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  • Articles  (354)
  • Springer  (354)
  • American Chemical Society (ACS)
  • American Geophysical Union
  • National Academy of Sciences
  • 2015-2019  (354)
  • 2005-2009
  • 1990-1994
  • 1980-1984
  • 2017  (354)
  • Communications in Mathematical Physics  (109)
  • 762
  • Physics  (354)
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  • Articles  (354)
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Publisher
  • Springer  (354)
  • American Chemical Society (ACS)
  • American Geophysical Union
  • National Academy of Sciences
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  • 2015-2019  (354)
  • 2005-2009
  • 1990-1994
  • 1980-1984
Year
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  • 1
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    Erratum to: A Higher Frobenius–Schur Indicator Formula for Group-Theoretical Fusion Categories (2017)
    Springer
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    Publication Date: 2017-02-11
    Print ISSN: 0010-3616
    Electronic ISSN: 1432-0916
    Topics: Mathematics , Physics
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  • 2
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    Scattering Theory for Lindblad Master Equations (2017)
    Springer
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    Publication Date: 2017-02-11
    Description: We study scattering theory for a quantum-mechanical system consisting of a particle scattered off a dynamical target that occupies a compact region in position space. After taking a trace over the degrees of freedom of the target, the dynamics of the particle is generated by a Lindbladian acting on the space of trace-class operators. We study scattering theory for a general class of Lindbladians with bounded interaction terms. First, we consider models where a particle approaching the target is always re-emitted by the target. Then we study models where the particle may be captured by the target. An important ingredient of our analysis is a scattering theory for dissipative operators on Hilbert space.
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  • 3
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    Exponential Decay of Loop Lengths in the Loop O ( n ) Model with Large n (2017)
    Springer
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    Publication Date: 2017-01-01
    Description: The loop O ( n ) model is a model for a random collection of non-intersecting loops on the hexagonal lattice, which is believed to be in the same universality class as the spin O ( n ) model. It has been conjectured that both the spin and the loop O ( n ) models exhibit exponential decay of correlations when \(n 〉 2\) . We verify this for the loop O ( n ) model with large parameter n , showing that long loops are exponentially unlikely to occur, uniformly in the edge weight x . Our proof provides further detail on the structure of typical configurations in this regime. Putting appropriate boundary conditions, when nx 6 is sufficiently small, the model is in a dilute, disordered phase in which each vertex is unlikely to be surrounded by any loops, whereas when nx 6 is sufficiently large, the model is in a dense, ordered phase which is a small perturbation of one of the three ground states.
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  • 4
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    Central Spectral Gaps of the Almost Mathieu Operator (2017)
    Springer
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    Publication Date: 2017-02-24
    Description: We consider the spectrum of the almost Mathieu operator \({H_\alpha}\) with frequency \({\alpha}\) and in the case of the critical coupling. Let an irrational \({\alpha}\) be such that \({|\alpha - p_n/q_n| 〈 c q_n^{-\varkappa}}\) , where \({p_n/q_n}\) , \({n=1,2,\ldots}\) , are the convergents to \({\alpha}\) , and \({c}\) , \({\varkappa}\) are positive absolute constants, \({\varkappa 〈 56}\) . Assuming certain conditions on the parity of the coefficients of the continued fraction of \({\alpha}\) , we show that the central gaps of \({H_{p_n/q_n}}\) , \({n=1,2,\ldots}\) , are inherited as spectral gaps of \({H_\alpha}\) of length at least \({c'q_n^{-\varkappa/2}}\) , \({c' 〉 0}\) .
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  • 5
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    The Vlasov–Maxwell–Boltzmann System Near Maxwellians in the Whole Space with Very Soft Potentials (2017)
    Springer
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    Publication Date: 2017-02-24
    Description: Since the work by Guo (Invent Math 153(3):593–630, 2003 ), it has remained an open problem to establish the global existence of perturbative classical solutions around a global Maxwellian to the Vlasov–Maxwell–Boltzmann system with the whole range of soft potentials. This is mainly due to the complex structure of the system, in particular, the degenerate dissipation at large velocity, the velocity-growth of the nonlinear term induced by the Lorentz force, and the regularity-loss of the electromagnetic fields. This paper solves this problem in the whole space provided that initial perturbation has sufficient regularity and velocity-integrability.
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  • 6
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    Thermalization and Pseudolocality in Extended Quantum Systems (2017)
    Springer
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    Publication Date: 2017-02-24
    Description: Recently, it was understood that modified concepts of locality played an important role in the study of extended quantum systems out of equilibrium, in particular in so-called generalized Gibbs ensembles. In this paper, we rigorously study pseudolocal charges and their involvement in time evolutions and in the thermalization process of arbitrary states with strong enough clustering properties. We show that the densities of pseudolocal charges form a Hilbert space, with inner product determined by thermodynamic susceptibilities. Using this, we define the family of pseudolocal states, which are determined by pseudolocal charges. This family includes thermal Gibbs states at high enough temperatures, as well as (a precise definition of) generalized Gibbs ensembles. We prove that the family of pseudolocal states is preserved by finite time evolution, and that, under certain conditions, the stationary state emerging at infinite time is a generalized Gibbs ensemble with respect to the evolution dynamics. If the evolution dynamics does not admit any conserved pseudolocal charges other than the evolution Hamiltonian, we show that any stationary pseudolocal state with respect to these dynamics is a thermal Gibbs state, and that Gibbs thermalization occurs. The framework is that of translation-invariant states on hypercubic quantum lattices of any dimensionality (including quantum chains) and finite-range Hamiltonians, and does not involve integrability.
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  • 7
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    Semidirect Products of C*-Quantum Groups: Multiplicative Unitaries Approach (2017)
    Springer
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    Publication Date: 2017-02-24
    Description: C*-quantum groups with projection are the noncommutative analogues of semidirect products of groups. Radford’s Theorem about Hopf algebras with projection suggests that any C*-quantum group with projection decomposes uniquely into an ordinary C*-quantum group and a “braided” C*-quantum group. We establish this on the level of manageable multiplicative unitaries.
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  • 8
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    SU(N) Transitions in M-Theory on Calabi–Yau Fourfolds and Background Fluxes (2017)
    Springer
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    Publication Date: 2017-02-25
    Description: We study M-theory on a Calabi–Yau fourfold with a smooth surface S of A N –1 singularities. The resulting three-dimensional theory has a \({\mathcal{N}=2}\) SU ( N ) gauge theory sector, which we obtain from a twisted dimensional reduction of a seven-dimensional \({\mathcal{N}=1}\) SU ( N ) gauge theory on the surface S . A variant of the Vafa–Witten equations governs the moduli space of the gauge theory, which—for a trivial SU ( N ) principal bundle over S —admits a Coulomb and a Higgs branch. In M-theory these two gauge theory branches arise from a resolution and a deformation to smooth Calabi–Yau fourfolds, respectively. We find that the deformed Calabi–Yau fourfold associated to the Higgs branch requires for consistency a non-trivial four-form background flux in M-theory. The flat directions of the flux-induced superpotential are in agreement with the gauge theory prediction for the moduli space of the Higgs branch. We illustrate our findings with explicit examples that realize the Coulomb and Higgs phase transition in Calabi–Yau fourfolds embedded in weighted projective spaces. We generalize and enlarge this class of examples to Calabi–Yau fourfolds embedded in toric varieties with an A N –1 singularity in codimension two.
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  • 9
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    Three Proofs of the Makeenko–Migdal Equation for Yang–Mills Theory on the Plane (2017)
    Springer
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    Publication Date: 2017-02-25
    Description: We give three short proofs of the Makeenko–Migdal equation for the Yang–Mills measure on the plane, two using the edge variables and one using the loop or lasso variables. Our proofs are significantly simpler than the earlier pioneering rigorous proofs given by Lévy and by Dahlqvist. In particular, our proofs are “local” in nature, in that they involve only derivatives with respect to variables adjacent to the crossing in question. In an accompanying paper with Gabriel, we show that two of our proofs can be adapted to the case of Yang–Mills theory on any compact surface.
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  • 10
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    On the Nodal Lines of Eisenstein Series on Schottky Surfaces (2017)
    Springer
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    Publication Date: 2017-02-25
    Description: On convex co-compact hyperbolic surfaces \({X=\Gamma \backslash \mathbb{H}^{2}}\) , we investigate the behavior of nodal curves of real valued Eisenstein series \({F_\lambda(z,\xi)}\) , where \({\lambda}\) is the spectral parameter, \({\xi}\) the direction at infinity. Eisenstein series are (non- \({L^2}\) ) eigenfunctions of the Laplacian \({\Delta_X}\) satisfying \({\Delta_X F_\lambda=(\frac{1}{4}+\lambda^2)F_\lambda}\) . As \({\lambda}\) goes to infinity (the high energy limit), we show that, for generic \({\xi}\) , the number of intersections of nodal lines with any compact segment of geodesic grows like \({\lambda}\) , up to multiplicative constants. Applications to the number of nodal domains inside the convex core of the surface are then derived.
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