ISSN: 1573-9333 eISSN: 0040-5779
Subject:
mathematics
physics
Published by Springer-Verlag 
No Issue Number- The physical inconsistency of the Schwarzschild and Kerr solutions
Abstract The metric of a neutral stationary “black hole” does not satisfy the causality conditions formulated by Hilbert. As a consequence, a trial body falling freely, for instance, into a rotating “black hole” develops a speed equal to the speed of light on the ergosphere shell during a finite time in the reference frame of a distant observer, which results in physical inconsistency and indicates the principal drawback of the vacuum solution of Einstein’s equation outside a source.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0077-4
- Authors
- V. V. Kiselev, SSC Institute for High-Energy Physics, Protvino, Moscow Oblast, Russia
- A. A. Logunov, SSC Institute for High-Energy Physics, Protvino, Moscow Oblast, Russia
- M. A. Mestvirishvili, Bogoliubov Institute for Theoretical Problems of Microphysics, Lomonosov Moscow State University, Moscow, Russia
- The Efimov effect for a model “three-particle” discrete Schrödinger operator
Abstract We study the existence of an infinite number of eigenvalues for a model “three-particle” Schrödinger operator H. We prove a theorem on the necessary and sufficient conditions for the existence of an infinite number of eigenvalues of the model operator H below the lower boundary of its essential spectrum.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0071-x
- Authors
- Yu. Kh. Éshkabilov, Ulugbek Uzbekistan National University, Tashkent, Uzbekistan
- Study of the essential spectrum of a matrix operator
Abstract We consider a matrix operator H corresponding to a system with a nonconserved finite number of particles on a lattice. We describe the structure of the essential spectrum of the operator H and prove that the essential spectrum is a union of at most four intervals.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0070-y
- Authors
- T. Kh. Rasulov, Bukhara State University, Bukhara, Uzbekistan
- Transcendental trace formulas for finite-gap potentials
Abstract We show that formulas differing from classical analogues of rational trace formulas for algebraic-geometric potentials occur in the theory of finite-gap integration of spectral equations. The new formulas contain transcendental modular functions and hypergeometric series. They result in transcendental relations for theta functions.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0073-8
- Authors
- Yu. V. Brezhnev, Tomsk State University, Tomsk, Russia
- Formula for the number of eigenvalues of a three-particle Schrödinger operator on a lattice
Abstract We consider a system of three arbitrary quantum particles on a three-dimensional lattice that interact via short-range attractive potentials. We obtain a formula for the number of eigenvalues in an arbitrary interval outside the essential spectrum of the three-particle discrete Schrödinger operator and find a sufficient condition for the discrete spectrum to be finite. We give an example of an application of our results.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0069-4
- Authors
- M. E. Muminov, Samarkand State University Samarkand Uzbekistan
- Wave function and the probability current distribution for a bound electron moving in a uniform magnetic field
Abstract We study the effects of electromagnetic fields on nonrelativistic charged spinning particles bound by a short-range potential. We analyze the exact solution of the Pauli equation for an electron moving in the potential field determined by the three-dimensional δ-well in the presence of a strong magnetic field. We obtain asymptotic expressions for this solution for different values of the problem parameters. In addition, we consider electron probability currents and their dependence on the magnetic field. We show that including the spin in the framework of the nonrelativistic approach allows correctly taking the effect of the magnetic field on the electric current into account. The obtained dependences of the current distribution, which is an experimentally observable quantity, can be manifested directly in scattering processes, for example.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0076-5
- Authors
- V. N. Rodionov, Russian State Geological Prospecting University, Moscow, Russia
- G. A. Kravtsova, Lomonosov Moscow State University, Moscow, Russia
- A. M. Mandel’, Moscow Aviation Institute (State Technical University), Moscow, Russia
- Vacuum symmetries in brane-world models
Abstract We discuss the symmetries of vacuum configurations in stabilized five-dimensional brane-world models and their relation to the properties of solutions of the corresponding equations of motion. With the example of a model admitting the four-dimensional de Sitter metric on the branes, we show that the existence of such symmetries in some cases leads to a decrease in the number of fundamental parameters to be fine tuned.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0075-6
- Authors
- I. S. Grinin, Lomonosov Moscow State University, Moscow, Russia
- S. R. Ramzanov, Lomonosov Moscow State University, Moscow, Russia
- M. N. Smolyakov, Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, Russia
- Combinatorial expansions of conformal blocks
Abstract A representation of Nekrasov partition functions in terms of a nontrivial two-dimensional conformal field theory was recently suggested. For a nonzero value of the deformation parameter ∈ = ∈ 1 + ∈ 2 , the instanton partition function is identified with a conformal block of the Liouville theory with the central charge c = 1 + 6 ∈ 2 /∈ 1 ∈ 2 . The converse of this observation means that the universal part of conformal blocks, which is the same for all two-dimensional conformal theories with nondegenerate Virasoro representations, has a nontrivial decomposition into a sum over Young diagrams that differs from the natural decomposition studied in conformal field theory. We provide some details about this new nontrivial correspondence in the simplest case of the four-point correlation functions.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0067-6
- Authors
- A. V. Marshakov, Institute for Theoretical and Experimental Physics, Moscow, Russia
- A. D. Mironov, Institute for Theoretical and Experimental Physics, Moscow, Russia
- A. Yu. Morozov, Institute for Theoretical and Experimental Physics, Moscow, Russia
- Quantum sℓ(2) action on a divided-power quantum plane at even roots of unity
Abstract We describe a nonstandard version of the quantum plane in which the basis is given by divided powers at an even root of unity q = e iπ/p . It can be regarded as an extension of the “nearly commutative” algebra ℂ[X, Y] with XY = (− 1 ) p YX by nilpotents. For this quantum plane, we construct a Wess-Zumino-type de Rham complex and find its decomposition into representations of the 2 p 3 -dimensional quantum group q sℓ( 2 ) and its Lusztig extension U q sℓ( 2 ); we also define the quantum group action on the algebra of quantum differential operators on the quantum plane.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0068-5
- Authors
- A. M. Semikhatov, RAS Lebedev Physical Institute Moscow Russia
- Dynamical magnetic susceptibility of the periodic anderson model in the chaotic phase approximation
Abstract Using the diagram technique in the atomic representation in the generalized chaotic phase approximation, we solve the problem of calculating the dynamical magnetic susceptibility of the periodic Anderson model in the strong electron correlation regime. We express the dynamical magnetic susceptibility in terms of four Matsubara Green’s functions describing partial contributions, which are calculated based on exact solutions of integral equations.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0087-2
- Authors
- V. V. Val’kov, Institute of Physics, Siberian Branch, RAS, Krasnoyarsk, Russia
- D. M. Dzebisashvili, Institute of Physics, Siberian Branch, RAS, Krasnoyarsk, Russia
- The ring of physical states in the M(2, 3) minimal Liouville gravity
Abstract We consider the M (2, 3) minimal Liouville gravity, whose state space in the gravity sector is realized as irreducible modules of the Virasoro algebra. We present a recursive construction for BRST cohomology classes based on using an explicit form of singular vectors in irreducible modules of the Virasoro algebra. We find a certain algebra acting on the BRST cohomology space and use this algebra to find the operator algebra of physical states.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0074-7
- Authors
- O. V. Alekseev, Landau Institute for Theoretical Physics, RAS, Chernogolovka, Moscow Oblast, Russia
- M. A. Bershtein, Landau Institute for Theoretical Physics, RAS, Chernogolovka, Moscow Oblast, Russia
- Entropic measure of the order-disorder character in lattice systems in the representation of coordination Cayley tree graphs
Abstract We systematically expound the infodynamical method for analyzing lattice and grid systems. We establish the logic and algorithm for mapping given objects to coordination Cayley tree graphs and present their main properties. Tree graphs of grid systems are complicated objects, and the principle of cluster-type simplicial decomposition can be used to study them. Based on a simplicial decomposition, we construct the enumerating structures, from which we construct entropy-type functionals. We pose the percolation problem on Cayley tree graphs in a nonconventional sense, which may be considered for both enumerating structures and their entropies. The corresponding entropy percolational dependences and their critical indices can be considered sufficiently universal measures of order in lattice systems. The simpliciality also implies an analogy with the fractality principle. We introduce three types of fractal characteristics and give analytic expressions for fractal dimensions for the tangential and streamer representations and for the Mandelbrot shell.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0072-9
- Authors
- V. V. Yudin, Far-East State University, Vladivostok, Russia
- P. L. Titov, Far-East State University, Vladivostok, Russia
- A. N. Mikhalyuk, Far-East State University, Vladivostok, Russia
- A possible combinatorial point for the XYZ spin chain
Abstract We formulate and discuss several conjectures related to the ground state vectors of odd-length XYZ spin chains with periodic boundary conditions and a special choice of the Hamiltonian parameters. In particular, we argue for the validity of a sum rule for the vector components that in a sense describes the degree of antiferromagneticity of the chain.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0078-3
- Authors
- A. V. Razumov, Institute for High Energy Physics, Protvino, Moscow Oblast, Russia
- Yu. G. Stroganov, Institute for High Energy Physics, Protvino, Moscow Oblast, Russia
- Nonlinear transparency regimes for three-component acoustic pulses in a system of electron and nuclear spins
Abstract We study acoustic solitons consisting of one longitudinal and two transverse components and propagating in the direction perpendicular to an external magnetic field in a crystal containing paramagnetic impurities of electron and nuclear spins. The coupling of the electron spin subsystem to the longitudinal sound allows making the velocity of the latter close to that of the transverse acoustic waves, which provides an effective interaction between all components of the elastic field by means of the nuclear spin subsystem. We derive a three-component system of material and reduced wave equations describing this process and construct its soliton solutions in the form of stationary and breather pulses. Based on them, we study the peculiarities of the dynamics of the elastic field components and reveal the differences from the two-component model. The existence of two families of breathers is an important distinctive feature of the considered case.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0082-7
- Authors
- S. V. Sazonov, Russian Research Centre “Kurchatov Institute”, Moscow, Russia
- N. V. Ustinov, Kaliningrad Branch, Moscow State University of Railway Engineering, Kaliningrad, Russia
- The Korteweg-de Vries equation with a self-consistent source in the class of periodic functions
Abstract We use the inverse spectral problem method to integrate the Korteweg-de Vries equation with a self-consistent source in the class of periodic functions.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0081-8
- Authors
- A. B. Khasanov, Urgench State University, Urgench, Uzbekistan
- A. B. Yakhshimuratov, Urgench State University, Urgench, Uzbekistan
- Casimir energy in noncompact lattice electrodynamics
Abstract We propose a new lattice method for calculating the Casimir energy for a U (1) gauge theory. Using this method, we analyze the standard problem of the Casimir interaction of two planar parallel plates with the boundary conditions induced by an additional Chern-Simons action localized on these boundary surfaces. From the physical standpoint, this boundary value problem models the interaction of two thin metal plates. The proposed method can be generalized to the case of more complicated surface shapes.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0084-5
- Authors
- O. V. Pavlovskii, Bogoliubov Institute for Theoretical Problems of Microworld, Lomonosov Moscow State University, Moscow, Russia
- M. V. Ulybyshev, Bogoliubov Institute for Theoretical Problems of Microworld, Lomonosov Moscow State University, Moscow, Russia
- Semiclassical spectral series of the Schrödinger operator with a delta potential on a straight line and on a sphere
Abstract We describe the spectral series of the Schrödinger operator H = −(h 2 /2)Δ + V(x) + αδ(x−x 0 ), α ∈ ℝ, with a delta potential on the real line and on the three- and two-dimensional standard spheres in the semiclassical limit as h → 0 . We consider a smooth potential V(x) such that lim x →∞ V(x)=+∞ in the first case and V(x) = 0 in the last two cases. In the semiclassical limit in each case, we describe the classical trajectories corresponding to the quantum problem with a delta potential.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0085-4
- Authors
- T. A. Filatova, Ishlinskii Institute for Problems in Mechanics, RAS, Moscow, Russia
- A. I. Shafarevich, Lomonosov Moscow State University, Moscow, Russia
- Some integral equations related to random Gaussian processes
Abstract To calculate the Laplace transform of the integral of the square of a random Gaussian process, we consider a nonlinear Volterra-type integral equation. This equation is a Ward identity for the generating correlation function. It turns out that for an important class of correlation functions, this identity reduces to a linear ordinary differential equation. We present sufficient conditions for this equation to be integrable (the equation coefficients are constant). We calculate the Laplace transform exactly for some concrete random Gaussian processes such as the “Brownian bridge” model and the Ornstein-Uhlenbeck model.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0079-2
- Authors
- V. G. Marikhin, Landau Institute for Theoretical Physics, RAS, Moscow, Russia
- V. V. Sokolov, Landau Institute for Theoretical Physics, RAS, Moscow, Russia
- Renormalization group approach to function approximation and to improving subsequent approximations
Abstract We establish a relation between bijective functions and renormalization group transformations and find their renormalization group invariants. For these functions, taking into account that they are globally one-to-one, we propose several improved approximations (compared with the power series expansion) based on this relation. We propose using the obtained approximations to improve the subsequent approximations of physical quantities obtained, in particular, by one of the main calculation techniques in theoretical physics, i.e., by perturbation theory. We illustrate the effectiveness of the renormalization group approximation with several examples: renormalization group approximations of several analytic functions and calculation of the nonharmonic oscillator ground-state energy. We also generalize our approach to the case of set maps, both continuous and discrete.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0083-6
- Authors
- G. N. Nikolaev, Institute of Automation and Electrometry, Siberian Branch, RAS, Novosibirsk, Russia
- Integrable vector evolution equations admitting zeroth-order conserved densities
Abstract In the symmetry approach framework, we solve the problem of classifying third-order integrable vector evolution equations that have zeroth-order conserved densities. We obtain the complete list of nine equations of this form. Two equations in the list were previously unknown. We find auto-Bäcklund transformations for the new equations.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0080-9
- Authors
- M. Yu. Balakhnev, Orel State University for Technology, Orel, Russia
- A. G. Meshkov, Orel State University for Technology, Orel, Russia
- Rodrigues solutions of the dirac equation for shape-invariant potentials: Master function approach
Abstract We show that a Schrödinger-like differential equation for the upper spinor component, derived from the Dirac equation for a charged spinor in spherically symmetric electromagnetic potentials, can be transformed into the Schrödinger equation with some shape-invariant potentials. By choosing different electrostatic potentials and relativistic energies and also introducing new functions and changing the variables, we show that this equation transforms into the differential equations in mathematical physics. We solve these equations using the master function approach and write the spinor wave functions in terms of Rodrigues polynomials associated with these differential equations.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0086-3
- Authors
- H. Panahi, Department of Physics, Guilan University, Rasht, Iran
- L. Jahangiry, Department of Physics, Guilan University, Rasht, Iran
- Two-particle wave function as an integral operator and the random field approach to quantum correlations
Abstract We propose a new interpretation of the wave function Ψ (x, y) of a two-particle quantum system, interpreting it not as an element of the functional space L 2 of square-integrable functions, i.e., as a vector, but as the kernel of an integral (Hilbert-Schmidt) operator. The first part of the paper is devoted to expressing quantum averages including the correlations in two-particle systems using the wave-function operator. This is a new mathematical representation in the framework of conventional quantum mechanics. But the new interpretation of the wave function not only generates a new mathematical formalism for quantum mechanics but also allows going beyond quantum mechanics, i.e., representing quantum correlations (including those in entangled systems) as correlations of (Gaussian) random fields.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0094-3
- Authors
- A. Yu. Khrennikov, International Center for Mathematical Modeling in Physics, Engineering, Economics, and Cognitive Science, Linnaeus University, Växjö-Kalmar, Sweden
- Multidimensional clustering and hypergraphs
Abstract We discuss a multidimensional generalization of the clustering method. In our approach, the clustering is realized by partially ordered hypergraphs belonging to some family. The suggested procedure is applicable in the case where the original metric depends on a set of parameters. The clustering hypergraph studied here can be regarded as an object describing all possible clustering trees corresponding to different values of the original metric.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0095-2
- Authors
- S. V. Kozyrev, Steklov Mathematical Institute, RAS, Moscow, Russia
- Spectrum of the energy operator of two-magnon systems in the isotropic Heisenberg ferromagnet model with impurity
Abstract We consider a two-magnon system in the isotropic Heisenberg ferromagnet model with impurity on a ν-dimensional lattice ℤ ν . We establish that the essential spectrum of the system consists of the union of at most four intervals. We obtain the lower and upper estimates for the number of three-particle bound states of the system.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0104-5
- Authors
- S. M. Tashpulatov, Institute for Nuclear Physics, Academy of Sciences, Republic of Uzbekistan, Tashkent, Uzbekistan
- Generalized entropy of the Heisenberg spin chain
Abstract We consider the XY quantum spin chain in a transverse magnetic field. We consider the Rényi entropy of a block of neighboring spins at zero temperature on an infinite lattice. The Rényi entropy is essentially the trace of some power α of the density matrix of the block. We calculate the entropy of the large block in terms of Klein’s elliptic λ-function. We study the limit entropy as a function of its parameter α. We show that the Rényi entropy is essentially an automorphic function with respect to a certain subgroup of the modular group. Using this, we derive the transformation properties of the Rényi entropy under the map α → α −1 .
- Content Type Journal Article
- DOI 10.1007/s11232-010-0091-6
- Authors
- A. R. Its, Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, Indianapolis, Indiana USA
- V. E. Korepin, Yang Institute for Theoretical Physics, State University of New York, Stony Brook, New York USA
- Regularized adelic formulas for string and superstring amplitudes in one-class quadratic fields
Abstract We obtain regularized adelic formulas for gamma and beta functions for fields of rational numbers and the one-class quadratic fields and arbitrary quasicharacters (ramified or not). We consider applications to four-tachyon tree string amplitudes, generalized Veneziano amplitudes (open string), perturbed Virasoro amplitudes (closed string), massless four-particle tree open and closed superstring amplitudes, Ramond-Neveu-Schwarz superstring amplitudes, and charged heterotic superstring amplitudes. We establish certain relations between different string and superstring amplitudes.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0088-1
- Authors
- V. S. Vladimirov, Steklov Mathematical Institute, RAS, Moscow, Russia
- Bogoliubov equations and functional mechanics
Abstract The functional classical mechanics based on the probability approach, where a particle is described not by a trajectory in the phase space but by a probability distribution, was recently proposed for solving the irreversibility problem, i.e., the problem of matching the time reversibility of microscopic dynamics equations and the irreversibility of macrosystem dynamics. In the framework of functional mechanics, we derive Bogoliubov-Boltzmann-type equations for finitely many particles. We show that a closed equation for a one-particle distribution function can be rigorously derived in functional mechanics without any additional assumptions required in the Bogoliubov method. We consider the possibility of using diffusion processes and the Fokker-Planck-Kolmogorov equation to describe isolated particles.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0090-7
- Authors
- I. V. Volovich, Steklov Mathematical Institute, RAS, Moscow, Russia
- Zero level of a purely magnetic two-dimensional nonrelativistic Pauli operator for SPIN-1/2 particles
Abstract We study the manifold of complex Bloch-Floquet eigenfunctions for the zero level of a two-dimensional nonrelativistic Pauli operator describing the propagation of a charged particle in a periodic magnetic field with zero flux through the elementary cell and a zero electric field. We study this manifold in full detail for a wide class of algebraic-geometric operators. In the nonzero flux case, the Pauli operator ground state was found by Aharonov and Casher for fields rapidly decreasing at infinity and by Dubrovin and Novikov for periodic fields. Algebraic-geometric operators were not previously known for fields with nonzero flux because the complex continuation of “magnetic” Bloch-Floquet eigenfunctions behaves wildly at infinity. We construct several nonsingular algebraic-geometric periodic fields (with zero flux through the elementary cell) corresponding to complex Riemann surfaces of genus zero. For higher genera, we construct periodic operators with interesting magnetic fields and with the Aharonov-Bohm phenomenon. Algebraic-geometric solutions of genus zero also generate soliton-like nonsingular magnetic fields whose flux through a disc of radius R is proportional to R (and diverges slowly as R → ∞). In this case, we find the most interesting ground states in the Hilbert space L 2 (ℝ 2 ).
- Content Type Journal Article
- DOI 10.1007/s11232-010-0089-0
- Authors
- P. G. Grinevich, Landau Institute for Theoretical Physics, RAS, Chernogolovka, Moscow Oblast, Russia
- A. E. Mironov, Sobolev Institute for Mathematics, Siberian Branch, RAS, Novosibirsk, Russia
- S. P. Novikov, University of Maryland, College Park, Maryland USA
- Nonlocal dynamics of p-adic strings
Abstract We consider the construction of Lagrangians that might be suitable for describing the entire p-adic sector of an adelic open scalar string. These Lagrangians are constructed using the Lagrangian for p-adic strings with an arbitrary prime number p. They contain space-time nonlocality because of the d’Alembertian in the argument of the Riemann zeta function. We present a brief review and some new results.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0093-4
- Authors
- B. G. Dragovich, Institute of Physics, Belgrade, Serbia
- Group averaging for de Sitter free fields in terms of hyperspherical functions
Abstract We study the convergence of inner products of free fields over the homogeneous spaces of the de Sitter group and show that the convergence of inner products in the case of N-particle states is defined by the asymptotic behavior of hypergeometric functions. We calculate the inner product for two-particle states on the four-dimensional hyperboloid in detail.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0105-4
- Authors
- V. V. Varlamov, Siberian State Industrial University, Novokuznetsk, Russia
- A special set of eigenvectors for the hyperbolic Sutherland systems
Abstract We construct the integrals of motion for Sutherland hyperbolic quantum systems of particles with internal degrees of freedom (su(n) spins) interacting with an external field of the Morse potential of an arbitrary strength τ 2 . These systems are confined if certain constraints are imposed on τ, the pair coupling constant λ, and the number of particles. The ground state is described by a wave function of the Jastrow form.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0098-z
- Authors
- B. I. Sadovnikov, Lomonosov Moscow State University, Moscow, Russia
- N. G. Inozemtseva, Dubna International University of Nature, Society, and Humanity, Dubna, Moscow Oblast, Russia
- V. I. Inozemtsev, Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia
- Multifield cosmology from string field theory: An exactly solvable approximation
Abstract We consider the appearance of multiple scalar fields in string field theory-based nonlocal models with a single scalar field at large times. In this regime, all the scalar fields are free. This system minimally coupled to gravity can be analyzed approximately or numerically. We construct an exactly solvable model that has an exact solution in the cosmological scenario with the Friedmann metric and restores the asymptotic behavior expected from string field theory. We consider different applications of such a potential to multifield cosmological models.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0096-1
- Authors
- F. Galli, International Solvay Institutes, Vrije Universiteit Brussel, Brussels, Belgium
- A. S. Koshelev, International Solvay Institutes, Vrije Universiteit Brussel, Brussels, Belgium
- Explicit solutions of an integrable boundary value problem for the two-dimensional toda lattice
Abstract We obtain an explicit solution of the integrable boundary value problem for the two-dimensional Toda lattice using the inverse scattering method. We interpret the integrability property in terms of the corresponding linear problem, the Gel’fand-Levitan-Marchenko equation, and the dressing procedure. The simplest initial solutions of the boundary value problem become new nontrivial solutions after the dressing procedure is applied.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0107-2
- Authors
- V. L. Vereshchagin, Institute of Mathematics with Computing Center, Ufa Science Center, RAS, Ufa, Russia
- Thermodynamics of the model of equal spin-spin interactions
Abstract We consider the thermodynamics of the model of equal spin-spin interactions. We obtain exact expressions for the correlation functions and heat capacity of finite clusters applicable in the entire range of temperature and external fields. We analyze the obtained thermodynamic characteristics depending on the interaction parameters, the external magnetic field, and the number of particles in the cluster. We find an anomalous behavior of the heat capacity and other thermodynamic quantities due to elementary spin gap excitations occurring in the spectrum. The absence of a long-range order in the system is ensured by the presence of topological excitations (solitons). We study the effect of an anisotropic interaction parameter on the soliton structure.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0115-2
- Authors
- A. A. Khamzin, Kazan State Power-Engineering University, Kazan, Russia
- R. R. Nigmatullin, Kazan (Volga Region) Federal University, Kazan, Russia
- Destruction of dissipative structures under random actions
Abstract We consider random-parameter chemical kinetic systems that are important in numerous physical, chemical, and biological applications. Random parameters describe the action of ambient medium fluctuations on the system. We estimate the probability that the system state remains in a given domain of the phase space during a time interval [ 0 , T] under the condition that the state at the initial instant was in u 0 , where u 0 is the equilibrium solution describing a dissipative structure. We show that in some cases, the problem of maximizing this probability is reducible to the known problem of minimizing the Hopfield Hamiltonian.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0116-1
- Authors
- S. A. Vakulenko, St. Petersburg State University for Technology and Design, St. Petersburg, Russia
- M. V. Cherkai, Institute for Problems in Mechanical Engineering, RAS, St. Petersburg, Russia
- Electromagnetic properties of non-Dirac particles with rest spin 1/2
Abstract We resolve a number of questions related to an analytic description of electromagnetic form factors of non-Dirac particles with the rest spin 1/2. We find the general structure of a matrix antisymmetric tensor operator. We obtain two recurrence relations for matrix elements of finite transformations of the proper Lorentz group and explicit formulas for a certain set of such elements. Within the theory of fields with double symmetry, we discuss writing the components of wave vectors of particles in the form of infinite continued fractions. We show that for Q 2 ≤ 0.5 (GeV/c) 2 , where Q 2 is the transferred momentum squared, electromagnetic form factors that decrease as Q 2 increases and are close to those experimentally observed in the proton can be obtained without explicitly introducing an internal particle structure.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0109-0
- Authors
- L. M. Slad, Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, Russia
- Space of C1-smooth skew products of maps of an interval
Abstract Using the notions of an Ω -function and of functions suitable for an Ω -function, we show that the space of C 1 -smooth skew products of maps of an interval such that the quotient map of each is Ω -stable in the space of C 1 -smooth maps of a closed interval into itself and has a type ≻ 2 ∞ (i.e., contains a periodic orbit with the period not equal to a power of 2) can be represented as a union of four nonempty pairwise nonintersecting subspaces. We give examples of maps belonging to each of the identified subspaces.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0102-7
- Authors
- L. S. Efremova, Lobachevsky Nizhnii Novgorod State University (Research University), Nizhnii Novgorod, Russia
- Averaging of quantum dynamical semigroups
Abstract In the framework of the elliptic regularization method, the Cauchy problem for the Schrödinger equation with discontinuous degenerating coefficients is associated with a sequence of regularized Cauchy problems and the corresponding regularized dynamical semigroups. We study a divergent sequence of quantum dynamical semigroups as a random process with values in the space of quantum states defined on a measurable space of regularization parameters with a finitely additive measure. The mathematical expectation of the considered processes determined by the Pettis integral defines a family of averaged dynamical transformations. We investigate the semigroup property and the injectivity and surjectivity of the averaged transformations. We establish the possibility of defining the process by its mathematical expectation at two different instants and propose a procedure for approximating an unknown initial state by solutions of a finite set of variational problems on compact sets.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0103-6
- Authors
- V. Zh. Sakbaev, Moscow Institute for Physics and Technology, Dolgoprudnyi, Moscow Oblast, Russia
- Integrable equations for the model with N sources and n-1 modes
Abstract We consider simplified models of coupling charged matter to radiation resonance modes generalizing the well-known Jaynes-Cummings and Dicke models. We find that these new models are integrable for arbitrary numbers of dipole sources and resonance modes of the radiation field. We discuss the problem of explicitly diagonalizing the corresponding Hamiltonians.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0097-0
- Authors
- B. I. Sadovnikov, Lomonosov Moscow State University, Moscow, Russia
- N. G. Inozemtseva, Dubna International University of Nature, Society, and Humanity, Dubna, Moscow Oblast, Russia
- V. I. Inozemtsev, Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia
- Irreversibility and the role of an instrument in the functional formulation of classical mechanics
Abstract We analyze the role of an instrument in the recently proposed functional formulation of classical mechanics, whose basic equation is the Liouville equation. Its solution has the delocalization (spreading) property, which is interpreted as irreversibility on the microlevel. We show that the reversible and recurrent dynamics for a particle can be observed by tracking the particle dynamics using instruments, but repeated measurements inevitably lead to a heat release and an increase in the entropy of the instrument. The irreversible behavior is thus transported from the system under study to the instrument, which is also a physical system.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0100-9
- Authors
- A. S. Trushechkin, Steklov Mathematical Institute, RAS, Moscow, Russia
- Existence and uniqueness of classical solutions of the Cauchy problem on nonglobally hyperbolic manifolds
Abstract We consider the Cauchy problem for the wave equation on the Misner space, a nonglobally hyperbolic manifold with closed timelike lines. We prove that the existence and uniqueness of a classical solution are equivalent to self-consistency conditions much more rigorous than a finite collection of pointlike conditions occurring in this problem on the Minkowski plane with an attached handle.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0101-8
- Authors
- O. V. Groshev, Steklov Mathematical Institute, RAS, Moscow, Russia
- Harmonic spheres conjecture
Abstract We discuss the harmonic spheres conjecture that the space of harmonic maps of the Riemann sphere into the loop space of a compact Lie group G are related to the moduli space of Yang-Mills G-fields on the four-dimensional Euclidean space.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0092-5
- Authors
- A. G. Sergeev, Steklov Mathematical Institute, RAS, Moscow, Russia
- Coordinate and momentum operators in p-adic quantum mechanics
Abstract We describe the coordinate and momentum operators in p-adic quantum mechanics using the language of projection-valued measures.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0099-y
- Authors
- Asymptotics of small deviations of the Bogoliubov processes with respect to a quadratic norm
Abstract We obtain results on small deviations of Bogoliubov’s Gaussian measure occurring in the theory of the statistical equilibrium of quantum systems. For some random processes related to Bogoliubov processes, we find the exact asymptotic probability of their small deviations with respect to a Hilbert norm.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0113-4
- Authors
- R. S. Pusev, St. Petersburg State University, St. Petersburg, Old Petershoff, Russia
- The relativistic operator of interaction of two quasimolecular electrons as a third-order effect of quantum electrodynamics
Abstract We solve the problem of interaction two quasimolecular electrons located at an arbitrary separation near different atoms (nuclei). We consider third-order effects in quantum electrodynamics, which include the virtual photon exchange between electrons with emission (absorption) of a real photon. We obtain the general expression for matrix elements of the operator of the effective interaction energy of two quasimolecular electrons with the external radiation field, which allows calculating probabilities of inelastic processes with rearrangement at slow collisions of multicharge ions with relativistic atoms. We demonstrate that consistently taking the natural condition of the interaction symmetry with respect to the two electrons into account results in the appearance of additional terms in the operators of spin-orbit, spin-spin, and retarded interactions compared with the previously obtained expressions for these operators. We construct the operator of the dipole-dipole interaction of two neutral atoms located at an arbitrary separation.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0110-7
- Authors
- V. Yu. Lazur, Uzhgorod National University, Uzhgorod, Ukraine
- O. F. Pavlyk, Uzhgorod National University, Uzhgorod, Ukraine
- A. K. Reity, Uzhgorod National University, Uzhgorod, Ukraine
- Three-dimensional N=4 supersymmetry in harmonic N=3 superspace
Abstract We consider the map of three-dimensional N =4 superfields to the N =3 harmonic superspace. The left and right representations of the N =4 superconformal group are constructed on N =3 analytic superfields. These representations are convenient for describing N =4 superconformal couplings of Abelian gauge superfields to hypermultiplets. We investigate the N =4 invariance in the non-Abelian N =3 Yang-Mills theory.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0111-6
- Authors
- B. M. Zupnik, Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia
- A discrete Schrödinger operator on a graph
Abstract We consider the discrete Schrödinger operator on the graph obtained in the strong-coupling approximation from the standard electron Schrödinger operator in the system composed of a quantum wire and quantum dot. We investigate the general spectral properties of this operator and the problem of the existence and behavior of the eigenvalues and resonances depending on the small coupling constant. We study the scattering problem for weak potentials in the stationary approach.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0112-5
- Authors
- Yu. P. Chuburin, Physico-Technical Institute, Ural Branch, RAS, Izhevsk, Russia
- Temperature jump in degenerate quantum gases with the Bogoliubov excitation energy and in the presence of the Bose-Einstein condensate
Abstract We construct a linearized kinetic equation modeling the behavior of degenerate quantum Bose gases with the collision rate dependent on the momentum of elementary excitations. We consider the general case where the energy of elementary excitations depends on the momentum according to the Bogoliubov formula. We analytically solve the half-space boundary value problem of the temperature jump at the boundary of the degenerate Bose gas in the presence of the Bose-Einstein condensate. We obtain an expression for the Kapitza resistance.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0114-3
- Authors
- A. V. Latyshev, Moscow State Regional University, Moscow, Russia
- A. A. Yushkanov, Moscow State Regional University, Moscow, Russia
- The equivalence of different approaches for generating multisoliton solutions of the KPII equation
Abstract The unexpectedly rich structure of the multisoliton solutions of the KPII equation has previously been explored using different approaches ranging from the dressing method to twisting transformations and the τ-function formulation. All these approaches proved useful for displaying different properties of these solutions and the corresponding Jost solutions. The aim of our investigation is to establish explicit formulas relating all these approaches. We discuss some hidden invariance properties of these multisoliton solutions.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0106-3
- Authors
- M. Boiti, Dipartimento di Fisica, Universitŕ del Salento, Lecce, Italy
- F. Pempinelli, Dipartimento di Fisica, Universitŕ del Salento, Lecce, Italy
- A. K. Pogrebkov, Steklov Mathematical Institute, RAS, Moscow, Russia
- B. Prinari, Dipartimento di Fisica, Universitŕ del Salento, Lecce, Italy
- Integral operators with the generalized sine kernel on the real axis
Abstract We study the asymptotic properties of integral operators with the generalized sine kernel acting on the real axis. We obtain the formulas for the Fredholm determinant and the resolvent in the large-x limit and consider some applications of the obtained results to the theory of integrable models.
- Content Type Journal Article
- DOI 10.1007/s11232-010-0108-1
- Authors
- N. A. Slavnov, Steklov Mathematical Institute, RAS, Moscow, Russia
No Issue Number - THE critical exponent of the tree lattice generating function in the eden model
Abstract 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
- A differential—Difference bicomplex
Abstract 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
- New exact solutions with functional parameters of the Nizhnik—Veselov—Novikov equation with constant asymptotic values at infinity
Abstract 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
- Three realizations of the quantum affine algebra Uq(A2(2)
Abstract 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
- Vorticity transport in a viscoelastic fluid in the presence of suspended particles through porous media
Abstract 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
- Large-scale structures as gradient lines: The case of the trkal flow
Abstract 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
- Kernel formula approach to the universal Whitham hierarchy
Abstract 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
- Calculation of the renormalized two-point function by adiabatic regularization
Abstract 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 Matemŕtica Aplicada I, Universitat Politčcnica de Catalunya, Barcelona, Spain
- Clocks and fisher information
Abstract 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
- A generating function for hermite polynomials associated with euclidean Landau levels
Abstract 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
- Erratum
<p class="abstract">Erratum</p><ul>
<li><span class="labelName">Content Type </span><span class="labelValue">Journal Article</span></li><li>Pages 139-139</li><li>DOI 10.1007/s11232-011-0011-4</li>
</ul><ul class="parents">
<ul class="details">
<li><span class="header labelName">Journal </span><span class="labelValue"><a href="http://www.springerlink.com/content/106500/">Theoretical and Mathematical Physics</a></span></li><li><span class="labelName">Online ISSN </span><span class="labelValue">1573-9333</span></li><li><span class="labelName">Print ISSN </span><span class="labelValue">0040-5779</span></li>
</ul><ul class="details">
<li><span class="header labelName">Journal Volume </span><span class="labelValue">Volume 166</span></li>
</ul><ul class="details">
<li><span class="header labelName">Journal Issue </span><span class="labelValue"><a href="http://www.springerlink.com/content/t2803305r526/">Volume 166, Number 1</a></span></li>
</ul>
</ul>
- Self-similar solutions of the Laplacian growth problem in the half-plane
Abstract 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
No Issue Number - Decoupling of the longitudinal polarization of the vector field in the massless Higgs-Kibble model
<h3 class="a-plus-plus">Abstract</h3> <p class="a-plus-plus">We show that the three-dimensionally longitudinal component of the vector field decouples in the massless limit of non-Abelian Higgs model.</p>
- Vasilii Sergeevich Vladimirov 9 January 1923–3 November 2012
- Double extensions of Lie algebras of Kac-Moody type and applications to some hamiltonian systems
<h3 class="a-plus-plus">Abstract</h3> <p class="a-plus-plus">We describe some Lie algebras of the Kac-Moody type, construct their double extensions, central and by derivations; we also construct the corresponding Lie groups in some cases. We study the case of the Lie algebra of unimodular vector fields in more detail and use the linear Poisson structure on their regular duals to construct generalizations of some infinite-dimensional Hamiltonian systems, such as magnetohydrodynamics.</p>
- Spectral properties of a thin layer with a doubly periodic family of thinning regions
<h3 class="a-plus-plus">Abstract</h3> <p class="a-plus-plus">We show that the spectrum of the Dirichlet problem for the Laplace operator in a layer with a doubly periodic structure has gaps and determine several characteristics of their location. The result is obtained by asymptotic analysis of a model spectral problem on the periodicity cell.</p>
- Blowup of solutions of nonlinear equations and systems of nonlinear equations in wave theory
<h3 class="a-plus-plus">Abstract</h3> <p class="a-plus-plus">We consider the phenomenon of solution blowup for the system of equations describing surface water waves and also for the acoustic wave equation in viscous medium using the test-function method developed by Galactionov, Pokhozhaev, and Mitidieri.</p>
- Analytic continuation of the pion form factor from the spacelike to the timelike domain
<h3 class="a-plus-plus">Abstract</h3> <p class="a-plus-plus">We solve the problem of analytically continuing the electromagnetic pion form factor into the complex domain of transferred momenta. We treat the pion as a composite quark-antiquark system. We demonstrate that the analytic properties of the form factor calculated in the framework of relativistic quantum mechanics with direct interaction agree with the analytic properties following from the general principles of quantum field theory.</p>
- Exact solutions and particle creation for nonconformal scalar fields in homogeneous isotropic cosmological models
<h3 class="a-plus-plus">Abstract</h3> <p class="a-plus-plus">We solve the problem of describing scaling factors of a homogeneous isotropic space-time such that the exact solution for the scalar field with a nonconformal coupling to curvature can be obtained from solutions for the conformally coupled field by redefining the mass and momentum. We give explicit expressions in the form of Abelian integrals for the dependence of time on the scaling factor in these cases. We obtain an exact solution for the scalar field coupled to the Gauss-Bonnet-type curvature and show that the corresponding nonconformal contributions can dominate in particle creation by the gravitational field.</p>
- Gauge theory of the liquid-glass transition in static and dynamical approaches
<h3 class="a-plus-plus">Abstract</h3> <p class="a-plus-plus">We propose static and dynamical formulations of the liquid-glass transition theory based on the glass gauge theory and the fluctuation theory of phase transitions. In accordance with the proposed theory, the liquid-glass transition is an unattainable second-order phase transition blocked by a premature critical slowing of the gauge field relaxation caused by the system frustration. We show that the proposed theory qualitatively agrees well with experimental data.</p>
- Coexistence of superconductivity and antiferromagnetism in heavy-fermion intermetallides
Abstract Using the two-time retarded Green’s function, we study the conditions for realizing the phase of the superconductivity and antiferromagnetism coexistence in the framework of the effective Hamiltonian for the periodic Anderson model. Such a phase was experimentally observed in rare-earth intermetallides with heavy fermions under an external pressure. In the chosen model, the Cooper instability is induced in the presence of long-range antiferromagnetic ordering as a result of the combined effect of a superexchange interaction in the subsystem of localized electrons and the hybridization between two groups of electrons. Applying an external pressure induces an increase in the energy of the localized level accompanied by an abrupt destruction of the long-range antiferromagnetic ordering in a certain region of the phase diagram. The superconductivity order parameter has a maximum value at the destruction point. We show that the decrease in the antiferromagnetic-sublattice magnetization with increasing pressure leads to a significant increase in the masses of Fermi quasiparticles, and the sign of the current carriers reverses at the critical point. The obtained results qualitatively agree well with the experimental data for the heavy-fermion intermetallide CeRhIn 5 .
- Perturbation theory series in quantum mechanics: Phase transition and exact asymptotic forms for the expansion coefficients
Abstract We consider the model of a harmonic oscillator with a power-law potential and derive new asymptotic formulas for the coefficients of the perturbation theory series in powers of the coupling constant in the case of a power-law perturbing potential x p , p > 0 . We prove the existence of a critical value p 0 and compute it. It is a threshold in the sense that the asymptotic forms of the studied coefficients for 0 < p < p 0 and for p > p 0 differ qualitatively. We note that the considered physical system undergoes a phase transition at p = p 0 . The analysis uses the Laplace method for functional integrals with Gaussian measures.
- Statistical field theory of a nonadditive system
Abstract Based on quantum field methods, we develop a statistical theory of complex systems with nonadditive potentials. Using the Martin-Siggia-Rose method, we find the effective system Lagrangian, from which we obtain evolution equations for the most probable values of the order parameter and its fluctuation amplitudes. We show that these equations are unchanged under deformations of the statistical distribution while the probabilities of realizing different phase trajectories depend essentially on the nonadditivity parameter. We find the generating functional of a nonadditive system and establish its relation to correlation functions; we introduce a pair of additive generating functionals whose expansion terms determine the set of multipoint Green’s functions and their self-energy parts. We find equations for the generating functional of a system having an internal symmetry and constraints. In the harmonic approximation framework, we determine the partition function and moments of the order parameter depending on the nonadditivity parameter. We develop a perturbation theory that allows calculating corrections of an arbitrary order to the indicated quantities.
- Effect of a measuring instrument in the “Bose condensate” of a classical gas in a phase transition and in experiments with negative pressure
<h3 class="a-plus-plus">Abstract</h3> <p class="a-plus-plus">We systematically present a new approach to classical thermodynamics using asymptotic distributions from number theory that generalize the Bose-Einstein distribution. We justify the transition to the liquid state, the thermodynamics of fluids, and also the behavior of liquids in the region of negative pressures We present a comparison with experimental data.</p>
- Periodic traveling-wave-type solutions in circular chains of unidirectionally coupled equations
<h3 class="a-plus-plus">Abstract</h3> <p class="a-plus-plus">We consider special systems of ordinary differential equations, so-called circular unidirectional chains. For this class of systems, we develop a new method for studying the existence and stability problems for periodic solutions. A feature of the proposed approach is that some auxiliary systems with delay are used in both seeking cycles and analyzing their stability properties. We illustrate the relevance of this approach with a concrete example of a circular Hopfield neural network</p>
- Pauli theorem in the description of <em class="a-plus-plus">n</em>-dimensional spinors in the Clifford algebra formalism
<h3 class="a-plus-plus">Abstract</h3> <p class="a-plus-plus">We discuss a generalized Pauli theorem and its possible applications for describing n-dimensional (Dirac, Weyl, Majorana, and Majorana-Weyl) spinors in the Clifford algebra formalism. We give the explicit form of elements that realize generalizations of Dirac, charge, and Majorana conjugations in the case of arbitrary space dimensions and signatures, using the notion of the Clifford algebra additional signature to describe conjugations. We show that the additional signature can take only certain values despite its dependence on the matrix representation</p>
- Transverse electrical conductivity of a quantum collisional plasma in the Mermin approach
<h3 class="a-plus-plus">Abstract</h3> <p class="a-plus-plus">We derive formulas for the transverse electrical conductivity and the permittivity in a quantum collisional plasma using the kinetic equation for the density matrix in the relaxation approximation in the momentum space. We show that the derived formula becomes the classical formula when the Planck constant tends to zero and that when the electron collision rate tends to zero (i.e., the plasma becomes collisionless), the derived formulas become the previously obtained Lindhard formulas. We also show that when the wave number tends to zero, the quantum conductivity becomes classical. We compare the obtained conductivity with the conductivity obtained by Lindhard and with the classical conductivity</p>
- <em class="a-plus-plus">p</em>-adic Gibbs measures and Markov random fields on countable graphs
<h3 class="a-plus-plus">Abstract</h3> <p class="a-plus-plus">The notions of the Gibbs measure and of the Markov random field are known to coincide in the real case. But in the p-adic case, the class of p-adic Markov random fields is broader than that of p-adic Gibbs measures. We construct p-adic Markov random fields (on finite graphs) that are not p-adic Gibbs measures. We define a p-adic Markov random field on countable graphs and show that the set of such fields is a nonempty closed subspace in the set of all p-adic probability measures</p>
- A note on the extended dispersionless Toda hierarchy
Abstract We derive dispersionless Hirota equations for the extended dispersionless Toda hierarchy. We show that the dispersionless Hirota equations are just a direct consequence of the genus-zero topological recurrence relation for the topological ℂ P 1 model. Using the dispersionless Hirota equations, we compute the twopoint functions and express the result in terms of Catalan numbers
- Fermions and Kaluza-Klein vacuum decay: A toy model
Abstract We address the question of whether fermions with a twisted periodicity condition suppress the semiclassical decay of the M 4 ×S 1 Kaluza-Klein vacuum. We consider a toy (1+1) -dimensional model with twisted fermions in a cigar-shaped Euclidean background geometry and calculate the fermion determinant. We find that the determinant is finite, contrary to expectations. We regard this as an indication that twisted fermions do not stabilize the Kaluza-Klein vacuum.
- The Yang-Mills theory as a massless limit of a massive gauge-invariant model
<h3 class="a-plus-plus">Abstract</h3> <p class="a-plus-plus">We construct a gauge-invariant infrared regularization of the Yang-Mills theory applicable beyond the perturbation theory.</p>
- Erratum to: “Quantization of stationary Gaussian random processes and their generalizations”
- The Yangian of the strange Lie superalgebra and its quantum double
Abstract We construct the Yangian of the strange Lie superalgebra as a particular case of the general construction of a twisted Yangian. We describe a Poincaré-Birkhoff-Witt basis of the Yangian of the type-Q n Lie superalgebra and construct the quantum double of the Yangian of the type-Q 2 strange Lie superalgebra.
- Correlation functions and spectral curves in models of minimal gravity
<h3 class="a-plus-plus">Abstract</h3> <p class="a-plus-plus">We discuss correlators for models of minimal gravity and propose an algorithm for calculating invariant relations from formulas for residues that can be compared with the expansion coefficients for the partition function in the Liouville theory. For <em class="a-plus-plus">(2, 2</em>K-<em class="a-plus-plus">1)</em> models, we explicitly obtain a factor corresponding to conversion from the semiclassical hierarchy basis to the Liouville theory basis and also test a hypothesis about the pattern of the spectral curve using a direct calculation.</p>
- Strong-coupling theory for multiband superconductors
Abstract We consider a microscopic theory of the strong coupling in multiband superconductors with an arbitrary electron-boson interaction. Based on the method of the equations of motion for two-time Green’s functions, we derive the Dyson equation with the self-energy operator in the form of the multiparticle Green’s function taking the interaction of electrons with phonons and spin fluctuations into account. We obtain a self-consistent system of equations for the normal and anomalous components of the Green’s function and the self-energy operator calculated in the approximation of noncrossing diagrams. We discuss the approximate solution of the system of equations taking only components of the self-energy operator that are diagonal with respect to the band index into account for studying superconductivity in iron-based compounds.
- Quantum rule for detection probability from Brownian motion in the space of classical fields
Abstract We obtain Born’s rule from the classical theory of random waves in combination with the use of thresholdtype detectors. We consider a model of classical random waves interacting with classical detectors and reproducing Born’s rule. We do not discuss complicated interpretational problems of quantum foundations. The reader can select between the “weak interpretation,” the classical mathematical simulation of the quantum measurement process, and the “strong interpretation,” the classical wave model of the real quantum (in fact, subquantum) phenomena.
- Four-dimensional superconformal index reloaded
Abstract We consider the four-dimensional N≥ 1 superconformal index and its generalization to the lens space. We discuss reductions of the latter to the three-dimensional N≥ 2 sphere partition function, the threedimensional N≥ 2 superconformal index, and the two-dimensional N≥ (2, 2) sphere partition function. We apply these reductions to a class of four-dimensional N =1 superconformal field theories dual to toric Calabi-Yau manifolds, and we find surprising connections with integrable spin chains and hyperbolic geometry. We comment on the problem of classifying infrared fixed points of four-dimensional and threedimensional supersymmetric gauge theories.
- An inductive approach to representations of complex reflection groups <em class="a-plus-plus">G</em>(<em class="a-plus-plus">m</em>, 1, <em class="a-plus-plus">n</em>)
Abstract We propose an inductive approach to the representation theory of the chain of complex reflection groups G(m, 1 , n). We obtain the Jucys-Murphy elements of G(m, 1 , n) from the Jucys-Murphy elements of the cyclotomic Hecke algebra and study their common spectrum using representations of a degenerate cyclotomic affine Hecke algebra. We construct representations of G(m, 1 , n) using a new associative algebra whose underlying vector space is the tensor product of the group ring ℂG(m, 1 , n) with a free associative algebra generated by the standard m-tableaux.
- The <em class="a-plus-plus">N</em>=4 super Landau models
<h3 class="a-plus-plus">Abstract</h3> <p class="a-plus-plus">We briefly describe a new superextended Landau model with a worldline N<em class="a-plus-plus">=4</em> supersymmetry and an internal target space ISU <em class="a-plus-plus">(2 2)</em> supersymmetry. It shares many features with the previously studied N<em class="a-plus-plus">=2</em> supersymmetric Landau model, which is also briefly described.</p>
- Models of <em class="a-plus-plus">p</em>-adic mechanics
Abstract We segregate the class of ultrametric (p-adic) systems within the standard models of classical and quantum mechanics. We show that ultrametric models can be described in the language of standard models but also have several distinguishing properties. In particular, we show that a stronger Poincaré recurrence theorem holds for classical ultrametric dynamical systems. As an example of a quantum p-adic system, we consider the algebra of commutation relations of the one-dimensional quantum mechanics. We show that this algebra, as in the real case, is isomorphic to the algebra of compact operators.
- Ultrametricity of the state space in glasses
<h3 class="a-plus-plus">Abstract</h3> <p class="a-plus-plus">We review the results related to the ultrametricity notion in glasses. We present the proof of the ultrametricity of the replica space for an arbitrary spin glass model with reflection symmetry. We solve the problem of describing the dynamics of a system with an ultrametric state space using the Keldysh functional method for nonequilibrium dynamics in which the quasinonergodicity of the system is taken into account by introducing a hierarchical spectrum of relaxation times.</p>
- Participation of V. S. Vladimirov in work on the USSR atomic project: A significant milestone in the development of the foundations of mathematical modeling of the processes of neutron physics
Abstract This paper is dedicated to the 90 th anniversary of the birth of a leading Soviet and Russian scientist and a member of the USSR Academy of Sciences: Academician Vasilii Sergeevich Vladimirov. Vladimirov, one of the strongest contemporary mathematicians, worked from 1951 through 1955 at KB-11 (today, the Russian Federal Nuclear Center — All-Russian Scientific Research Institute for Experimental Physics), the “secret facility” where development of atomic weaponry was conducted. We present the main results of Vladimirov’s scientific activity connected with his work on the USSR atomic project.
- The formal de Rham complex
<h3 class="a-plus-plus">Abstract</h3> <p class="a-plus-plus">We propose a formal construction generalizing the classic de Rham complex to a wide class of models in mathematical physics and analysis. The presentation is divided into a sequence of definitions and elementary, easily verified statements; proofs are therefore given only in the key case. Linear operations are everywhere performed over a fixed number field <span class="a-plus-plus inline-equation id-i-eq1"> <span class="a-plus-plus equation-source format-t-e-x">$\mathbb{F} = \mathbb{R},\mathbb{C}$</span> </span>. All linear spaces, algebras, and modules, although not stipulated explicitly, are by definition or by construction endowed with natural locally convex topologies, and their morphisms are continuous.</p>
- Functional Fourier transformation and renormalization group transformation in bosonic field theory models
<h3 class="a-plus-plus">Abstract</h3> <p class="a-plus-plus">We introduce the notion of a functional Fourier transformation in bosonic p-adic and Euclidean models of statistical physics. We prove a commutation relation between the Fourier transformation and the Wilson renormalization group transformation and discuss the similarity of renormalization group formalisms in p-adic and Euclidean models.</p>
- Extreme bosonic linear channels
<h3 class="a-plus-plus">Abstract</h3> <p class="a-plus-plus">The set of all channels with a fixed input and output is convex. We first give a convenient formulation of the necessary and sufficient condition for a channel to be an extreme point of this set in terms of the complementary channel, a notion of great importance in quantum information theory. This formulation is based on the general approach to extremality of completely positive maps in an operator algebra in the spirit of Arveson. We then use this formulation to prove our main result: under certain nondegeneracy conditions, environmental purity is necessary and sufficient for the extremality of a bosonic linear (quasifree) channel. It hence follows that a Gaussian channel between finite-mode bosonic systems is extreme if and only if it has minimum noise.</p>
- Multidimensional nonlinear wave equations with multivalued solutions
Abstract We present the theory of breaking waves in nonlinear systems whose dynamics and spatial structure are described by multidimensional nonlinear hyperbolic wave equations. We obtain a general relation between systems of first-order quasilinear equations and nonlinear hyperbolic equations of higher orders, which, in particular, describe electromagnetic waves in a medium with nonlinear polarization of an arbitrary form. We use this approach to construct exact multivalued solutions of such equations and to study their spatial structure and dynamics. The results are generalized to a wide class of multidimensional equations such as d’Alembert equations, nonlinear Klein-Gordon equations, and nonlinear telegraph equations.
- Holographic thermalization
<h3 class="a-plus-plus">Abstract</h3> <p class="a-plus-plus">We consider the transition of a quantum field system toward the state of thermal equilibrium based on the holographic description using the duality between the quantum field system in the d-dimensional Minkowski space and the gravity theory in the (d+<em class="a-plus-plus">1</em>)-dimensional anti-de Sitter space. In this construction, the thermalization in the d-dimensional space is described in the holographic language as the formation of a black hole in the (d+<em class="a-plus-plus">1</em>)-dimensional space. We use a holographic model of thermalization of the quark-gluon plasma describing the black hole formation by the Vaidya metric. We show that evaporation of the black hole, also modeled by the Vaidya metric, leads to an interesting effect in the d-dimensional space: thermalization occurs only at small distances and is impossible in the infrared region. In the considered model, the thermal behavior at small distances is possible only during a certain time, after which the dethermalization process begins.</p>
- Nonexistence of solutions of the <em class="a-plus-plus">p</em>-adic strings
Abstract We discuss mathematical aspects of the nonexistence of continuous (nontrivial) solutions of boundary value problems for equations of p-adic closed and open strings in the one-dimensional case. We find that the number of sign changes of the solution ψ(t) is not equal to the order of zeros of the function ψ n (t) and that nonnegative (nonpositive) solutions do not exist. In the case of even n, if a solution ψ exists, then the orders of zeros of the function ψn and the order of its tangency to positive maximums (minimums) are not divisible by four and therefore have the form 2(2 r + 1), r ≥ 0.
- Impossibility of gravitational collapse
<h3 class="a-plus-plus">Abstract</h3> <p class="a-plus-plus">In the framework of the relativistic theory of gravity, we show that a universal mechanism for stopping the process of gravitational compression of a body with large mass with its subsequent radial expansion appears because of the gravitational field tensor. This excludes the gravitational collapse and the possibility of black hole formation.</p>
- <em class="a-plus-plus">L</em>
<sub class="a-plus-plus">
<em class="a-plus-plus">p</em>
</sub>-estimates for solutions of second-order elliptic equation Dirichlet problem
<h3 class="a-plus-plus">Abstract</h3> <p class="a-plus-plus">For solutions of the Dirichlet problem for a second-order elliptic equation, we establish an analogue of the Carleson theorem on L<sub class="a-plus-plus">p</sub>-estimates. Under the same conditions on the coefficients for which the unique solvability of the considered problem is known, we prove this criterion for the validity of estimate of the solution norm in the space L<sub class="a-plus-plus">p</sub> with a measure. We require their Dini continuity on the boundary, but we assume only their measurability and boundedness in the domain under consideration.</p>
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