématiques, 16 route de Gray, 25030 Besançon Cedex, France Arnd Scheel, University of Minnesota, School of Mathematics, 206 Church St. S.E., Minneapolis, MN 55455, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    Let f be a Dirichlet or Neumann eigenfunction of the Laplace-Beltrami operator on a compact Riemannian manifold with boundary. We prove lower bounds for the size of the nodal set { f = 0} . Content Type Journal Article Pages 1-9 DOI 10.1007/s00220-012-1554-4 Authors Sinan Ariturk, Department of Mathematics, Johns Hopkins University, Baltimore, MD 21218, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    The regularized determinant of the Paneitz operator arises in quantum gravity [see Connes in (Noncommutative geometry, 1994 ), IV.4. γ ]. An explicit formula for the relative determinant of two conformally related metrics was computed by Branson in (Commun Math Phys 178:301–309, 1996 ). A similar formula holds for Cheeger’s half-torsion, which plays a role in self-dual field theory [see Juhl in (Families of conformally covariant differential operators, q-curvature and holography. Progress in Mathematics, vol 275, 2009 )], and is defined in terms of regularized determinants of the Hodge laplacian on p -forms ( p 〈  n /2). In this article we show that the corresponding actions are unbounded (above and below) on any conformal four-manifold. We also show that the conformal class of the round sphere admits a second solution which is not given by the pull-back of the round metric by a conformal map, thus violating uniqueness up to gauge equivalence. These results differ from the properties of the determinant of the conformal Laplacian established in (Commun Math Phys 149:241–262, 1992 ), (Ann Math 142:171–212, 1995 ), (Commun Math Phys 189:655–665, 1997 ). We also study entire solutions of the Euler-Lagrange equation of log det P and the half-torsion τ h on \mathbb R 4 \{ 0 } , and show the existence of two families of periodic solutions. One of these families includes Delaunay -type solutions. Content Type Journal Article Pages 1-37 DOI 10.1007/s00220-012-1535-7 Authors Matthew Gursky, Department of Mathematics, University of Notre Dame, 255 Hurley Hall, Notre Dame, IN 46556, USA Andrea Malchiodi, Sector of Mathematical Analysis, SISSA, Via Bonomea 265, 34136 Trieste, Italy Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We study the distribution of eigenvalues for non-selfadjoint perturbations of selfadjoint semiclassical analytic pseudodifferential operators in dimension two, assuming that the classical flow of the unperturbed part is completely integrable. An asymptotic formula of Weyl type for the number of eigenvalues in a spectral band, bounded from above and from below by levels corresponding to Diophantine invariant Lagrangian tori, is established. The Weyl law is given in terms of the long time averages of the leading non-selfadjoint perturbation along the classical flow of the unperturbed part. Content Type Journal Article Pages 373-417 DOI 10.1007/s00220-012-1530-z Authors Michael Hitrik, Department of Mathematics, University of California, Los Angeles, CA 90095-1555, USA Johannes Sjöstrand, IMB, Université de Bourgogne, 9, Av. A. Savary, BP 47870, 21078 Dijon Cédex, France Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616 Journal Volume Volume 314 Journal Issue Volume 314, Number 2

Description:    This paper generalizes Bismut’s equivariant Chern character to the setting of abelian gerbes. In particular, associated to an abelian gerbe with connection, an equivariantly closed differential form is constructed on the space of maps of a torus into the manifold. These constructions are made explicit using a new local version of the higher Hochschild complex, resulting in differential forms given by iterated integrals. Connections to two dimensional topological field theories are indicated. Similarly, this local higher Hochschild complex is used to calculate the 2-holonomy of an abelian gerbe along any closed oriented surface, as well as the derivative of 2-holonomy, which in the case of a torus fits into a sequence of higher holonomies and their differentials. Content Type Journal Article Pages 1-70 DOI 10.1007/s00220-012-1529-5 Authors Thomas Tradler, Department of Mathematics, College of Technology, City University of New York, 300 Jay Street, Brooklyn, NY 11201, USA Scott O. Wilson, Department of Mathematics, Queens College, City University of New York, 65-30 Kissena Blvd., Flushing, NY 11367, USA Mahmoud Zeinalian, Department of Mathematics, C.W. Post Campus of Long Island University, 720 Northern Boulevard, Brookville, NY 11548, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We introduce a “Coulombian renormalized energy” W which is a logarithmic type of interaction between points in the plane, computed by a “renormalization.” We prove various of its properties, such as the existence of minimizers, and show in particular, using results from number theory, that among lattice configurations the triangular lattice is the unique minimizer. Its minimization in general remains open. Our motivation is the study of minimizers of the two-dimensional Ginzburg-Landau energy with applied magnetic field, between the first and second critical fields H c 1 and H c 2 . In that regime, minimizing configurations exhibit densely packed triangular vortex lattices, called Abrikosov lattices. We derive, in some asymptotic regime, W as a Γ-limit of the Ginzburg-Landau energy. More precisely we show that the vortices of minimizers of Ginzburg-Landau, blown-up at a suitable scale, converge to minimizers of W , thus providing a first rigorous hint at the Abrikosov lattice. This is a next order effect compared to the mean-field type results we previously established. The derivation of W uses energy methods: the framework of Γ-convergence, and an abstract scheme for obtaining lower bounds for “2-scale energies” via the ergodic theorem, that we introduce. Content Type Journal Article Pages 1-109 DOI 10.1007/s00220-012-1508-x Authors Etienne Sandier, Université Paris-Est, LAMA – CNRS UMR 8050, 61, Avenue du Général de Gaulle, 94010 Créteil, France Sylvia Serfaty, UPMC Univ. Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, 75005 Paris, France Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    In this article we give new examples of models in boundary quantum field theory, i.e. local time-translation covariant nets of von Neumann algebras, using a recent construction of Longo and Witten, which uses a local conformal net A on the real line together with an element of a unitary semigroup associated with A . Namely, we compute elements of this semigroup coming from Hölder continuous symmetric inner functions for a family of (completely rational) conformal nets which can be obtained by starting with nets of real subspaces, passing to its second quantization nets and taking local extensions of the former. This family is precisely the family of conformal nets associated with lattices, which as we show contains as a special case the level 1 loop group nets of simply connected, simply laced groups. Further examples come from the loop group net of Spin ( n ) at level 2 using the orbifold construction. Content Type Journal Article Pages 1-32 DOI 10.1007/s00220-012-1511-2 Authors Marcel Bischoff, Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 1, 00133 Roma, Italy Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We develop the Batalin-Vilkovisky formalism for classical field theory on generic globally hyperbolic spacetimes. A crucial aspect of our treatment is the incorporation of the principle of local covariance which amounts to formulate the theory without reference to a distinguished spacetime. In particular, this allows a homological construction of the Poisson algebra of observables in classical gravity. Our methods heavily rely on the differential geometry of configuration spaces of classical fields. Content Type Journal Article Pages 1-35 DOI 10.1007/s00220-012-1487-y Authors Klaus Fredenhagen, II Inst. f. Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany Katarzyna Rejzner, II Inst. f. Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    The issue of the inviscid limit for the incompressible Navier-Stokes equations when a no-slip condition is prescribed on the boundary is a famous open problem. A result by Kato (Math Sci Res Inst Publ 2:85–98, 1984 ) says that convergence to the Euler equations holds true in the energy space if and only if the energy dissipation rate of the viscous flow in a boundary layer of width proportional to the viscosity vanishes. Of course, if one considers the motion of a solid body in an incompressible fluid, with a no-slip condition at the interface, the issue of the inviscid limit is as least as difficult. However it is not clear if the additional difficulties linked to the body’s dynamic make this issue more difficult or not. In this paper we consider the motion of a rigid body in an incompressible fluid occupying the complementary set in the space and we prove that a Kato type condition implies the convergence of the fluid velocity and of the body velocity as well, which seems to indicate that an answer in the case of a fixed boundary could also bring an answer to the case where there is a moving body in the fluid. Content Type Journal Article Pages 1-26 DOI 10.1007/s00220-012-1516-x Authors Franck Sueur, CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, 75005 Paris, France Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We study an exactly solvable quantum field theory (QFT) model describing interacting fermions in 2+1 dimensions. This model is motivated by physical arguments suggesting that it provides an effective description of spinless fermions on a square lattice with local hopping and density-density interactions if, close to half filling, the system develops a partial energy gap. The necessary regularization of the QFT model is based on this proposed relation to lattice fermions. We use bosonization methods to diagonalize the Hamiltonian and to compute all correlation functions. We also discuss how, after appropriate multiplicative renormalizations, all short- and long distance cutoffs can be removed. In particular, we prove that the renormalized two-point functions have algebraic decay with non-trivial exponents depending on the interaction strengths, which is a hallmark of Luttinger-liquid behavior. Content Type Journal Article Pages 1-56 DOI 10.1007/s00220-012-1518-8 Authors Jonas de Woul, Department of Theoretical Physics, Royal Institute of Technology (KTH), 106 91 Stockholm, Sweden Edwin Langmann, Department of Theoretical Physics, Royal Institute of Technology (KTH), 106 91 Stockholm, Sweden Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    In this paper, we construct an adiabatic invariant for a large 1– d lattice of particles, which is the so called Klein Gordon lattice. The time evolution of such a quantity is bounded by a stretched exponential as the perturbation parameters tend to zero. At variance with the results available in the literature, our result holds uniformly in the thermodynamic limit. The proof consists of two steps: first, one uses techniques of Hamiltonian perturbation theory to construct a formal adiabatic invariant; second, one uses probabilistic methods to show that, with large probability, the adiabatic invariant is approximately constant. As a corollary, we can give a bound from below to the relaxation time for the considered system, through estimates on the autocorrelation of the adiabatic invariant. Content Type Journal Article Pages 1-33 DOI 10.1007/s00220-012-1522-z Authors Andrea Carati, Università di Milano, Dipartimento di Matematica, Via Saldini 50, 20133 Milano, Italy Alberto Mario Maiocchi, Università di Milano, Dipartimento di Matematica, Via Saldini 50, 20133 Milano, Italy Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We propose a definition of a quantum homogeneous space of a locally compact quantum group. We show that classically it reduces to the notion of homogeneous spaces, giving rise to an operator algebraic characterization of the transitive group actions. On the quantum level our definition goes beyond the quotient case providing a framework which, besides the Vaes’ quotient of a locally compact quantum group by its closed quantum subgroup (our main motivation) is also compatible with, generically non-quotient, quantum homogeneous spaces of a compact quantum group studied by P. Podleś as well as the Rieffel deformation of G-homogeneous spaces. Finally, our definition rules out the paradoxical examples of the non-compact quantum homogeneous spaces of a compact quantum group. Content Type Journal Article Pages 1-19 DOI 10.1007/s00220-012-1491-2 Authors P. Kasprzak, Department of Mathematical Methods in Physics, Faculty of Physics, Warsaw University, Warsaw, Poland Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description: Erratum to: On a Class of Integrable Systems with a Cubic First Integral Content Type Journal Article Category Erratum Pages 1-1 DOI 10.1007/s00220-012-1497-9 Authors Galliano Valent, Laboratoire de Physique Théorique et des Hautes Energies, Unité associée au CNRS UMR 7589, 2 Place Jussieu, 75251 Paris Cedex 05, France Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We consider a construction of a family of almost-sharp fronts for the Surface Quasi-Geostrophic equation. The family is indexed by a parameter indicating the thickness of the almost-sharp front. In this paper we obtain the limit equation when the parameter approaches zero and construct approximate solutions of SQG in the analytic class. Content Type Journal Article Pages 1-23 DOI 10.1007/s00220-012-1486-z Authors Charles Fefferman, Princeton University, Princeton, USA José L. Rodrigo, Warwick University, Coventry, CV4 7AL UK Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We prove conjecture due to Erickson-Semenoff-Zarembo and Drukker-Gross which relates supersymmetric circular Wilson loop operators in the N =4 supersymmetric Yang-Mills theory with a Gaussian matrix model. We also compute the partition function and give a new matrix model formula for the expectation value of a supersymmetric circular Wilson loop operator for the pure N =2 and the N =2 * supersymmetric Yang-Mills theory on a four-sphere. A four-dimensional N =2 superconformal gauge theory is treated similarly. Content Type Journal Article Pages 1-59 DOI 10.1007/s00220-012-1485-0 Authors Vasily Pestun, Physics Department, Princeton University, Princeton, NJ 08544, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    In this article we prove that there exists a Dixmier map for nilpotent super Lie algebras. In other words, if we denote by Prim ( U (\mathfrak g )) the set of (graded) primitive ideals of the enveloping algebra U (\mathfrak g ) of a nilpotent Lie superalgebra \mathfrak g and A d 0 the adjoint group of \mathfrak g 0 , we prove that the usual Dixmier map for nilpotent Lie algebras can be naturally extended to the context of nilpotent super Lie algebras, i.e. there exists a bijective map I : \mathfrak g 0 * / A d 0 ® Prim ( U (\mathfrak g )) defined by sending the equivalence class [ λ ] of a functional λ to a primitive ideal I ( λ ) of U (\mathfrak g ) , and which coincides with the Dixmier map in the case of nilpotent Lie algebras. Moreover, the construction of the previous map is explicit, and more or less parallel to the one for Lie algebras, a major difference with a previous approach ( cf . [ 18 ]). One key fact in the construction is the existence of polarizations for super Lie algebras, generalizing the concept defined for Lie algebras. As a corollary of the previous description, we obtain the isomorphism U (\mathfrak g )/ I ( l ) @ Cliff q ( k ) Ä A p ( k ) , where ( p , q ) = ( dim (\mathfrak g 0 /\mathfrak g 0 l )/2, dim (\mathfrak g 1 /\mathfrak g 1 l )) , we get a direct construction of the maximal ideals of the underlying algebra of U (\mathfrak g ) and also some properties of the stabilizers of the primitive ideals of U (\mathfrak g ) . Content Type Journal Article Pages 1-34 DOI 10.1007/s00220-012-1505-0 Authors Estanislao Herscovich, Fakultät für Mathematik, Universität Bielefeld, 33615 Bielefeld, Germany Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We solve the quantum version of the A 1 T -system by use of quantum networks. The system is interpreted as a particular set of mutations of a suitable (infinite-rank) quantum cluster algebra, and Laurent positivity follows from our solution. As an application we re-derive the corresponding quantum network solution to the quantum A 1 Q -system and generalize it to the fully non-commutative case. We give the relation between the quantum T -system and the quantum lattice Liouville equation, which is the quantized Y -system. Content Type Journal Article Pages 1-22 DOI 10.1007/s00220-012-1488-x Authors Philippe Di Francesco, Institut de Physique Théorique du Commissariat à l’Energie Atomique, Unité de Recherche Associée du CNRS, CEA Saclay/IPhT/Bat 774, 91191 Gif sur Yvette Cedex, France Rinat Kedem, Department of Mathematics, University of Illinois, MC-382, Urbana, IL 61821, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    For a two-dimensional Schrödinger operator H α V  = −Δ − αV with the radial potential V ( x ) =  F (| x |), F ( r ) ≥ 0, we study the behavior of the number N − ( H α V ) of its negative eigenvalues, as the coupling parameter α tends to infinity. We obtain the necessary and sufficient conditions for the semi-classical growth N − ( H α V ) =  O ( α ) and for the validity of the Weyl asymptotic law. Content Type Journal Article Pages 1-13 DOI 10.1007/s00220-012-1501-4 Authors A. Laptev, Department of Mathematics, Imperial College London, Huxley Building, 180 Queen’s Gate, London, SW7 2AZ UK M. Solomyak, Department of Mathematics, Weizmann Institute, Rehovot, Israel Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    The symmetric states on a quasi local C *–algebra on the infinite set of indices J are those invariant under the action of the group of the permutations moving only a finite, but arbitrary, number of elements of J . The celebrated De Finetti Theorem describes the structure of the symmetric states (i.e. exchangeable probability measures) in classical probability. In the present paper we extend the De Finetti Theorem to the case of the CAR algebra, that is for physical systems describing Fermions. Namely, after showing that a symmetric state is automatically even under the natural action of the parity automorphism, we prove that the compact convex set of such states is a Choquet simplex, whose extremal (i.e. ergodic w.r.t. the action of the group of permutations previously described) are precisely the product states in the sense of Araki–Moriya. In order to do that, we also prove some ergodic properties naturally enjoyed by the symmetric states which have a self–containing interest. Content Type Journal Article Pages 1-18 DOI 10.1007/s00220-012-1506-z Authors Vitonofrio Crismale, Dipartimento di Matematica, Università degli Studi di Bari, Via E. Orabona, 4, 70125 Bari, Italy Francesco Fidaleo, Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, Roma, 00133 Italy Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We develop an adiabatic theory for generators of contracting evolution on Banach spaces. This provides a uniform framework for a host of adiabatic theorems ranging from unitary quantum evolutions through quantum evolutions of open systems generated by Lindbladians all the way to classically driven stochastic systems. In all these cases the adiabatic evolution approximates, to lowest order, the natural notion of parallel transport in the manifold of instantaneous stationary states. The dynamics in the manifold of instantaneous stationary states and transversal to it have distinct characteristics: The former is irreversible and the latter is transient in a sense that we explain. Both the gapped and gapless cases are considered. Some applications are discussed. Content Type Journal Article Pages 1-29 DOI 10.1007/s00220-012-1504-1 Authors J. E. Avron, Department of Physics, Technion, 32000 Haifa, Israel M. Fraas, Department of Physics, Technion, 32000 Haifa, Israel G. M. Graf, Theoretische Physik, ETH Zurich, 8093 Zurich, Switzerland P. Grech, Theoretische Physik, ETH Zurich, 8093 Zurich, Switzerland Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description: Erratum to: The Holst Action by the Spectral Action Principle Content Type Journal Article Category Erratum Pages 1-2 DOI 10.1007/s00220-012-1507-y Authors Frank Pfäffle, Mathematisches Institut, Georg-August Universität Göttingen, Bunsenstraße 3-5, Göttingen, Germany Christoph A. Stephan, Fachbereich Mathematik, Universität Hamburg, Bundesstraße 55, Hamburg, Germany Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    In previous work, the authors have developed a geometric theory of fundamental strata to study connections on the projective line with irregular singularities of parahoric formal type. In this paper, the moduli space of connections that contain regular fundamental strata with fixed combinatorics at each singular point is constructed as a smooth Poisson reduction. The authors then explicitly compute the isomonodromy equations as an integrable system. This result generalizes work of Jimbo, Miwa, and Ueno to connections whose singularities have parahoric formal type. Content Type Journal Article Pages 1-34 DOI 10.1007/s00220-012-1493-0 Authors Christopher L. Bremer, Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA Daniel S. Sage, Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    Following work of Ecker (Comm Anal Geom 15:1025–1061, 2007 ), we consider a weighted Gibbons-Hawking-York functional on a Riemannian manifold-with-boundary. We compute its variational properties and its time derivative under Perelman’s modified Ricci flow. The answer has a boundary term which involves an extension of Hamilton’s differential Harnack expression for the mean curvature flow in Euclidean space. We also derive the evolution equations for the second fundamental form and the mean curvature, under a mean curvature flow in a Ricci flow background. In the case of a gradient Ricci soliton background, we discuss mean curvature solitons and Huisken monotonicity. Content Type Journal Article Pages 1-17 DOI 10.1007/s00220-012-1503-2 Authors John Lott, Department of Mathematics, University of California at Berkeley, Berkeley, CA 94720-3840, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    One major obstacle in extending the classification of small index subfactors beyond 3 + Ö 3 is the appearance of infinite families of candidate principal graphs with 4-valent vertices (in particular, the “weeds” Q and Q ¢ from Part 1 (Morrison and Snyder in Commun. Math. Phys., doi: 10.1007/s00220-012-1426-y , 2012 ). Thus instead of using triple point obstructions to eliminate candidate graphs, we need to develop new quadruple point obstructions. In this paper we prove two quadruple point obstructions. The first uses quadratic tangles techniques and eliminates the weed Q ¢ immediately. The second uses connections, and when combined with an additional number theoretic argument it eliminates both weeds Q and Q ¢ . Finally, we prove the uniqueness (up to taking duals) of the 3311 Goodman-de la Harpe-Jones subfactor using a combination of planar algebra techniques and connections. Content Type Journal Article Pages 1-24 DOI 10.1007/s00220-012-1472-5 Authors Masaki Izumi, Department of Mathematics, Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto, 606-8502 Japan Vaughan F. R. Jones, Department of Mathematics, University of California, Berkeley, CA 94720, USA Scott Morrison, Department of Mathematics, University of California, Berkeley, CA 94720, USA Noah Snyder, Department of Mathematics, Columbia University, New York, NY 10026, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We give a presentation of the centralizer algebras for tensor products of spinor representations of quantum groups via generators and relations. In the even-dimensional case, this can be described in terms of non-standard q -deformations of orthogonal Lie algebras; in the odd-dimensional case only a certain subalgebra will appear. In the classical case q  = 1 the relations boil down to Lie algebra relations. Content Type Journal Article Pages 1-21 DOI 10.1007/s00220-012-1494-z Authors Hans Wenzl, Department of Mathematics, University of California, San Diego, La Jolla, CA 92093, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We consider a class of nonlinear Boltzmann equations describing return to thermal equilibrium in a gas of colliding particles suspended in a thermal medium. We study solutions in the space L 1 ( G (1) , d l ), where G (1) =\mathbb R 3 ×\mathbb T 3 is the one-particle phase space and d l = d 3 v d 3 x is the Liouville measure on Γ (1) . Special solutions of these equations, called “Maxwellians,” are spatially homogenous static Maxwell velocity distributions at the temperature of the medium. We prove that, for dilute gases, the solutions corresponding to smooth initial conditions in a weighted L 1 -space converge to a Maxwellian in L 1 ( G (1) , d l ) , exponentially fast in time. Content Type Journal Article Pages 1-30 DOI 10.1007/s00220-012-1499-7 Authors Jürg Fröhlich, Institute for Theoretical Physics, ETH Zurich, 8093 Zürich, Switzerland Zhou Gang, Institute for Theoretical Physics, ETH Zurich, 8093 Zürich, Switzerland Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We define a class of lattice models for two-dimensional topological phases with boundary such that both the bulk and the boundary excitations are gapped. The bulk part is constructed using a unitary tensor category C as in the Levin-Wen model, whereas the boundary is associated with a module category over C . We also consider domain walls (or defect lines) between different bulk phases. A domain wall is transparent to bulk excitations if the corresponding unitary tensor categories are Morita equivalent. Defects of higher codimension will also be studied. In summary, we give a dictionary between physical ingredients of lattice models and tensor-categorical notions. Content Type Journal Article Pages 1-23 DOI 10.1007/s00220-012-1500-5 Authors Alexei Kitaev, California Institute of Technology, Pasadena, CA 91125, USA Liang Kong, Institute for Advanced Study, Tsinghua University, Beijing, 100084 China Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We study the actions of local conformal vector fields X Î conf ( M , g ) on the spinor bundle of ( M , g ) and on its classical counterpart: the supercotangent bundle M of ( M , g ). We first deal with the classical framework and determine the Hamiltonian lift of conf ( M , g ) to M . We then perform the geometric quantization of the supercotangent bundle of ( M , g ), which constructs the spinor bundle as the quantum representation space. The Kosmann Lie derivative of spinors is obtained by quantization of the comoment map. The quantum and classical actions of conf ( M , g ) turn, respectively, the space of differential operators acting on spinor densities and the space of their symbols into conf ( M , g )-modules. They are filtered and admit a common associated graded module. In the conformally flat case, the latter helps us determine the conformal invariants of both conf ( M , g )-modules, in particular the conformally odd powers of the Dirac operator. Content Type Journal Article Pages 1-34 DOI 10.1007/s00220-012-1475-2 Authors J.-P. Michel, Institut Camille Jordan, Université Claude Bernard Lyon 1, 43 Boulevard du 11 Novembre 1918, 69622 Villeurbanne Cedex, France Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We discuss a class of normal forms of the completely resonant non-linear Schrödinger equation on a torus. We stress the geometric and combinatorial constructions arising from this study. Content Type Journal Article Pages 1-57 DOI 10.1007/s00220-012-1483-2 Authors M. Procesi, Department of Mathematics, University of Naples Federico II, Naples, 80138 Italy C. Procesi, Department of Mathematics, University of Rome, La Sapienza, Rome, 00185 Italy Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We first rigourously establish, for any N ≥ 2, that the toroidal modular invariant partition functions for the (not necessarily unitary) W N ( p , q ) minimal models biject onto a well-defined subset of those of the SU( N ) × SU( N ) Wess-Zumino-Witten theories at level ( p − N , q − N ). This permits considerable simplifications to the proof of the Cappelli-Itzykson-Zuber classification of Virasoro minimal models. More important, we obtain from this the complete classification of all modular invariants for the W 3 ( p , q ) minimal models. All should be realised by rational conformal field theories. Previously, only those for the unitary models, i.e. W 3 ( p , p  + 1), were classified. For all N our correspondence yields for free an extensive list of W N ( p , q ) modular invariants. The W 3 modular invariants, like the Virasoro minimal models, all factorise into SU(3) modular invariants, but this fails in general for larger N . We also classify the SU(3) × SU(3) modular invariants, and find there a new infinite series of exceptionals. Content Type Journal Article Pages 1-24 DOI 10.1007/s00220-012-1473-4 Authors Elaine Beltaos, Mathematics Department, Grant MacEwan University, 10700-104 Ave, Edmonton, AB T5J 4S2, Canada Terry Gannon, Mathematics Department, University of Alberta, Edmonton, AB T6G 2G1, Canada Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    In the present work, we give the coercivity estimates for the Boltzmann collision operator Q (·, ·) without angular cut-off to clarify in which case the functional á - Q ( g , f ), f ñ will become the truly sub-elliptic. Based on this observation and commutator estimates in Alexandre et al. (Arch Rat Mech Anal 198:39–123, 2010 ), the upper bound estimates for the collision operator in Chen and He (Arch Rat Mech Anal 201(2):501–548, 2011 ) and the stability results in Desvillettes and Mouhot (Arch Rat Mech Anal 193(2):227–253, 2009 ), in the function space L 1 q Ç H N , we establish global well-posedness or local well-posedness for the spatially homogeneous Boltzmann equation with full-range interaction(covering most of physical collision kernels). Content Type Journal Article Pages 1-30 DOI 10.1007/s00220-012-1481-4 Authors Lingbing He, Department of Mathematical Sciences, Tsinghua University, Beijing, 100084 P. R. China Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We prove that the maximum number N c of non-relativistic electrons that a nucleus of charge Z can bind is less than 1.22 Z  + 3 Z 1/3 . This improves Lieb’s upper bound N c  〈 2 Z  + 1 Lieb (Phys Rev A 29:3018–3028, 1984 ) when Z  ≥ 6. Our method also applies to non-relativistic atoms in magnetic field and to pseudo-relativistic atoms. We show that in these cases, under appropriate conditions, limsup Z ® ¥   N c / Z £ 1.22 . Content Type Journal Article Pages 1-19 DOI 10.1007/s00220-012-1479-y Authors Phan Thành Nam, Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    Let M be a six dimensional manifold, endowed with a cohomogeneity one action of G  = SU 2 × SU 2 , and M reg Ì M its subset of regular points. We show that M reg admits a smooth, 2-parameter family of G -invariant, non-isometric strict nearly Kähler structures and that a 1-parameter subfamily of such structures smoothly extends over a singular orbit of type S 3 . This determines a new class of examples of nearly Kähler structures on T S 3 . Content Type Journal Article Pages 1-24 DOI 10.1007/s00220-012-1482-3 Authors Fabio Podestà, Dip. di Matematica “U.Dini”, Università di Firenze, Viale Morgagni 67/A, 50134 Firenze, Italy Andrea Spiro, Scuola di Scienze e Tecnologie, Università di Camerino, Via Madonna delle Carceri, 62032 Camerino (Macerata), Italy Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We consider a class of lattice topological field theories, among which are the weak-coupling limit of 2d Yang-Mills theory and 3d Riemannian quantum gravity, whose dynamical variables are flat discrete connections with compact structure group on a cell 2-complex. In these models, it is known that the path integral measure is ill-defined because of a phenomenon known as ‘bubble divergences’. In this paper, we extend recent results of the authors to the cases where these divergences cannot be understood in terms of cellular cohomology. We introduce in its place the relevant twisted cohomology, and use it to compute the divergence degree of the partition function. We also relate its dominant part to the Reidemeister torsion of the complex, thereby generalizing previous results of Barrett and Naish-Guzman. The main limitation to our approach is the presence of singularities in the representation variety of the fundamental group of the complex; we illustrate this issue in the well-known case of two-dimensional manifolds. Content Type Journal Article Pages 1-28 DOI 10.1007/s00220-012-1477-0 Authors Valentin Bonzom, Centre de Physique Théorique, Campus de Luminy, Case 907, 13288 Marseille Cedex 09, France Matteo Smerlak, Centre de Physique Théorique, Campus de Luminy, Case 907, 13288 Marseille Cedex 09, France Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    A state that an inertial observer in Minkowski space perceives to be the vacuum will appear to an accelerating observer to be a thermal bath of radiation. We study the impact of this Davies-Fulling-Unruh noise on communication, particularly quantum communication from an inertial sender to an accelerating observer and private communication between two inertial observers in the presence of an accelerating eavesdropper. In both cases, we establish compact, tractable formulas for the associated communication capacities assuming encodings that allow a single excitation in one of a fixed number of modes per use of the communications channel. Our contributions include a rigorous presentation of the general theory of the private quantum capacity as well as a detailed analysis of the structure of these channels, including their group-theoretic properties and a proof that they are conjugate degradable. Connections between the Unruh channel and optical amplifiers are also discussed. Content Type Journal Article Pages 1-38 DOI 10.1007/s00220-012-1476-1 Authors Kamil Brádler, School of Computer Science, McGill University, Montreal, Quebec, Canada Patrick Hayden, School of Computer Science, McGill University, Montreal, Quebec, Canada Prakash Panangaden, School of Computer Science, McGill University, Montreal, Quebec, Canada Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We prove global well-posedness in H 1 for the energy-critical defocusing initial-value problem ( i ¶ t + D x ) u = u | u | 2 ,    u (0)= f , in the semiperiodic setting x Î \mathbb R ×\mathbb T 3 . Content Type Journal Article Pages 1-51 DOI 10.1007/s00220-012-1474-3 Authors Alexandru D. Ionescu, Department of Mathematics, Princeton University, Princeton, NJ 08544, USA Benoit Pausader, Department of Mathematics, Brown University, Providence, RI 02912, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We set up, purely in A-model terms, a novel formalism for the global solution of the open and closed topological A-model on toric Calabi-Yau threefolds. The starting point is to build on recent progress in the mathematical theory of open Gromov-Witten invariants of orbifolds; we interpret the localization formulae as relating D-brane amplitudes to closed string amplitudes perturbed with twisted masses through an analogue of the “loop insertion operator” of matrix models. We first generalize this form of open/closed string duality to general toric backgrounds in all chambers of the stringy Kähler moduli space; secondly, we display a neat connection of the (gauged) closed string side to tau functions of 1+1 Hamiltonian integrable hierarchies, and exploit it to provide an effective computation of open string amplitudes. In doing so, we also provide a systematic treatment of the change of flat open moduli induced by a phase transition in the closed moduli space. We test our proposal in detail by providing an extensive number of checks. We also use our formalism to give a localization-based derivation of the Hori-Vafa spectral curves as coming from a resummation of A-model disc instantons. Content Type Journal Article Pages 1-46 DOI 10.1007/s00220-012-1489-9 Authors Andrea Brini, Section de Mathématiques and Département de Physique Théorique, Université de Genève, 24 quai Ansermet, CH-1211 Geneva, Switzerland Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We consider the Einstein equations coupled to an ultrastiff perfect fluid and prove the existence of a family of solutions with an initial singularity whose structure is that of explicit isotropic models. This family of solutions is ‘generic’ in the sense that it depends on as many free functions as a general solution, i.e., without imposing any symmetry assumptions, of the Einstein-Euler equations. The method we use is a that of a Fuchsian reduction. Content Type Journal Article Pages 1-19 DOI 10.1007/s00220-012-1496-x Authors J. Mark Heinzle, University of Vienna, Faculty of Physics, Gravitational Physics, Boltzmanngasse 5, 1090 Vienna, Austria Patrik Sandin, Department of Physics, University of Karlstad, 651 88 Karlstad, Sweden Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    Aiming at a complete classification of unitary N  = 2 minimal models (where the assumption of space-time supersymmetry has been dropped), it is shown that each modular invariant candidate partition function of such a theory is indeed the partition function of a fully-fledged unitary N  = 2 minimal model, subject to the assumptions that orbifolding is a ‘physical’ process and that the space-time supersymmetric A - D - E models are physical. A family of models constructed via orbifoldings of either the diagonal model or of the space-time supersymmetric exceptional models then demonstrates that there exists a unitary N  = 2 minimal model for every one of the allowed partition functions in the list obtained from Gannon’s work (Gannon in Nucl Phys B 491:659–688, 1997 ). Kreuzer and Schellekens’ conjecture (Nucl Phys B 411:97–121, 1994 ) that all simple current invariants can be obtained as orbifolds of the diagonal model, even when the extra assumption of higher-genus modular invariance is dropped, is confirmed in the case of the unitary N  = 2 minimal models by simple counting arguments. Content Type Journal Article Pages 1-44 DOI 10.1007/s00220-012-1478-z Authors Oliver Gray, Mathematics Department, University of Bristol, Bristol, BS8 1TH UK Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We show that limits for the critical exponent tending to ∞ exist in both critical circle homeomorphism of golden mean rotation number and Fibonacci circle coverings. Moreover, they are the same. The limit map is not analytic at the critical point, which is flat, but has non-trivial complex dynamics. Content Type Journal Article Pages 1-40 DOI 10.1007/s00220-012-1471-6 Authors Genadi Levin, Einstein Institute of Mathematics, Hebrew University, Givat Ram, 91904 Jerusalem, Israel Grzegorz Świa¸tek, Department of Mathematics and Information Science, Politechnika Warszawska, Plac Politechniki 1, 00-661 Warszawa, Poland Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    The present paper deals with the question of representability of nets of C*-algebras whose underlying poset, indexing the net, is not upward directed. A particular class of nets, called C*-net bundles, is classified in terms of C*-dynamical systems having as group the fundamental group of the poset. Any net of C*-algebras has a canonical morphism into a C*-net bundle, the enveloping net bundle, which generalizes the notion of universal C*-algebra given by Fredenhagen to nonsimply connected posets. This allows a classification of nets; in particular, we call injective those nets such that the canonical morphism is faithful. Injectivity turns out to be equivalent to the existence of faithful representations. We further relate injectivity to a generalized Čech cocycle of the net, and this allows us to give examples of nets exhausting the above classification. Using these results we have shown, in another paper, that any conformal net over S 1 is injective. Content Type Journal Article Pages 1-40 DOI 10.1007/s00220-012-1490-3 Authors Giuseppe Ruzzi, Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 00133 Roma, Italy Ezio Vasselli, Dipartimento di Matematica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 5, 00185 Roma, Italy Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    Self-attractive random walks (polymers) undergo a phase transition in terms of the applied drift (force): If the drift is strong enough, then the walk is ballistic, whereas in the case of small drifts self-attraction wins and the walk is sub-ballistic. We show that, in any dimension d  ≥ 2, this transition is of first order. In fact, we prove that the walk is already ballistic at critical drifts, and establish the corresponding LLN and CLT. Content Type Journal Article Pages 1-27 DOI 10.1007/s00220-012-1492-1 Authors Dmitry Ioffe, Faculty of Industrial Engineering and Management, Technion, Haifa, 32000 Israel Yvan Velenik, Section de Mathématiques, Université de Genève, 2-4 rue du Lièvre Case Postal 64, 1211 Genève 4, Switzerland Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We explore the tunneling behavior of a quantum particle on a finite graph in the presence of an asymptotically large potential with two or three potential wells. The behavior of the particle is primarily governed by the local spectral symmetry of the graph around the wells. In the case of two wells the behavior is stable in the sense that it can be predicted from a sufficiently large neighborhood of the wells. However in the case of three wells we are able to exhibit examples where the tunneling behavior can be changed significantly by perturbing the graph arbitrarily far from the wells. Content Type Journal Article Pages 1-20 DOI 10.1007/s00220-012-1453-8 Authors Yong Lin, Department of Mathematics, Information School, Renmin University of China, Beijing, People’s Republic of China Gábor Lippner, Department of Mathematics, Harvard University, Cambridge, MA 02138, USA Shing-Tung Yau, Department of Mathematics, Harvard University, Cambridge, MA 02138, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We prove that the supergravity r- and c-maps preserve completeness. As a consequence, any component H of a hypersurface { h  = 1} defined by a homogeneous cubic polynomial h such that - ¶ 2 h is a complete Riemannian metric on H defines a complete projective special Kähler manifold and any complete projective special Kähler manifold defines a complete quaternionic Kähler manifold of negative scalar curvature. We classify all complete quaternionic Kähler manifolds of dimension less or equal to 12 which are obtained in this way and describe some complete examples in 16 dimensions. Content Type Journal Article Pages 1-23 DOI 10.1007/s00220-012-1443-x Authors V. Cortés, Department of Mathematics and Center for Mathematical Physics, University of Hamburg, Bundesstraße 55, 20146 Hamburg, Germany X. Han, Department of Mathematics and Center for Mathematical Physics, University of Hamburg, Bundesstraße 55, 20146 Hamburg, Germany T. Mohaupt, Theoretical Physics Division, Department of Mathematical Sciences, University of Liverpool, Peach Street, Liverpool, L69 7ZL UK Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We study the dynamics of strongly dissipative Hénon-like maps, around the first bifurcation parameter a * at which the uniform hyperbolicity is destroyed by the formation of tangencies inside the limit set. We prove that a * is a full Lebesgue density point of the set of parameters for which Lebesgue almost every initial point diverges to infinity under positive iteration. A key ingredient is that a * corresponds to the “non-recurrence of every critical point”, reminiscent of Misiurewicz parameters in one-dimensional dynamics. Adapting on the one hand Benedicks & Carleson’s parameter exclusion argument, we construct a set of “good parameters” having a * as a full density point. Adapting Benedicks & Viana’s volume control argument on the other, we analyze Lebesgue typical dynamics corresponding to these good parameters. Content Type Journal Article Pages 1-49 DOI 10.1007/s00220-012-1442-y Authors Hiroki Takahasi, Department of Mathematics, Faculty of Science, Kyoto University, Kyoto, 606-8502 Japan Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    Let G be a simply connected semisimple compact Lie group with standard Poisson structure, K a closed Poisson-Lie subgroup, 0 〈  q  〈 1. We study a quantization C ( G q / K q ) of the algebra of continuous functions on G / K . Using results of Soibelman and Dijkhuizen-Stokman we classify the irreducible representations of C ( G q / K q ) and obtain a composition series for C ( G q / K q ). We describe closures of the symplectic leaves of G / K refining the well-known description in the case of flag manifolds in terms of the Bruhat order. We then show that the same rules describe the topology on the spectrum of C ( G q / K q ). Next we show that the family of C * -algebras C ( G q / K q ), 0 〈  q  ≤ 1, has a canonical structure of a continuous field of C * -algebras and provides a strict deformation quantization of the Poisson algebra \mathbb C [ G / K ] . Finally, extending a result of Nagy, we show that C ( G q / K q ) is canonically KK-equivalent to C ( G / K ). Content Type Journal Article Pages 1-28 DOI 10.1007/s00220-012-1455-6 Authors Sergey Neshveyev, Department of Mathematics, University of Oslo, P. O. Box 1053, Blindern, 0316 Oslo, Norway Lars Tuset, Faculty of Engineering, Oslo University College, P. O. Box 4, St. Olavs Plass, 0130 Oslo, Norway Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    In this series of papers we show that there are exactly ten subfactors, other than A ∞ subfactors, of index between 4 and 5. Previously this classification was known up to index 3+ Ö 3 . In the first paper we give an analogue of Haagerup’s initial classification of subfactors of index less than 3+ Ö 3 , showing that any subfactor of index less than 5 must appear in one of a large list of families. These families will be considered separately in the three subsequent papers in this series. Content Type Journal Article Pages 1-34 DOI 10.1007/s00220-012-1426-y Authors Scott Morrison, Mathematics Department, University of California, Berkeley, CA 94720, USA Noah Snyder, Department of Mathematics, Columbia University, New York, NY 10027, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We study the local semicircle law for Gaussian β -ensembles at the edge of the spectrum. We prove that at the almost optimal level of n - 2/3+ e , the local semicircle law holds for all β ≥ 1 at the edge. The proof of the main theorem relies on the calculation of the moments of the tridiagonal model of Gaussian β -ensembles up to the p n -moment, where p n = O ( n 2/3 - e ) . The result is analogous to the result of Sinai and Soshnikov (Funct Anal Appl 32(2), 1998 ) for Wigner matrices, but the combinatorics involved in the calculations are different. Content Type Journal Article Pages 1-13 DOI 10.1007/s00220-012-1456-5 Authors Percy Wong, Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We study multi-component elliptic Schrödinger systems arising in nonlinear optics and Bose-Einstein condensation phenomena. We prove new Liouville-type nonexistence theorems, as well as a priori bounds, decay and singularity estimates. This is shown under an optimal Sobolev growth restriction on the nonlinearities, thus improving on recent results of Dancer et al. and of Tavares et al. These systems are of non-cooperative form and hence cannot be tackled by maximum principle methods such as moving planes. Instead we rely on a delicate combination of Rellich-Pohozaev type identities, Sobolev and interpolation inequalities on S n -1 and feedback and measure arguments. We also extend our results to a rather general class of gradient-type systems. Content Type Journal Article Pages 1-19 DOI 10.1007/s00220-012-1440-0 Authors Pavol Quittner, Department of Applied Mathematics and Statistics, Comenius University, 84248 Bratislava, Slovakia Philippe Souplet, Université Paris 13, CNRS UMR 7539, Laboratoire Analyse Géométrie et Applications, 93430 Villetaneuse, France Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    We construct open sets of C k ( k ≥ 2) vector fields with singularities that have robust exponential decay of correlations with respect to the unique physical measure. In particular we prove that the geometric Lorenz attractor has exponential decay of correlations with respect to the unique physical measure. Content Type Journal Article Pages 1-32 DOI 10.1007/s00220-012-1445-8 Authors Vítor Araújo, Instituto de Matemática, Universidade Federal da Bahia, Av. Ademar de Barros s/n, 40170-110 Salvador, Brazil Paulo Varandas, Departamento de Matemática, Universidade Federal da Bahia, Av. Ademar de Barros s/n, 40170-110 Salvador, Brazil Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616

Description:    It is known that the number of different classical messages which can be communicated with a single use of a classical channel with zero probability of decoding error can sometimes be increased by using entanglement shared between sender and receiver. It has been an open question to determine whether entanglement can ever increase the zero-error communication rates achievable in the limit of many channel uses. In this paper we show, by explicit examples, that entanglement can indeed increase asymptotic zero-error capacity, even to the extent that it is equal to the normal capacity of the channel. Content Type Journal Article Pages 1-15 DOI 10.1007/s00220-012-1451-x Authors Debbie Leung, Institute for Quantum Computing, University of Waterloo, 200 University Ave. West, Waterloo, ON N2L 3G1, Canada Laura Mancinska, Institute for Quantum Computing, University of Waterloo, 200 University Ave. West, Waterloo, ON N2L 3G1, Canada William Matthews, Institute for Quantum Computing, University of Waterloo, 200 University Ave. West, Waterloo, ON N2L 3G1, Canada Maris Ozols, Institute for Quantum Computing, University of Waterloo, 200 University Ave. West, Waterloo, ON N2L 3G1, Canada Aidan Roy, Institute for Quantum Computing, University of Waterloo, 200 University Ave. West, Waterloo, ON N2L 3G1, Canada Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616