ALBERT

Beschreibung:    We show that the Foldy-Wouthuysen transformation and its generalizations are simplified if the methods of pseudodifferential operators are used, which also allow estimating the exactness of the transition from the Dirac equation to the reduced equations for electrons and positrons. The methods and techniques used can be useful not only in studying asymptotic solutions of the Dirac equation but also in other problems. Content Type Journal Article Pages 547-566 DOI 10.1007/s11232-011-0041-y Authors J. Brüning, Humboldt University, Berlin, Germany V. V. Grushin, Moscow State Institute for Electronics and Mathematics, Moscow, Russia S. Yu. Dobrokhotov, Moscow Institute for Physics and Technology, Moscow, Russia T. Ya. Tudorovskii, Institute for Molecules and Materials Radboud, University of Nijmegen, Nijmegen, The Netherlands Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 2

Beschreibung:    We present the bi-Hamiltonian structure and Lax pair of the equation ρ t = bu x +( 1/2 )[(u 2 −u x 2 )ρ] x , where ρ = u − u xx and b = const , which guarantees its integrability in the Lax pair sense. We study nonsmooth soliton solutions of this equation and show that under the vanishing boundary condition u → 0 at the space and time infinities, the equation has both “W/M-shape” peaked soliton (peakon) and cusped soliton (cuspon) solutions. Content Type Journal Article Pages 584-589 DOI 10.1007/s11232-011-0044-8 Authors Zhijun Qiao, Department of Mathematics, The University of Texas-Pan American, Edinburg, Texas, USA Xianqi Li, Department of Mathematics, The University of Texas-Pan American, Edinburg, Texas, USA Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 2

Beschreibung:    We study the Wigner function in noncommutative quantum mechanics. By solving the time-independent Schrödinger equation on both a noncommutative space and a noncommutative phase space, we obtain the Wigner function for the Landau problem on those spaces. Content Type Journal Article Pages 628-635 DOI 10.1007/s11232-011-0047-5 Authors S. Dulat, School of Physics Science and Technology, Xinjiang University, Urumqi, China Kang Li, Department of Physics, Hangzhou Normal University, Hangzhou, China Jianhua Wang, Department of Physics, Shaanxi University of Technology, Hanzhong, China Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 2

Beschreibung:    We review several purely mathematical results concerning boundary value problems for nonlinear pseudodifferential equations for p-adic closed and open strings in the tree approximation in the case d = 1 . For the solutions of these problems, we present formulas establishing the relations between the numbers of their zeros, the multiplicities of the zeros, and the numbers indicating how many times the solutions change sign. Content Type Journal Article Pages 539-546 DOI 10.1007/s11232-011-0040-z Authors V. S. Vladimirov, Steklov Mathematical Institute, RAS, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 2

Beschreibung:    Based on number theory, we present a new concept of gas without the particle interaction taken into account in which there are first-order phase transitions for T 〈 T cr on isotherms. We present formulas for new ideal gases, solving the Gibbs paradox, and also formulas for the transition to real gases based on the concept of the Zeno line. Content Type Journal Article Pages 654-667 DOI 10.1007/s11232-011-0050-x Authors V. P. Maslov, Lomonosov Moscow State University, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 2

Beschreibung:    We establish that by choosing a smooth local perturbation of the boundary of a planar quantum waveguide, we can create an eigenvalue near any given threshold of the continuous spectrum and the corresponding trapped wave exponentially decaying at infinity. Based on an analysis of an auxiliary object, a unitary augmented scattering matrix, we asymptotically interpret Wood’s anomalies, the phenomenon of fast variations in the diffraction pattern due to variations in the near-threshold wave frequency. Content Type Journal Article Pages 606-627 DOI 10.1007/s11232-011-0046-6 Authors S. A. Nazarov, Institute of Mechanical Engineering Problems, RAS, St. Petersburg, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 2

Beschreibung:    Starting from the matrix KP hierarchy and adding a new τ B flow, we obtain a new extended matrix KP hierarchy and its Lax representation with the symmetry constraint on squared eigenfunctions taken into account. The new hierarchy contains two sets of times t A and τ B and also eigenfunctions and adjoint eigenfunctions as components. We propose a generalized dressing method for solving the extended matrix KP hierarchy and present some solutions. We study the soliton solutions of two types of ( 2+1 )-dimensional AKNS equations with self-consistent sources and two types of Davey-Stewartson equations with selfconsistent sources. Content Type Journal Article Pages 590-605 DOI 10.1007/s11232-011-0045-7 Authors Yehui Huang, Department of Mathematical Science, Tsinghua University, Beijing, China Xiaojun Liu, Department of Applied Mathematics, China Agricultural University, Beijing, China Yuqin Yao, Department of Applied Mathematics, China Agricultural University, Beijing, China Yunbo Zeng, Department of Mathematical Science, Tsinghua University, Beijing, China Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 2

Beschreibung:    We propose a model on the Cayley tree and prove that a uncountable set of Ĝ-periodic Gibbs measures exists for this model, in contrast to models studied previously. Content Type Journal Article Pages 668-679 DOI 10.1007/s11232-011-0051-9 Authors U. A. Rozikov, Institute of Mathematics and Information Technologies, Uzbek Academy of Sciences, Tashkent, Uzbekistan G. T. Madgoziev, Institute of Mathematics and Information Technologies, Uzbek Academy of Sciences, Tashkent, Uzbekistan Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 2

Beschreibung:    We propose a construction of a Lagrangian torus fibration of the full flag variety in ℂ 3 . In contrast to the classical fibration obtained from the Gelfand-Zeitlin system, the proposed fibration is special Lagrangian. Content Type Journal Article Pages 567-576 DOI 10.1007/s11232-011-0042-x Authors N. A. Tyurin, Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 2

Beschreibung:    We propose a method for describing quasiequilibrium processes in a quasistable anharmonic oscillator affected by heat noise. We introduce effective thermodynamic parameters analogous to those of an equilibrium system but differing from them in numerical value. We define the parameter characterizing the nonequilibrium of the system, prove the mathematical consistency of the proposed method, and obtain the quasiequilibrium analogue of the theorem on energy distribution over degrees of freedom. Content Type Journal Article Pages 636-644 DOI 10.1007/s11232-011-0048-4 Authors A. V. Kargovsky, Lomonosov Moscow State University, Moscow, Russia L. S. Bulushova, Lomonosov Moscow State University, Moscow, Russia O. A. Chichigina, Lomonosov Moscow State University, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 2

Beschreibung:    We develop the recent proposal to use dimensional reduction from the four-dimensional space-time (D = 1 + 3 ) to the variant with a smaller number of space dimensions D = 1 + d, d 〈 3, at sufficiently small distances to construct a renormalizable quantum field theory. We study the Klein-Gordon equation with a few toy examples (“educational toys”) of a space-time with a variable spatial geometry including a transition to a dimensional reduction. The examples considered contain a combination of two regions with a simple geometry (two-dimensional cylindrical surfaces with different radii) connected by a transition region. The new technique for transforming the study of solutions of the Klein-Gordon problem on a space with variable geometry into solution of a one-dimensional stationary Schrödinger-type equation with potential generated by this variation is useful. We draw the following conclusions: ( 1 ) The signal related to the degree of freedom specific to the higher-dimensional part does not penetrate into the smaller-dimensional part because of an inertial force inevitably arising in the transition region (this is the centrifugal force in our models). ( 2 ) The specific spectrum of scalar excitations resembles the spectrum of real particles; it reflects the geometry of the transition region and represents its “fingerprints.” ( 3 ) The parity violation due to the asymmetric character of the construction of our models could be related to the CP symmetry violation. Content Type Journal Article Pages 680-691 DOI 10.1007/s11232-011-0052-8 Authors P. P. Fiziev, Sofia University St. Kliment Ohridski, Sofia, Bulgaria D. V. Shirkov, Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 2

Beschreibung:    In the mode-coupling approximation, we consider the transition to the glass state in a system of collapsing hard spheres (a system with the hard-core potential to which a repulsive step is added). We propose an approximation for the structure factor of the system, which we use to construct the phase diagram of the transition to the glass state. We show that there exists a maximum on the liquid-glass curve corresponding to the reentrant transition to the glass state in the system. In the framework of the proposed model, we consider bifurcations of solutions of the equations describing the transition to the glass state and show that there exist bifurcations of the “swallow-tail” type corresponding to the glass-glass transition. Content Type Journal Article Pages 645-653 DOI 10.1007/s11232-011-0049-3 Authors V. N. Ryzhov, Institute for High Pressure Physics, RAS, Troitsk, Moscow Oblast, Russia E. E. Tareyeva, Institute for High Pressure Physics, RAS, Troitsk, Moscow Oblast, Russia Yu. D. Fomin, Institute for High Pressure Physics, RAS, Troitsk, Moscow Oblast, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 2

Beschreibung:    We consider two initial boundary value problems on an interval with homogeneous Dirichlet conditions. These problems were proposed by M. I. Rabinovich and D. I. Trubetskov and are given by nonlinear fourth-order Sobolev-type equations. We prove the local-in-time existence of a strong generalized solution of one problem, and for both problems, we obtain sufficient conditions for the destruction of their strong generalized solutions in a finite time. Content Type Journal Article Pages 577-583 DOI 10.1007/s11232-011-0043-9 Authors M. O. Korpusov, Lomonosov Moscow State University, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 2

Beschreibung:    We consider the evolution of the spatial distribution of fast atomic particles as they pass through a crystal. At small penetration depths where the particles move without significant loss of coherence, the joint probability density function becomes smoother at the expense of the gradient of the anharmonic potential of the planar channel. We show that as a result of this smoothing, there arises a quasiequilibrium (quasistationary) state of the subsystem of fast particles. The further evolution of the particle distribution is caused by nonelastic scattering and is described by the kinetic equation. At this stage, the anharmonic character of particle oscillations between the channel walls results in a renormalization of the total phonon scattering cross section of particles, and the renormalization is determined by the fourth-order anharmonic interaction. Content Type Journal Article Pages 506-516 DOI 10.1007/s11232-011-0038-6 Authors Yu. A. Kashlev, Baikov Institute for Metallurgy and Material Science, RAS, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 1

Beschreibung:    We propose a method for calculating vacuum means of the scalar field energy-momentum tensor on Lie groups and homogeneous spaces. We use the generalized harmonic analysis based on the method of coadjoint representation orbits. Content Type Journal Article Pages 468-483 DOI 10.1007/s11232-011-0035-9 Authors A. I. Breev, Tomsk State University, Tomsk, Russia I. V. Shirokov, Omsk State Technical University, Omsk, Russia A. A. Magazev, Irtysh Branch of Novosibirsk State Academy of Water Transport, Novosibirsk, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 1

Beschreibung:    We construct the group bundle for the inverse Fibonacci semigroups in the axiomatic approach framework. The proper Fibonacci semigroup is the corresponding group bundle for the Penrose semigroups, which can be interpreted as the generating grammar of the morphogenetic synthesis of the pentasymmetric Penrose parquet in the numbers of tiling by golden rhombuses. This morphogenetic synthesis of the Penrose parquet satisfies the scaling principle. Parquet plates are not absolutely rigid, and the relations between their metric characteristics are governed by the golden section and other magic numbers. The characteristic form factors of three-level dual alphabets are the corresponding invariants. We realize the morphogenetic synthesis in the examples of square-octagonal and bihexagonal lattices. We consider cumulative properties of magic series and the evolutionary aspects of semigroup orbits in the entropy representation. Content Type Journal Article Pages 517-537 DOI 10.1007/s11232-011-0039-5 Authors V. V. Yudin, Far-East State University, Vladivostok, Russia E. S. Startzev, Far-East State University, Vladivostok, Russia I. G. Permyakova, Far-East State University, Vladivostok, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 1

Beschreibung:    We obtain an expression for the NMR line at low temperatures for a system of nuclear spins described by a Hamiltonian with equal spin-spin coupling constants. We show that in the case of “easy axis” anisotropy, the line has a logarithmic low-frequency singularity and an exponentially decreasing high-frequency asymptotic behavior at the temperature of an anomalous peak of heat capacity. In the case of “easy plane” anisotropy, the line has the traditional Gaussian form. We discuss the possibility of using NMR data to discover specific thermodynamic and magnetic properties of the considered model system. Content Type Journal Article Pages 496-505 DOI 10.1007/s11232-011-0037-7 Authors A. A. Khamzin, Kazan State Energy University, Kazan, Russia R. R. Nigmatullin, Kazan (Volga Region) Federal University, Kazan, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 1

Beschreibung:    We attempt to propose an algebraic approach to the theory of integrable difference equations. We define the concept of a recursion operator for difference equations and show that it generates an infinite sequence of symmetries and canonical conservation laws for a difference equation. As in the case of partial differential equations, these canonical densities can serve as integrability conditions for difference equations. We obtain the recursion operators for the Viallet equation and all the Adler-Bobenko-Suris equations. Content Type Journal Article Pages 421-443 DOI 10.1007/s11232-011-0033-y Authors A. V. Mikhailov, Applied Mathematics Department, University of Leeds, Leeds, UK Jing Ping Wang, School of Mathematics and Statistics, University of Kent, Kent, UK P. Xenitidis, Applied Mathematics Department, University of Leeds, Leeds, UK Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 1

Beschreibung:    We propose a Lie-Noether-symmetry solution of two problems that arise with classical quantization: the quantization of higher-order (more than second) Euler-Lagrange ordinary differential equations of classical mechanics and the quantization of any second-order Euler-Lagrange ordinary differential equation that classically comes from a simple linear equation via nonlinear canonical transformations. Content Type Journal Article Pages 994-1001 DOI 10.1007/s11232-011-0081-3 Authors M. C. Nucci, Dipartimento di Matematica e Informatica, Università di Perugia and INFN, Sezione di Perugia, Perugia, Italy Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 168 Journal Issue Volume 168, Number 1

Beschreibung: Nonlinear physics: Theory and experiment VI Content Type Journal Article Pages 857-857 DOI 10.1007/s11232-011-0068-0 Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 168 Journal Issue Volume 168, Number 1

Beschreibung:    We consider the propagation of electromagnetic pulses in isotropic media taking a third-order nonlinearity into account. We develop a method for transforming Maxwell’s equations based on a complete set of projection operators corresponding to wave-dispersion branches (in a waveguide or in matter) with the propagation direction taken into account. The most important result of applying the method is a system of equations describing the one-dimensional dynamics of pulses propagating in opposite directions without accounting for dispersion. We derive the corresponding self-action equations. We thus introduce dispersion in the media and show how the operators change. We obtain generalized Schäfer-Wayne short-pulse equations accounting for both propagation directions. In the three-dimensional problem, we focus on optic fibers with dispersive matter, deriving and numerically solving equations of the waveguide-mode interaction. We discuss the effects of the interaction of unidirectional pulses. For the coupled nonlinear Schrödinger equations, we discuss a concept of numerical integrability and apply the developed calculation schemes. Content Type Journal Article Pages 974-984 DOI 10.1007/s11232-011-0079-x Authors M. Kuszner, Gdansk University of Technology, Gdansk, Poland S. Leble, Gdansk University of Technology, Gdansk, Poland B. Reichel, Gdansk University of Technology, Gdansk, Poland Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 168 Journal Issue Volume 168, Number 1

Beschreibung:    We study properties of the purely solitonic τ-function and potential of the heat equation in detail. We describe the asymptotic behavior of the potential and establish the ray structure of this asymptotic behavior on the plane (x 1 , x 2 ) in dependence on the parameters of the potential. Content Type Journal Article Pages 865-874 DOI 10.1007/s11232-011-0070-6 Authors M. Boiti, Dipartimento di Fisica, Università del Salento and INFN, Sezione di Lecce, Lecce, Italy F. Pempinelli, Dipartimento di Fisica, Università del Salento and INFN, Sezione di Lecce, Lecce, Italy A. K. Pogrebkov, Steklov Mathematical Institute, RAS, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 168 Journal Issue Volume 168, Number 1

Beschreibung:    We briefly review the half-a-century period (1959–2009) of the creation, development, and application of the method of two-time temperature retarded and advanced Green’s functions, introduced by Bogoliubov and Tyablikov in 1959. This method has not exhausted its resources by far, as is evidenced by its effective modification proposed by Plakida in 1970 and Tserkovnikov in 1971 and then, in a much more advanced form, by Tserkovnikov in 1981. Currently, a self-consistent description of both one-particle (transverse) and collective (longitudinal) Green’s functions and correlation functions is achieved based on the Green’s function method in the Bogoliubov-Tyablikov-Plakida-Tserkovnikov formulation. Content Type Journal Article Pages 1318-1329 DOI 10.1007/s11232-011-0108-9 Authors Yu. G. Rudoy, Peoples’ Friendship University of Russia, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 168 Journal Issue Volume 168, Number 3

Beschreibung:    We apply the Bogoliubov-Tyablikov method of two-time Green’s functions to a multielectron theory of metals in the framework of the models with strong correlations, which are the Hubbard model and the Vonsovskii s-d(f) exchange model. We discuss the atomic representation in the problem of describing electron states, the metal-insulator transition, the problem of noncoherent states, and the Kondo effect. We analyze the ferromagnetism criterion in systems of strongly correlated electrons, which differs drastically from the Stoner condition. Content Type Journal Article Pages 1246-1257 DOI 10.1007/s11232-011-0102-2 Authors V. Yu. Irkhin, Institute of Metal Physics, Ural Branch, RAS, Ekaterinburg, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 168 Journal Issue Volume 168, Number 3

Beschreibung:    We develop a formulation of quantum electrodynamics in the presence of a dispersive and absorptive medium, giving a unified description of both relativistic and nonrelativistic interactions. It is based on using the electric field as the fundamental dynamical variable and introducing extra dynamical variables for the medium. As an application, we consider the Lamb shift in the presence a dielectric occupying a half-space. Content Type Journal Article Pages 1413-1422 DOI 10.1007/s11232-011-0117-8 Authors M. A. Braun, Saint Petersburg State University, St. Petersburg, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 169 Journal Issue Volume 169, Number 1

Beschreibung: Erratum to: An integrable equation with nonsmooth solitons Content Type Journal Article Category Erratum Pages 1515-1515 DOI 10.1007/s11232-011-0128-5 Authors Zhijun Qiao Xianqi Li Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 169 Journal Issue Volume 169, Number 1

Beschreibung: To the 70th anniversary of the birth of Aleksandr Nikolaevich Vasiliev Content Type Journal Article Pages 1365-1369 DOI 10.1007/s11232-011-0112-0 Authors N. V. Antonov, Physics Faculty, St. Petersburg State University, St. Petersburg, Germany S. É. Derkachev, St. Petersburg Department of Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Germany Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 169 Journal Issue Volume 169, Number 1

Beschreibung:    We study correlation functions of the totally asymmetric simple exclusion process (TASEP) in discrete time with backward sequential update. We prove a determinant formula for the generalized Green’s function describing transitions between particle positions at given instants. As an example, we calculate the current correlation function, i.e., the joint probability distribution of times required by each particle to travel a given distance. An asymptotic analysis shows that current fluctuations converge to the Airy 2 process. Content Type Journal Article Pages 1507-1514 DOI 10.1007/s11232-011-0127-6 Authors A. M. Povolotsky, Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia V. B. Priezzhev, Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 169 Journal Issue Volume 169, Number 1

Beschreibung:    In the framework of a field theory model obtained by “second quantization” of a Doi-type master equation, we investigate the effects of random sources and sinks on the reaction kinetics in the master-equation description. We show that random sources and sinks significantly affect the asymptotic behavior of the model and identify two universality classes when describing them using scaling analysis. We compare the results with the Langevin-equation description of the same process. Content Type Journal Article Pages 1489-1498 DOI 10.1007/s11232-011-0125-8 Authors M. Hnatich, Institute of Experimental Physics, Slovak Academy of Sciences, Košice, Slovakia J. Honkonen, National Defence University, Helsinki, Finland T. Lučivjanský, Institute of Experimental Physics, Slovak Academy of Sciences, Košice, Slovakia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 169 Journal Issue Volume 169, Number 1

Beschreibung:    We discuss and compare two popular methods used for analyzing fluctuations in the number of active agents: the approach of Martin, Siggia, and Rose, usually connected with the Langevin-equation description of fluctuation kinetics, and the approach of Doi, directly related to the master-equation description of stochastic birth-death processes. Content Type Journal Article Pages 1460-1469 DOI 10.1007/s11232-011-0122-y Authors J. Honkonen, National Defence University, Helsinki, Finland Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 169 Journal Issue Volume 169, Number 1

Beschreibung:    In a simple example of a bosonic three-matrix model, we show how a background geometry can condense as the temperature or coupling constant passes through a critical value. We show that this example belongs to a new universality class of phase transitions where the background geometry is itself emergent. Content Type Journal Article Pages 1405-1412 DOI 10.1007/s11232-011-0116-9 Authors D. O’Connor, School of Theoretical Physics, Dublin Institute for Advanced Studies, Dublin, Ireland Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 169 Journal Issue Volume 169, Number 1

Beschreibung:    The Chern-Simons potential occurs in quantum electrodynamics in constructing a model for the interaction of a material surface with the photon field if the locality, gauge invariance, and renormalizability requirements are imposed. In the framework of such a model, we consider the problem of an electromagnetic wave scattering on a plane. Content Type Journal Article Pages 1423-1431 DOI 10.1007/s11232-011-0118-7 Authors D. Yu. Pismak, Saint Petersburg State University, St. Petersburg, Russia Yu. M. Pismak, Saint Petersburg State University, St. Petersburg, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 169 Journal Issue Volume 169, Number 1

Beschreibung:    We derive a nonlinear recurrence equation for the infrared leading logarithms (LLs) in the four-dimensional σ-model with fields on an arbitrary Riemann manifold. The derived equation allows computing the LLs to an essentially unlimited loop order in terms of the geometric characteristics of the Riemann manifold. We reduce solving the SU( ∞ ) principal chiral field in an arbitrary number of dimensions in the LL approximation to solving a very simple recurrence equation. This result prepares a way to solve the model in an arbitrary number of dimensions as N → ∞ . Content Type Journal Article Pages 1499-1506 DOI 10.1007/s11232-011-0126-7 Authors M. V. Polyakov, Konstantinov Petersburg Nuclear Physics Institute, Gatchina, Leningrad Oblast, Russia A. A. Vladimirov, Institut für Theoretische Physik II, Ruhr-Universität, Bochum, Germany Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 169 Journal Issue Volume 169, Number 1

Beschreibung:    We use a simplified (0+1) -dimensional theory to develop approaches for studying the higher-order asymptotic behavior of quantum field expansions in the two-dimensional theory of fully developed turbulence. We consider the asymptotic behavior of the correlation function in the small-time limit in the theory of fully developed turbulence and derive and investigate the stationarity equation. We show that the perturbation series in this limit has a finite convergence radius. Content Type Journal Article Pages 1432-1440 DOI 10.1007/s11232-011-0119-6 Authors M. Yu. Nalimov, Saint Petersburg State University, St. Petersburg, Russia V. A. Sergeev, Saint Petersburg State University, St. Petersburg, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 169 Journal Issue Volume 169, Number 1

Beschreibung: Abstrafct   We propose a model for studying the mutual influence of critical fluctuations in the vicinity of the critical point of phase transition to a superfluid state and the velocity fluctuations in the developed turbulence regime. We demonstrate the presence of two different regimes: the turbulence regime and the equilibrium regime. We show that the standard critical behavior can break in the turbulence regime. The viscosity becomes an infrared-irrelevant parameter in the equilibrium regime. We justify the assumption that the viscosity critical dimension in this regime is determined by critical indices of the critical behavior statistical model, which are currently known with sufficient accuracy. Content Type Journal Article Pages 1441-1449 DOI 10.1007/s11232-011-0120-0 Authors M. V. Komarova, Saint Petersburg State University, St. Petersburg, Russia D. M. Krasnov, Saint Petersburg State University, St. Petersburg, Russia M. Yu. Nalimov, Saint Petersburg State University, St. Petersburg, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 169 Journal Issue Volume 169, Number 1

Beschreibung:    In the framework of the renormalization group and the ɛ-expansion, we propose expressions for the β-function and anomalous dimensions in terms of renormalized one-irreducible functions. These expressions are convenient for numerical calculations. We choose the renormalization scheme in which the quantities calculated using R operations are represented by integrals that do not contain singularities in ɛ. We develop a completely automated calculation system starting from constructing diagrams, determining relevant subgraphs, combinatorial coefficients, etc., up to determining critical exponents. As an example, we calculate the critical exponents of the φ 3 model in the order ɛ 4 . Content Type Journal Article Pages 1450-1459 DOI 10.1007/s11232-011-0121-z Authors L. Ts. Adzhemyan, Saint Petersburg State University, St. Petersburg, Russia M. V. Kompaniets, Saint Petersburg State University, St. Petersburg, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 169 Journal Issue Volume 169, Number 1

Beschreibung:    We consider the Gribov approach to hadron-hadron high-energy scattering, which is based on an effective field theory for the Pomeron interactions. Because the gluons and gravitons in QCD and in gravity are Reggeized, it seems natural to reformulate these theories at high energies in terms of Reggeons. We review the basic ideas of the BFKL approach in QCD and in supersymmetric models and present it in the form of a gauge-invariant effective theory for the Reggeized gluon interactions. We formulate the analogous generally covariant action for the Reggeized gravitons in terms of effective currents satisfying the Hamilton-Jacobi equation. Content Type Journal Article Pages 1370-1379 DOI 10.1007/s11232-011-0113-z Authors L. N. Lipatov, Konstantinov Petersburg Nuclear Physics Institute, Gatchina, Leningrad Oblast, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 169 Journal Issue Volume 169, Number 1

Beschreibung:    We discuss the latest progress in understanding the infrared behavior of inclusive cross sections and the form factors for the so-called half-BPS operators in the N= 4 SYM theory. In both cases, we observe the exponentiation of the infrared divergences while the finite parts do not have such a simple behavior. We show how the infrared divergences cancel in inclusive cross sections when the emission of soft and collinear quanta is taken into account. We calculate the finite parts of the form factors in the two-loop approximation. They are rather complicated and are expressed in terms of generalized polylogarithms of several variables. But the principle of maximal transcendentality is nevertheless still satisfied. Content Type Journal Article Pages 1390-1404 DOI 10.1007/s11232-011-0115-x Authors L. V. Bork, Institute for Theoretical and Experimental Physics, Moscow, Russia D. I. Kazakov, Institute for Theoretical and Experimental Physics, Moscow, Russia G. S. Vartanov, Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, Golm, Germany Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 169 Journal Issue Volume 169, Number 1

Beschreibung:    Using the perturbative renormalization group, we study the influence of a random velocity field on the kinetics of the single-species annihilation reaction A + A → Ø at and below its critical dimension d c = 2 . We use the second-quantization formalism of Doi to bring the stochastic problem to a field theory form. We investigate the reaction in spaces of dimension d ∼ 2 using a two-parameter expansion in ε and Δ, where ε is the deviation from the Kolmogorov scaling parameter and Δ is the deviation from the space dimension d = 2 . We evaluate all the necessary quantities, including fixed points with their regions of stability, up to the second order of the perturbation theory. Content Type Journal Article Pages 1481-1488 DOI 10.1007/s11232-011-0124-9 Authors M. Hnatich, Institute of Experimental Physics, Slovak Academy of Sciences, Košice, Slovakia J. Honkonen, National Defence University, Helsinki, Finland T. Lučivjanský, Institute of Experimental Physics, Slovak Academy of Sciences, Košice, Slovakia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 169 Journal Issue Volume 169, Number 1

Beschreibung:    Using the field theory renormalization group, we study the critical behavior of two systems subjected to turbulent mixing. The first system, described by the equilibrium model A, corresponds to the relaxational dynamics of a nonconserved order parameter. The second system is the strongly nonequilibrium reaction-diffusion system, known as the Gribov process or directed percolation process. The turbulent mixing is modeled by the stochastic Navier-Stokes equation with a random stirring force with the correlator ∞ δ(t − t′)p 4 −d−y , where p is the wave number, d is the space dimension, and y is an arbitrary exponent. We show that the systems exhibit various types of critical behavior depending on the relation between y and d. In addition to known regimes (original systems without mixing and a passively advected scalar field), we establish the existence of new strongly nonequilibrium universality classes and calculate the corresponding critical dimensions to the first order of the double expansion in y and ɛ = 4 − d (one-loop approximation). Content Type Journal Article Pages 1470-1480 DOI 10.1007/s11232-011-0123-x Authors N. V. Antonov, Saint Petersburg State University, St. Petersburg, Russia A. S. Kapustin, Saint Petersburg State University, St. Petersburg, Russia A. V. Malyshev, Saint Petersburg State University, St. Petersburg, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 169 Journal Issue Volume 169, Number 1

Beschreibung:    The 20th century has witnessed the emergence of the physics of fluctuating systems both statistical and quantum. This to some extent explains the important role played by functional integrals in modern physics. We describe a few striking examples of physics problems where using path and, more generally, field integrals has proved decisive. Content Type Journal Article Pages 1380-1389 DOI 10.1007/s11232-011-0114-y Authors J. Zinn-Justin, Centre de Saclay, CEA-IRFU and Institut de Physique Théorique, Gif-sur-Yvette, France Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 169 Journal Issue Volume 169, Number 1

Beschreibung:    We use the method of dressing by a linear operator of general form to construct new solutions of Schrödinger-type two-dimensional equations in a magnetic field. In the case of a nonunit metric, we integrate the class of solutions that admit a variable separation before dressing. In particular, we show that the ratio of the coefficients of the differential operators in the unit metric case satisfies the Hopf equation. We establish a relation between the solutions of the two-dimensional eikonal equation with the unit right-hand side and solutions of the Hopf equation. Content Type Journal Article Pages 1041-1047 DOI 10.1007/s11232-011-0086-y Authors V. G. Marikhin, Landau Institute for Theoretical Physics, RAS, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 168 Journal Issue Volume 168, Number 2

Beschreibung:    Within the formalism of difference jets, we develop an algebro-geometric analysis of systems of difference equations on multidimensional integer lattices and study their symmetries and conservation laws. Content Type Journal Article Pages 1019-1034 DOI 10.1007/s11232-011-0084-0 Authors V. V. Zharinov, Steklov Mathematical Institute, RAS, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 168 Journal Issue Volume 168, Number 2

Beschreibung:    We review new classes of exact solutions with functional parameters with constant asymptotic values at infinity of the Nizhnik-Veselov-Novikov equation and new classes of exact solutions with functional parameters of two-dimensional generalizations of the Kaup-Kupershmidt and Sawada-Kotera equations, constructed using the Zakharov-Manakov -dressing method. We present subclasses of multisoliton and periodic solutions of these equations and give examples of linear superpositions of exact solutions of the Nizhnik-Veselov-Novikov equation. Content Type Journal Article Pages 725-739 DOI 10.1007/s11232-011-0057-3 Authors V. G. Dubrovsky, Novosibirsk State Technical University, Novosibirsk, Russia A. V. Topovsky, Novosibirsk State Technical University, Novosibirsk, Russia M. Yu. Basalaev, Novosibirsk State Technical University, Novosibirsk, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 3

Beschreibung:    In the short-string limit, we present results for the one-loop correction to the energy of string solutions in AdS 5 × S 5 that belong to a certain class. The computations are based on the observation that the fluctuation operators, just as for rigid spinning-string elliptic solutions, can be written in the single-gap Lamé form. Based on these computations, we reveal a remarkable universality of the expression for the energy of short semiclassical strings, which may help in better understanding the structure of the strongcoupling expansion of the anomalous dimensions of dual gauge theory operators. Content Type Journal Article Pages 695-704 DOI 10.1007/s11232-011-0054-6 Authors M. Beccaria, Dipartimento di Fisica, Università del Salento and INFN, Sezione di Lecce, Lecce, Italy, Italy G. Macorini, Dipartimento di Fisica, Università del Salento and INFN, Sezione di Lecce, Lecce, Italy, Italy A. Tirziu, American Physical Society, Ridge, New York, USA Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 3

Beschreibung:    We extend the analysis of the generalized Gribov-Lipatov reciprocity to the higher conserved charges of the type-IIB superstring on AdS 5 × S 5 . We show that the property holds for operators of twist L = 2 and L = 3 in the sl(2) subsector. Content Type Journal Article Pages 811-815 DOI 10.1007/s11232-011-0064-4 Authors G. Macorini, Dipartimento di Fisica, Università del Salento and INFN, Sezione di Lecce, Lecce, Italy M. Beccaria, Dipartimento di Fisica, Università del Salento and INFN, Sezione di Lecce, Lecce, Italy Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 3

Beschreibung:    We study algebraic varieties and curves arising in the Birkhoff strata of the Sato Grassmannian Gr (2) . We show that the big cell Σ 0 contains the tower of families of the normal rational curves of all odd orders. The strata Σ 2 n , n = 1, 2, 3 ,..., contain hyperelliptic curves of genus n and their coordinate rings. The strata Σ 2 n +1 , n = 0, 1, 2, 3 ,..., contain ( 2 m + 1, 2 m + 3 ) plane curves for n = 2 m, 2 m − 1 (m ≥ 2 ) and also (3, 4) and (3, 5) curves in Σ 3 and Σ 5 . Curves in the strata Σ 2 n+ 1 have zero genus. Content Type Journal Article Pages 785-799 DOI 10.1007/s11232-011-0062-6 Authors B. G. Konopelchenko, Dipartimento di Fisica, Università del Salento and INFN, Sezione di Lecce, Lecce, Italy G. Ortenzi, Dipartimento di Matematica Pura ed Applicazioni, Università di Milano Bicocca, Milano, Italy Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 3

Beschreibung:    We consider a chain of SU(2) 4 anyons with transitions to a topologically ordered phase state. For half-integer and integer indices of the type of strongly correlated excitations, we find an effective low-energy Hamiltonian that is an analogue of the standard Heisenberg Hamiltonian for quantum magnets. We describe the properties of the Hilbert spaces of the system eigenstates. For the Drinfeld quantum SU( 2 ) k × doubles, we use numerical computations to show that the largest eigenvalues of the adjacency matrix for graphs that are extended Dynkin diagrams coincide with the total quantum dimensions for the levels k = 2, 3, 4, 5 . We also formulate a hypothesis about the reason for the universal behavior of the system in the long-wave limit. Content Type Journal Article Pages 843-855 DOI 10.1007/s11232-011-0067-1 Authors V. A. Verbus, Institute for Physics of Microstructures, RAS, Nizhny Novgorod, Russia L. Martina, Dipartimento di Fisica, Università del Salento and INFN, Sezione di Lecce, Lecce, Italy A. P. Protogenov, Institute of Applied Physics, RAS, Nizhny Novgorod, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 3

Beschreibung:    In terms of the Lagrange-Souriau 2-form formalism, we describe a wide set of Hamiltonian dynamical systems with first-order Lagrangians. We consider a wide class of systems derived in different phenomenological contexts. The noncommutativity of the particle position coordinates are a natural consequence. We present various explicit examples. Content Type Journal Article Pages 816-825 DOI 10.1007/s11232-011-0065-3 Authors L. Martina, Dipartimento di Fisica, Università del Salento and INFN, Sezione di Lecce, Lecce, Italy Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 3

Beschreibung:    Let E 0 be a holomorphic vector bundle over P 1 (C) and † 0 be a meromorphic connection of E 0 . We introduce the notion of an integrable connection that describes the movement of the poles of † 0 in the complex plane with integrability preserved. We show the that such a deformation exists under sufficiently weak conditions on the deformation space. We also show that if the vector bundle E 0 is trivial, then the solutions of the corresponding nonlinear equations extend meromorphically to the deformation space. Content Type Journal Article Pages 1637-1649 DOI 10.1007/s11232-010-0134-z Authors G. F. Helminck, Korteweg—de Vries Institute of Mathematics, University of Amsterdam, Amsterdam, The Netherlands V. A. Poberezhny, Institute for Theoretical and Experimental Physics, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 165 Journal Issue Volume 165, Number 3

Beschreibung:    We introduce the notion of a skew-holomorphic Lie algebroid on a complex manifold and explore some cohomology theories that can be associated with it. We present examples and applications of this notion in terms of different types of holomorphic Poisson structures. Content Type Journal Article Pages 1598-1609 DOI 10.1007/s11232-010-0132-1 Authors U. Bruzzo, Scuola Internazionale Superiore di Studi Avanzati, Trieste, Italy V. N. Rubtsov, Département de Mathématiques LAREMA, VFR Sciences, Université d’Angers, Angers, France Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 165 Journal Issue Volume 165, Number 3

Beschreibung:    We consider a new approach to thermodynamics and hydrodynamics. The phase transition of He 3 and He 4 to the superfluid state at low temperatures is interpreted as the transition to a semiclassical nonholonomic liquid crystal. Content Type Journal Article Pages 1699-1720 DOI 10.1007/s11232-010-0137-9 Authors V. P. Maslov, Lomonosov Moscow State University, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 165 Journal Issue Volume 165, Number 3

Beschreibung: In memoriam of Albert Nikiforovich Tavkhelidze Content Type Journal Article Pages 1565-1566 DOI 10.1007/s11232-010-0130-3 Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 165 Journal Issue Volume 165, Number 3

Beschreibung:    We present a complete list of nonlinear one-field hyperbolic equations with integrable third-order x and y symmetries. The list includes both equations of the sine-Gordon type and equations linearizable by differential substitutions. Content Type Journal Article Pages 43-57 DOI 10.1007/s11232-011-0004-3 Authors A. G. Meshkov, Orel State Technical University, Orel, Russia V. V. Sokolov, Landau Institute for Theoretical Physics, RAS, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 166 Journal Issue Volume 166, Number 1

Beschreibung:    We construct an Euler-Darboux transformation for the Fokker-Planck equation. As an example, we present solutions of the Fokker-Planck equation with given initial and boundary conditions. Content Type Journal Article Pages 58-65 DOI 10.1007/s11232-011-0005-2 Authors I. V. Verevkin, Institute for Computational Modeling, Siberian Branch, RAS, Krasnoyarsk, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 166 Journal Issue Volume 166, Number 1

Beschreibung:    We investigate a version of the Laplacian growth problem with zero surface tension in the upper half-plane. Using the method of time-dependent conformal maps, we find families of self-similar exact solutions that are expressible in terms of the hypergeometric function. Content Type Journal Article Pages 23-36 DOI 10.1007/s11232-011-0002-5 Authors D. V. Vasiliev, Institute for Theoretical and Experimental Physics, Moscow, Russia A. V. Zabrodin, Institute for Theoretical and Experimental Physics, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 166 Journal Issue Volume 166, Number 1

Beschreibung:    We obtain an exact scheme describing the dynamics of the N-particle state in the BCS model that is similar to the Gel’fand-Yaglom procedure for finding the transition amplitude of the harmonic oscillator with a time-dependent frequency. We find the many-particle spectrum and the eigenfunctions of the BCS Hamiltonian in the limit as the system volume tends to infinity. Content Type Journal Article Pages 94-103 DOI 10.1007/s11232-011-0008-z Authors V. V. Losyakov, Lebedev Physical Institute, RAS, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 166 Journal Issue Volume 166, Number 1

Beschreibung:    We consider the entropy gain for infinite-dimensional evolutions and show that unlike in the finitedimensional case, there are many channels with positive minimal entropy gain. We obtain a new lower bound and compute the minimal entropy gain for a broad class of bosonic Gaussian channels. We mathematically formulate the Choi-Jamiolkowski ( CJ ) correspondence between channels and states in the infinite-dimensional case in a form close to the form used in quantum information theory. In particular, we obtain an explicit expression for the CJ operator defining a general nondegenerate bosonic Gaussian channel and compute its norm. Content Type Journal Article Pages 123-138 DOI 10.1007/s11232-011-0010-5 Authors A. S. Holevo, Steklov Mathematical Institute, RAS, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 166 Journal Issue Volume 166, Number 1

Beschreibung:    We consider a model operator H associated with the system of three particles interacting via nonlocal pair potentials on a ν-dimensional lattice. We identify channel operators and use their spectra to describe the position and structure of the essential spectrum of H. We obtain an analogue of the Faddeev equation for the eigenfunctions of H. Content Type Journal Article Pages 81-93 DOI 10.1007/s11232-011-0007-0 Authors T. Kh. Rasulov, Bukhara State University, Bukhara, Uzbekistan Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 166 Journal Issue Volume 166, Number 1

Beschreibung:    We define cut-and-join operators in Hurwitz theory for merging two branch points of an arbitrary type. These operators have two alternative descriptions : (1) the GL characters are their eigenfunctions and the symmetric group characters are their eigenvalues ; (2) they can be represented as W-type differential operators ( in particular, acting on the time variables in the Hurwitz-Kontsevich τ-function ). The operators have the simplest form when expressed in terms of the Miwa variables. They form an important commutative associative algebra, a universal Hurwitz algebra, generalizing all group algebra centers of particular symmetric groups used to describe the universal Hurwitz numbers of particular orders. This algebra expresses arbitrary Hurwitz numbers as values of a distinguished linear form on the linear space of Young diagrams evaluated on the product of all diagrams characterizing particular ramification points of the branched covering . Content Type Journal Article Pages 1-22 DOI 10.1007/s11232-011-0001-6 Authors A. D. Mironov, Lebedev Physical Institute, RAS, Moscow, Russia A. Yu. Morozov, Institute for Theoretical and Experimental Physics, Moscow, Russia S. M. Natanzon, Higher School of Economics, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 166 Journal Issue Volume 166, Number 1

Beschreibung:    We derive several series representations for the Bloch-Gruneisen function of an arbitrary ( integer or noninteger ) order and show that it is related to other, more familiar special functions more commonly used in mathematical physics. In particular, the Bloch-Gruneisen function of integer order is expressible in terms of the Bose-Einstein function of different orders . Content Type Journal Article Pages 37-42 DOI 10.1007/s11232-011-0003-4 Authors D. Cvijović, Atomic Physics Laboratory, Vinča Institute of Nuclear Sciences, Belgrade, Republic of Serbia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 166 Journal Issue Volume 166, Number 1

Beschreibung:    We compute the period integrals on degenerate Seiberg—Witten curves for supersymmetric QCD explicitly and also show how these periods determine the changes in the quantum numbers of the states when passing from the weak- to strong-coupling domains in the mass moduli space of the theory. We discuss the confinement of monopoles at a strong coupling and demonstrate that the ambiguities in choosing the path in the moduli space do not affect the physical conclusions on confinement of monopoles in the phase with condensed light dyons. Content Type Journal Article Pages 1650-1661 DOI 10.1007/s11232-010-0135-y Authors A. V. Marshakov, Lebedev Physical Institute, RAS, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 165 Journal Issue Volume 165, Number 3

Beschreibung:    We consider a directed polymer model with an additive p-spin (p〉2) ferromagnetic term in the Hamiltonian. We give a rigorous proof for the specific free energy and derive the phase diagram. This model was proposed previously, and a detailed proof was given in the case p = 2, while the main result was only stated for p 〉 2. We give a detailed proof of the main result and show the behavior of the model as p → ∞ by constructing the phase diagram also in this case. These results are important in many applications, for instance, in telecommunication and immunology. Our major finding is that in the phase diagram for p 〉 2, a new transition curve (absent for p = 2) emerges between the paramagnetic region and the so-called mixed region and that the ferromagnetic region diminishes as p → ∞. Content Type Journal Article Pages 104-122 DOI 10.1007/s11232-011-0009-y Authors J. R. Wedagedera, Department of Mathematics, University of Ruhuna, Matara, Sri Lanka Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 166 Journal Issue Volume 166, Number 1

Beschreibung:    In the framework of the zeta-regularization approach, we consider the polarization of the scalar field vacuum with nontrivial boundary conditions originating from electrodynamics in the presence of a conducting infinitely thin boundary layer. Boundary conditions of the first type correspond to the case where the field is continuous on the boundary while its derivative has a jump proportional to the boundary value of the field. Boundary conditions of the second type correspond to the case where the field derivative is continuous on the boundary but the field itself has a jump proportional to the field derivative on the boundary. We explicitly obtain the zeta function of the scalar field Laplace operator with the above boundary conditions and calculate all the heat kernel coefficients. We obtain an expression for the energy of the scalar field vacuum fluctuations. Content Type Journal Article Pages 66-80 DOI 10.1007/s11232-011-0006-1 Authors N. R. Khusnutdinov, Kazan (Volga Region) Federal University, Kazan, Russia A. R. Khabibullin, Tatar State University of Humanities and Education, Kazan, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 166 Journal Issue Volume 166, Number 1

Beschreibung:    We develop the Ercolani—Sinha construction of SU(2) monopoles, which provides a gauge transform of the Nahm data. Content Type Journal Article Pages 1567-1597 DOI 10.1007/s11232-010-0131-2 Authors H. W. Braden, School of Mathematics, Edinburgh University, Edinburgh, UK V. Z. Enolski, Hanse-Wissenschaftskolleg (Institute for Advanced Study), Delmenhorst, Germany Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 165 Journal Issue Volume 165, Number 3

Beschreibung:    We develop a group theory approach for constructing solutions of integrable hierarchies corresponding to the deformation of a collection of commuting directions inside the Lie algebra of upper-triangular ZxZ matrices. Depending on the choice of the set of commuting directions, the homogeneous space from which these solutions are constructed is the relative frame bundle of an infinite-dimensional flag variety or the infinite-dimensional flag variety itself. We give the evolution equations for the perturbations of the basic directions in the Lax form, and they reduce to a tower of differential and difference equations for the coefficients of these perturbed matrices. The Lax equations follow from the linearization of the hierarchy and require introducing a proper analogue of the Baker—Akhiezer function. Content Type Journal Article Pages 1610-1636 DOI 10.1007/s11232-010-0133-0 Authors G. F. Helminck, Korteweg—de Vries Institute of Mathematics, University of Amsterdam, Amsterdam, The Netherlands A. G. Helminck, North Carolina State University, Raleigh, North Carolina, USA A. V. Opimakh, Orenburg State Pedagogical University, Orenburg, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 165 Journal Issue Volume 165, Number 3

Beschreibung:    Explicitly verifying the Alday—Gaiotto—Tachikawa (AGT) relation between the conformal blocks controlled by the WN symmetry and U(N) Nekrasov functions requires knowing the Shapovalov matrix and various triple correlators for W-algebra descendants. We collect the simplest expressions of this type for N = 3 and for the two lowest descendant levels together with the detailed derivations, which can now be computerized and used in more general studies of conformal blocks and AGT relations at higher levels. Content Type Journal Article Pages 1662-1698 DOI 10.1007/s11232-010-0136-x Authors A. D. Mironov, Lebedev Physical Institute, RAS, Moscow, Russia S. A. Mironov, Institute for Theoretical and Experimental Physics, Moscow, Russia A. Yu. Morozov, Institute for Theoretical and Experimental Physics, Moscow, Russia A. A. Morozov, Institute for Theoretical and Experimental Physics, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 165 Journal Issue Volume 165, Number 3

Beschreibung:    We consider the effect of strongly anisotropic turbulent mixing on the critical behavior of two systems: a φ 3 critical dynamics model describing universal properties of metastable states in the vicinity of a firstorder phase transition and a reaction-diffusion system near the point of a second-order transition between fluctuation and absorption states (a simple epidemic process or the Gribov process). In both cases, we demonstrate the existence of a new strongly nonequilibrium, anisotropic scaling regime (universality class) for which both the mixing and the nonlinearity in the order parameter are relevant. We evaluate the corresponding critical dimensions in the one-loop approximation of the renormalization group. Content Type Journal Article Pages 444-467 DOI 10.1007/s11232-011-0034-x Authors N. V. Antonov, Fock Institute of Physics, St. Petersburg State University, St. Petersburg, Russia A. V. Malyshev, Fock Institute of Physics, St. Petersburg State University, St. Petersburg, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 1

Beschreibung:    We study bi-Hamiltonian systems of hydrodynamic type with nonsingular (semisimple) nonlocal bi-Hamiltonian structures. We prove that all such systems of hydrodynamic type are diagonalizable and that the metrics of the bi-Hamiltonian structure completely determine the complete set of Riemann invariants constructed for any such system. Moreover, we prove that for an arbitrary nonsingular (semisimple) nonlocally bi-Hamiltonian system of hydrodynamic type, there exist local coordinates (Riemann invariants) such that all matrix differential-geometric objects related to this system, namely, the matrix (affinor) V j i (u) of this system of hydrodynamic type, the metrics g 1 ij (u) and g 2 ij (u), the affinor υ j i (u) = g 1 is (u)g 2 ,sj (u), and also the affinors (w 1 ,n ) j i (u) and (w 2 ,n ) j i (u) of the nonsingular nonlocal bi-Hamiltonian structure of this system, are diagonal in these special “diagonalizing” local coordinates (Riemann invariants of the system). The proof is a natural corollary of the general results of our previously developed theories of compatible metrics and of nonlocal bi-Hamiltonian structures; we briefly review the necessary notions and results in those two theories. Content Type Journal Article Pages 403-420 DOI 10.1007/s11232-011-0032-z Authors O. I. Mokhov, Landau Institute for Theoretical Physics, RAS, Chernogolovka, Moscow Oblast, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 1

Beschreibung:    We derive equations of motion for the electromagnetic field operators a q′ + a q″ for a three-level multimode laser with a spatial dependence of the interaction of atoms with the field of a standing wave in a cavity taken into account. We calculate and analyze the dynamics of means of photon numbers in the field modes and of the correlation function of field modes. We explore the effect of intermode correlations on the dynamics of establishing stationary laser generation. We find that taking the spatial dependence of the interaction of atoms with the field and the intermode correlation into account in investigating the means of photon numbers leads to revealing new properties of laser generation, such as saturation of the laser radiation intensity in a single-mode regime and generation of short light pulses of side below-threshold modes with the amplitudes depending on the initial state of the field in a cavity. Content Type Journal Article Pages 484-495 DOI 10.1007/s11232-011-0036-8 Authors A. V. Kozlovskii, Lebedev Physical Institute, RAS, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 167 Journal Issue Volume 167, Number 1

Beschreibung:    Based on the kernel formula proposed by Carroll and Kodama, we derive the dispersionless Hirota equations of the universal Whitham hierarchy. We also verify the associativity equations in this hierarchy from the dispersionless Hirota equations and give a realization of the associative algebra with the structure constants expressed in terms of residue formulas. Content Type Journal Article Pages 1456-1469 DOI 10.1007/s11232-010-0121-4 Authors Hsin-Fu Shen, Department of Mechanical Engineering, WuFeng Institute of Technology, Chiayi, Taiwan Niann-Chern Lee, General Education Center, National Chinyi University of Technology, Taichung, Taiwan Ming-Hsien Tu, Department of Physics, National Chung Cheng University, Chiayi, Taiwan Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 165 Journal Issue Volume 165, Number 2

Beschreibung:    In a broad sense, any parametric family of quantum states can be viewed as a quantum clock. The time, which is the parameter, is encoded in the corresponding quantum states. The quality of such a clock depends on how precisely we can distinguish the states or, equivalently, estimate the parameter. In view of the quantum Cramér—Rao inequalities, the quality of quantum clocks can be characterized by the quantum Fisher information. We address the issue of quantum clock synchronization in terms of quantum Fisher information and demonstrate its fundamental difference from the classical paradigm. The key point is the superadditivity of Fisher information, which always holds in the classical case but can be violated in quantum mechanics. The violation can occur for both pure and mixed states. Nevertheless, we establish the superadditivity of quantum Fisher information for any classical-quantum state. We also demonstrate an alternative form of superadditivity and propose a weak form of superadditivity. The violation of superadditivity can be exploited to enhance quantum clock synchronization. Content Type Journal Article Pages 1552-1564 DOI 10.1007/s11232-010-0129-9 Authors Ping Chen, Department of Economics, University of Melbourne, Melbourne, Australia Shunlong Luo, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, P. R. China Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 165 Journal Issue Volume 165, Number 2

Beschreibung:    We calculate the symmetry factors of diagrams for real and complex scalar fields in general form using an analysis of the Wick expansion for Green’s functions. We separate two classes of symmetry factors: factors corresponding to connected diagrams and factors corresponding to vacuum diagrams. The symmetry factors of vacuum diagrams play an important role in constructing the effective action and phase transitions in cosmology. In the complex scalar field theory, diagrams with different topologies can contribute the same, and the inverse symmetry factor for the total contribution is therefore the sum of the inverse symmetry factors. Content Type Journal Article Pages 1500-1511 DOI 10.1007/s11232-010-0124-1 Authors P. V. Dong, Institute of Physics, Vietnamese Academy of Science and Technology, Bo Ho, Hanoi, Vietnam L. T. Hue, Institute of Physics, Vietnamese Academy of Science and Technology, Bo Ho, Hanoi, Vietnam H. T. Hung, Institute of Physics, Vietnamese Academy of Science and Technology, Bo Ho, Hanoi, Vietnam H. N. Long, Institute of Physics, Vietnamese Academy of Science and Technology, Bo Ho, Hanoi, Vietnam N. H. Thao, Institute of Physics, Vietnamese Academy of Science and Technology, Bo Ho, Hanoi, Vietnam Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 165 Journal Issue Volume 165, Number 2

Beschreibung:    We construct an infinite-dimensional dynamical Hamiltonian system that can be interpreted as a localized structure (“quasiparticle”) on the plane E 2 . The model is based on the theory of an infinite string in the Minkowski space E 1,3 formulated in terms of the second fundamental forms of the worldsheet. The model phase space H is parameterized by the coordinates, which are interpreted as “internal” ( E (2)- invariant ) and “external” ( elements of T*E 2 ) degrees of freedom. The construction is nontrivial because H contains a finite number of constraints entangling these two groups of coordinates. We obtain the expressions for the energy and for the effective mass of the constructed system and the formula relating the proper angular momentum and the energy. We consider a possible interpretation of the proposed construction as an anyon model. Content Type Journal Article Pages 1517-1526 DOI 10.1007/s11232-010-0126-z Authors S. V. Talalov, Tolyatti State University, Tolyatti, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 165 Journal Issue Volume 165, Number 2

Beschreibung:    We use the Zakharov—Manakov δ-dressing method to construct new classes of exact solutions with functional parameters of the hyperbolic and elliptic versions of the Nizhnik—Veselov—Novikov equation with constant asymptotic values at infinity. We show that the constructed solutions contain classes of multisoliton solutions, which at a fixed time are exact potentials of the perturbed telegraph equation (the perturbed string equation) and the two-dimensional stationary Schrödinger equation. We interpret the stationary states of a microparticle in soliton-type potential fields physically in accordance with the constructed exact wave functions for the two-dimensional stationary Schrödinger equation. Content Type Journal Article Pages 1470-1489 DOI 10.1007/s11232-010-0122-3 Authors V. G. Dubrovsky, Novosibirsk State University for Technology, Novosibirsk, Russia A. V. Topovsky, Novosibirsk State University for Technology, Novosibirsk, Russia M. Yu. Basalaev, Novosibirsk State University for Technology, Novosibirsk, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 165 Journal Issue Volume 165, Number 2

Beschreibung:    We consider the increase in the number of trees as their size increases in the Eden growth model on simple and face-centered hypercubic lattices in different space dimensions. We propose a first-order partial differential equation for the tree generating function, which allows relating the exponent at the critical point of this function to the perimeter of the most probable tree. We estimate tree perimeters for the lattices considered. The theoretical values of the exponents agree well with the values previously obtained by computer modeling. We thus explain the closeness of the dimension dependences of the exponents of the simple and face-centered lattices and their difference from the results in the Bethe lattice approximation. Content Type Journal Article Pages 1443-1455 DOI 10.1007/s11232-010-0120-5 Authors V. E. Zobov, Kirensky Institute of Physics, Siberian Branch, RAS, Krasnoyarsk, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 165 Journal Issue Volume 165, Number 2

Beschreibung:    We construct a simple analytic solution of the cubic Neveu—Schwarz (NS) string field theory including the GSO(-) sector. This solution is analogous to the Erler—Schnabl solution in the bosonic case and to the solution in the pure GSO(+) case previously proposed by one of us. We construct exact gauge transformations of the new solution to other known solutions for the NS string tachyon condensation. This gauge equivalence manifestly supports the previous observation that the Erler solution for the pure GSO(+) sector and our solution containing both the GSO(+) and the GSO(-) sectors have the same value of the action density. Content Type Journal Article Pages 1512-1516 DOI 10.1007/s11232-010-0125-0 Authors I. Ya. Aref’eva, Steklov Mathematical Institute, RAS, Moscow, Russia R. V. Gorbachev, Steklov Mathematical Institute, RAS, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 165 Journal Issue Volume 165, Number 2

Beschreibung:    We calculate a renormalized two-point function using the adiabatic regularization method. We study the conformally and minimally coupled cases for massless and massive scalar fields in full detail. We reproduce previous results in a rigorous mathematical form and clarify some empirical approximations and bounds. We consider some applications to inflationary models. Content Type Journal Article Pages 1490-1499 DOI 10.1007/s11232-010-0123-2 Authors J. Haro, Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Barcelona, Spain Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 165 Journal Issue Volume 165, Number 2

Beschreibung:    Based on expansion terms of the Beltrami-flow type, we use multiscale methods to effectively construct an asymptotic expansion at large Reynolds numbers R for the long-wavelength perturbation of the nonstationary anisotropic helical solution of the force-free Navier—Stokes equation (the Trkal solution). We prove that the systematic asymptotic procedure can be implemented only in the case where the scaling parameter is R 1/2 . Projections of quasistationary large-scale streamlines on a plane orthogonal to the anisotropy direction turn out to be the gradient lines of the energy density determined by the initial conditions for two modulated anisotropic Beltrami flows (modulated as a result of scaling) with the same eigenvalues of the curl operator. The three-dimensional streamlines and the curl lines, not coinciding, fill invariant vorticity tubes inside which the velocity and vorticity vectors are collinear up to terms of the order of 1/ R . Content Type Journal Article Pages 1534-1551 DOI 10.1007/s11232-010-0128-x Authors A. S. Libin Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 165 Journal Issue Volume 165, Number 2

Beschreibung:    We establish explicit isomorphisms between three realizations of the quantum twisted affine algebra U q ( A 2 (2) : the Drinfeld current realization, the Chevalley realization, and the so-called RLL realization proposed by Reshetikhin, Takhtajan, and Faddeev. Content Type Journal Article Pages 1421-1434 DOI 10.1007/s11232-010-0118-z Authors A. M. Shapiro, Institute of Theoretical and Experimental Physics, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 165 Journal Issue Volume 165, Number 2

Beschreibung:    We consider the transport of vorticity in an Oldroydian viscoelastic fluid in the presence of suspended magnetic particles through porous media. We obtain the equations governing such a transport of vorticity from the equations of magnetic fluid flow. It follows from these equations that the transport of solid vorticity is coupled to the transport of fluid vorticity in a porous medium. Further, we find that because of a thermokinetic process, fluid vorticity can exist in the absence of solid vorticity in a porous medium, but when fluid vorticity is zero, then solid vorticity is necessarily zero. We also study a two-dimensional case. Content Type Journal Article Pages 1527-1533 DOI 10.1007/s11232-010-0127-y Authors P. Kumar, Department of Mathematics, ICDEOL, Himachal Pradesh University, Shimla, India G. J. Singh, SCD Government College, Ludhiana, Punjab, India Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 165 Journal Issue Volume 165, Number 2

Beschreibung:    We develop the method of difference jets on a multidimensional integer lattice. Based on this, we construct a lattice differential—difference bicomplex in the class of functions of a locally finite order and prove that it is acyclic. Content Type Journal Article Pages 1401-1420 DOI 10.1007/s11232-010-0117-0 Authors V. V. Zharinov, Steklov Mathematical Institute, RAS, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 165 Journal Issue Volume 165, Number 2

Beschreibung:    We construct a generating function for the Hermite polynomials by comparing two expressions for the same coherent states associated with Landau levels in the planar problem. The first expression is found using a group theory construction, and the second expression is obtained using generalized canonical coherent states expanded as series in the basis of number states. Content Type Journal Article Pages 1435-1442 DOI 10.1007/s11232-010-0119-y Authors Z. Mouayn, Department of Mathematics, Faculty of Sciences and Technics (M’Ghila), Sultan Moulay Slimane University, Béni Mellal, Morocco Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 165 Journal Issue Volume 165, Number 2

Beschreibung:    Several models solvable in terms of special functions of the Heun class are widely used in quantum mechanics. They are all characterized by the presence of a parameter that can be regarded as an adiabatic variable. An antiquantization procedure applied to such a model generates a dynamical model with properties of the Painlevé equations. The mentioned parameter plays the role of time. We consider examples of such models. Content Type Journal Article Pages 224-227 DOI 10.1007/s11232-011-0016-z Authors A. Mylläri, University of Turku, Turku, Finland S. Yu. Slavyanov, St. Petersburg State University, St. Petersburg, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 166 Journal Issue Volume 166, Number 2

Beschreibung:    We prove two lemmas and one theorem that allow integrating the product of an arbitrary number of unit vectors and the Legendre polynomials over a sphere of arbitrary radius. Such integral tensor products appear in solving inhomogeneous Helmholtz equations whose right-hand side is proportional to the product of a nonfixed number of unit vectors. Content Type Journal Article Pages 186-193 DOI 10.1007/s11232-011-0013-2 Authors P. A. Vshivtseva, Lomonosov Moscow State University, Moscow, Russia V. I. Denisov, Lomonosov Moscow State University, Moscow, Russia I. P. Denisova, Lomonosov Moscow State University, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 166 Journal Issue Volume 166, Number 2

Beschreibung:    We obtain a new relativistic Coulomb-like resummation factor (L-factor) for an arbitrary orbital moment ℓ ≥ 0. We work within the fully covariant quasipotential approach in quantum field theory formulated in the relativistic configuration representation in the case of two interacting relativistic particles with arbitrary masses. Content Type Journal Article Pages 194-209 DOI 10.1007/s11232-011-0014-1 Authors O. P. Solovtsova, International Center for Advanced Studies, Gomel State University for Technology, Gomel, Belarus Yu. D. Chernichenko, International Center for Advanced Studies, Gomel State University for Technology, Gomel, Belarus Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 166 Journal Issue Volume 166, Number 2

Beschreibung:    We construct the solution of the loop equations of the β-ensemble model in a form analogous to the solution in the case of the Hermitian matrices β = 1. The solution for β = 1 is expressed in terms of the algebraic spectral curve given by y 2 = U(x). The spectral curve for arbitrary β converts into the Schrödinger equation (ħ∂) 2 − U(x) ψ(x) = 0, where ħ ∝ ( Ö { b } - 1 \mathord / \vphantom Ö { b } - 1 Ö { b } Ö { b } ) \mathord / \vphantom ( Ö { b } - 1 \mathord / \vphantom Ö { b } - 1 Ö { b } Ö { b } ) N N . The basic ingredients of the method based on the algebraic solution retain their meaning, but we use an alternative approach to construct a solution of the loop equations in which the resolvents are given separately in each sector. Although this approach turns out to be more involved technically, it allows consistently defining the B-cycle structure for constructing the quantum algebraic curve (a D-module of the form y 2 − U(x), where [y, x] = ħ) and explicitly writing the correlation functions and the corresponding symplectic invariants Fh or the terms of the free energy in an 1/N 2 -expansion at arbitrary ħ. The set of “flat” coordinates includes the potential times t k and the occupation numbers ~ e   a   . We define and investigate the properties of the A- and B-cycles, forms of the first, second, and third kinds, and the Riemann bilinear identities. These identities allow finding the singular part of F 0 , which depends only on ~ e   a   . Content Type Journal Article Pages 141-185 DOI 10.1007/s11232-011-0012-3 Authors L. O. Chekhov, Steklov Mathematical Institute, Moscow, Russia B. Eynard, Institute de Physique Théorique, Centre des Etudes Atomiques, Gif-sur-Yvette, France O. Marchal, Institute de Physique Théorique, Centre des Etudes Atomiques, Gif-sur-Yvette, France Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 166 Journal Issue Volume 166, Number 2

Beschreibung:    We study the class of integrable self-action potentials satisfying the conditions that (1) they spontaneously break the symmetry, (2) they describe the inflation phase with a graceful exit ( i.e., with an exit that does not require fine tuning parameters ) , and (3) they feature several consecutive inflation phases. The first condition ensures that the inflation mechanism is qualitatively consistent with elementary particle physics, the second is a necessary ingredient of any inflation theory, and the third is necessary for a theory to be consistent with contemporary observational data, which support the accelerated expansion of the Universe. Content Type Journal Article Pages 259-269 DOI 10.1007/s11232-011-0020-3 Authors A. V. Yurov, Immanuel Kant State University of Russia, Kaliningrad, Russia V. A. Yurov, Immanuel Kant State University of Russia, Kaliningrad, Russia S. V. Chervon, Ul’yanovsk State Pedagogical University, Ul’yanovsk, Russia M. Sami, Centre for Theoretical Physics, Jamia Millia Islamia (A Central University), New Delhi, India Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 166 Journal Issue Volume 166, Number 2

Beschreibung:    We describe an alternative formalism for Einstein’s theory of gravity. The role of dynamical variables is played by a collection of ten vector fields f μ A , A = 1,..., 10. The metric is a composite variable, g µν = f µ A f ν A . The proposed scheme may lead to further progress in a theory of gravity where Einstein’s theory is to play the role of an effective theory, with Newton’s constant appearing by introducing an anomalous Green’s function. Content Type Journal Article Pages 279-290 DOI 10.1007/s11232-011-0023-0 Authors L. D. Faddeev, St. Petersburg Branch of the Steklov Institute of Mathematics, RAS, St. Petersburg, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 166 Journal Issue Volume 166, Number 3

Beschreibung:    We consider the Husimi Q-functions, which are quantum quasiprobability distributions in the phase space, and investigate their transformation properties under a scale transformation (q, p) → (λq, λp). We prove a theorem that under this transformation, the Husimi function of a physical state is transformed into a function that is also a Husimi function of some physical state. Therefore, the scale transformation defines a positive map of density operators. We investigate the relation of Husimi functions to Wigner functions and symplectic tomograms and establish how they transform under the scale transformation. As an example, we consider the harmonic oscillator and show how its states transform under the scale transformation. Content Type Journal Article Pages 356-368 DOI 10.1007/s11232-011-0028-8 Authors V. A. Andreev, Lebedev Physical Institute, RAS, Moscow, Russia D. M. Davidović, Vinca Institute of Nuclear Sciences, Belgrade, Serbia L. D. Davidović, Institute of Physics, Belgrade, Serbia M. D. Davidović, Faculty of Civil Engineering, Belgrade University, Belgrade, Serbia V. I. Man’ko, Lebedev Physical Institute, RAS, Moscow, Russia M. A. Man’ko, Lebedev Physical Institute, RAS, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 166 Journal Issue Volume 166, Number 3

Beschreibung:    We calculate the scalar Casimir energy and Casimir force for an ℝ 3 × N Kaluza-Klein piston setup in which the extra-dimensional space N contains a noncommutative two-dimensional sphere S fz . We study the cases with T d × S fz and S fz as the extra-dimensional spaces, where T d is the d -dimensional commutative torus, and examine the validity of the results and the regularization obtained in the piston setup in each case. We examine the Casimir energy with one-loop corrections for one piston chamber due to the self-interacting scalar field in the noncommutative geometry. We compute with some approximations. We compare the obtained results with the results of analogous computations for the Minkowski space-time M D . In conclusion, we discuss the stabilization of the extra-dimensional space in the piston setup. Content Type Journal Article Pages 337-355 DOI 10.1007/s11232-011-0027-9 Authors V. K. Oikonomou, Department of Theoretical Physics, Aristotle University of Thessaloniki, Thessaloniki, Greece Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 166 Journal Issue Volume 166, Number 3

Beschreibung:    We regard an ultrarelativistic hadron moving on a brane embedded in a higher-dimensional space-time as a membrane propagating on a three-brane. For hadron sizes exceeding the compactification radius and characteristic scales of five-dimensional gravitational interaction, this membrane can be regarded as a cosmic membrane in the sense that it extends to the infinities. In the five-dimensional case, a cosmic membrane produces a topological defect similar to the defect produced by a cosmic string in the four-dimensional space-time. This representation allows calculating the effects of the influence of the hadron mass on the gravitational interaction of partons belonging to the colliding hadrons. Content Type Journal Article Pages 385-391 DOI 10.1007/s11232-011-0030-1 Authors I. Ya. Aref’eva, Steklov Mathematical Institute, RAS, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 166 Journal Issue Volume 166, Number 3

Beschreibung:    Based on a general multidimensional Riemann theta function and the super Hirota bilinear form, we extend the Hirota method to construct explicit super quasiperiodic (multiperiodic) wave solutions of N = 1 supersymmetric KdV-type equations in superspace. We show that the supersymmetric KdV equation does not have an N-periodic wave solution with arbitrary parameters for N ≥ 2. In addition, an interesting influencing band occurs among the super quasiperiodic waves under the presence of a Grassmann variable. We also observe that the super quasiperiodic waves are symmetric about this band but collapse along with it. We present a limit procedure for analyzing the asymptotic properties of the super quasiperiodic waves and rigorously show that the super periodic wave solutions tend to super soliton solutions under some “small amplitude” limits. Content Type Journal Article Pages 317-336 DOI 10.1007/s11232-011-0026-x Authors Y. C. Hon, Department of Mathematics, City University of Hong Kong, Hongkong SAR, China Engui Fan, School of Mathematical Sciences and Key Laboratory of Mathematics for Nonlinear Science, Fudan University, Shanghai, China Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 166 Journal Issue Volume 166, Number 3

Beschreibung: Erratum to: “Zero level of a purely magnetic two-dimensional nonrelativistic Pauli operator for spin-1/2 particles” Content Type Journal Article Pages 278-278 DOI 10.1007/s11232-011-0022-1 Authors P. G. Grinevich A. E. Mironov S. P. Novikov Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 166 Journal Issue Volume 166, Number 2

Beschreibung:    We introduce the concept of an evolving random tree. The proposed model is a combination of a preferential attachment model and a uniform model. We consider the branch structure and maximum degree of the evolving random tree, which can partially explain the robustness under random attack and the vulnerability to targeted attack in the world wide web. Content Type Journal Article Pages 270-277 DOI 10.1007/s11232-011-0021-2 Authors Zhimin Li, School of Mathematics and Physics, Anhui Polytechnic University, Wuhu, Anhui, China Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 166 Journal Issue Volume 166, Number 2

Beschreibung:    We consider the multidimensional Schrödinger operator in an electromagnetic field. Under certain Stummel-type conditions imposed on the magnetic and electric potentials, we prove the essential self-adjointness of the magnetic Schrödinger operator. Content Type Journal Article Pages 228-233 DOI 10.1007/s11232-011-0017-y Authors A. R. Aliev, Baku State University, Baku, Azerbaijan E. H. Eyvazov, Baku State University, Baku, Azerbaijan Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 166 Journal Issue Volume 166, Number 2

Beschreibung:    We study the transmission and reflection coefficients for the Hamiltonian of a spin-polarized electron passing through the domain wall in a ferromagnetic quantum wire. We prove that total reflection occurs for energies λ ∈ ( −α, α ) ( −α is the boundary of the essential spectrum ) for both sufficiently small and sufficiently large λ, which agrees with the ballistic magnetoresistance effect in ferromagnetic nanocontacts. For energies λ 〉 α, almost total reflection becomes almost total transmission, and both effects occur without a spin flip. Content Type Journal Article Pages 234-243 DOI 10.1007/s11232-011-0018-x Authors Yu. P. Chuburin, Physical-Technical Institute, Ural Branch, RAS, Izhevsk, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 166 Journal Issue Volume 166, Number 2

Beschreibung:    Based on the variational principle, we obtain an expression for the resistance coefficient of simple disordered metals that is valid in the fourth order of the perturbation theory with respect to the electron-ion interaction. We assume that the ion subsystem is static and do not take temperature corrections into account. The decoupling parameters of higher-order Green’s functions appearing in the derivation of the quantum kinetic equation are chosen from the condition that the Boltzmann equation and the quantum kinetic equation coincide in the lowest order of the perturbation theory. Calculating the resistance of a disordered metal reduces to seeking the minimum of the corresponding functional. Such an approach allows calculating, for the first time, the contribution of crossed scattering to the resistivity of disordered metals in the low-temperature limit. The known results are reproduced in the second and third orders of the perturbation theory. We show that in the fourth and higher orders, the resistance coefficient can be expressed not only in terms of the relaxation time but also in terms of the density of states of the electron gas interacting with the ions. Content Type Journal Article Pages 244-258 DOI 10.1007/s11232-011-0019-9 Authors T. V. Shvets, Odessa State Academy of Refrigeration, Odessa, Ukraine V. T. Shvets, Odessa State Academy of Refrigeration, Odessa, Ukraine Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 166 Journal Issue Volume 166, Number 2

Beschreibung:    We consider a method for seeking exact solutions of the equation of a nonlocal scalar field in a nonflat metric. In the Friedmann-Robertson-Walker metric, the proposed method can be used in the case of an arbitrary potential except linear and quadratic potentials, and it allows obtaining solutions in quadratures depending on two arbitrary parameters. We find exact solutions for an arbitrary cubic potential, which consideration is motivated by string field theory, and also for exponential, logarithmic, and power potentials. We show that the k-essence field can be added to the model to obtain exact solutions satisfying all the Einstein equations. Content Type Journal Article Pages 392-402 DOI 10.1007/s11232-011-0031-0 Authors S. Yu. Vernov, Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 166 Journal Issue Volume 166, Number 3

Beschreibung:    We propose a renormalizable formulation of the Higgs-Kibble model free of the Gribov ambiguity. Content Type Journal Article Pages 291-302 DOI 10.1007/s11232-011-0024-z Authors A. Quadri, Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany A. A. Slavnov, Steklov Mathematical Institute, RAS, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 166 Journal Issue Volume 166, Number 3