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PHYSICS (580 journals)

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Journal Cover Russian Journal of Mathematical Physics
  [SJR: 0.949]   [H-I: 23]   [0 followers]  Follow
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 1531-8621 - ISSN (Online) 1061-9208
   Published by Springer-Verlag Homepage  [2335 journals]
  • Electromagnetic field generated by a modulated moving point source in a
           planarly layered waveguide
    • Authors: V. Barrera-Figueroa; V. S. Rabinovich
      Pages: 139 - 163
      Abstract: Abstract In the present work, we consider a modulated point source in an arbitrary motion in an isotropic planarly layered waveguide. The radiation field generated by this source is represented in the form of double oscillatory integrals in terms of the time and the frequency, depending on the large parameter λ. By means of the stationary phase method, we analyze, in the waveguide, the Doppler effect, the retarded time, and the Vavilov–Cherenkov radiation. Numerically, the problem of the moving source is approached by the method of spectral parameter power series.
      PubDate: 2016-04-01
      DOI: 10.1134/s1061920816020011
      Issue No: Vol. 23, No. 2 (2016)
  • Identities for Apostol-type Frobenius–Euler polynomials resulting from
           the study of a nonlinear operator
    • Authors: A. Bayad; T. Kim
      Pages: 164 - 171
      Abstract: Abstract We introduce a special nonlinear differential operator and, using its properties, reduce higher-order Frobenius–Euler Apostol-type polynomials to a finite series of first-order Apostol-type Frobenius–Euler polynomials and Stirling numbers. Interesting identities are established.
      PubDate: 2016-04-01
      DOI: 10.1134/s1061920816020023
      Issue No: Vol. 23, No. 2 (2016)
  • Belavkin filtering with squeezed light sources
    • Authors: A. Dąbrowska; J. Gough
      Pages: 172 - 184
      Abstract: Abstract We derive the filtering equation for Markovian systems undergoing homodyne measurement in the situation where the output processes being monitored are squeezed. The filtering theory applies to case where the system is driven by Fock noise (that is, quantum input processes in a coherent state) and where the output is mixed with a squeezed signal. It also applies to the case of a system driven by squeezed noise, but here there is a physical restriction to emission/absorption coupling only. For the special case of a cavity mode where the dynamics is linear, we are able to derive explicitly the filtered estimate π t (a) for the mode annihilator a based on the homodyne quadrature observations up to time t.'
      PubDate: 2016-04-01
      DOI: 10.1134/s1061920816020035
      Issue No: Vol. 23, No. 2 (2016)
  • Nonsmooth nonoscillating WKB–Maslov-type asymptotics for linear
           parabolic PDE
    • Authors: V. G. Danilov
      Pages: 185 - 199
      Abstract: Abstract We discuss the meaning of WKB–Maslov-type asymptotic solutions with nonsmooth phase function to parabolic PDE of Kolmogorov–Feller-type with a small parameter.
      PubDate: 2016-04-01
      DOI: 10.1134/s1061920816020047
      Issue No: Vol. 23, No. 2 (2016)
  • Asymptotic analysis of evolution of a neck in extended thin rigid plastic
    • Authors: D. V. Georgievskii; B. E. Pobedrya
      Pages: 200 - 206
      Abstract: Abstract We carry out an asymptotic analysis with natural small geometric parameter of the stress-strain state realized under the stretch of a rigid-plastic rod of round section and of a flat sheet infinite in one direction, taking into account the presence of areas of thinning (a neck) and thickening with respect to the medium size. In examples, we stress qualitative effects of possible inertia-free development of a neck.
      PubDate: 2016-04-01
      DOI: 10.1134/s1061920816020059
      Issue No: Vol. 23, No. 2 (2016)
  • Contribution to the symplectic structure in the quantization rule due to
           noncommutativity of adiabatic parameters
    • Authors: M. V. Karasev
      Pages: 207 - 218
      Abstract: Abstract A geometric construction of the `ala Planck action integral (quantization rule) determining adiabatic terms for fast-slow systems is considered. We demonstrate that in the first (after zero) adiabatic approximation order, this geometric rule is represented by a deformed fast symplectic 2-form. The deformation is controlled by the noncommutativity of the slow adiabatic parameters. In the case of one fast degree of freedom, the deformed symplectic form incorporates the contraction of the slow Poisson tensor with the adiabatic curvature. The same deformed fast symplectic structure is used to represent the improved adiabatic invariant in a geometric form.
      PubDate: 2016-04-01
      DOI: 10.1134/s1061920816020060
      Issue No: Vol. 23, No. 2 (2016)
  • A finite-dimensional version of Fredholm representations
    • Authors: V. Manuilov
      Pages: 219 - 224
      Abstract: Abstract We consider pairs of mappings from a discrete group Γ to the unitary group. The deficiencies of these mappings from being homomorphisms may be great, but if they are close to each other, then we call such pairs balanced. We show that balanced pairs determine elements in the K 0 group of the classifying space of the group. We also show that a Fredholm representation of Γ determines balanced pairs.
      PubDate: 2016-04-01
      DOI: 10.1134/s1061920816020072
      Issue No: Vol. 23, No. 2 (2016)
  • Propagation and interaction of solitons for nonintegrable equations
    • Authors: G. Omel’yanov
      Pages: 225 - 243
      Abstract: Abstract We describe an approach to the construction of multi-soliton asymptotic solutions for nonintegrable equations. The general idea is realized in the case of N waves, N = 1, 2, 3, and for the KdV-type equation with nonlinearity u 4. A brief review of asymptotic methods as well as results of numerical simulation are included.
      PubDate: 2016-04-01
      DOI: 10.1134/s1061920816020084
      Issue No: Vol. 23, No. 2 (2016)
  • On the distribution of energy of localized solutions of the Schrödinger
           equation that propagate along symmetric quantum graphs
    • Authors: A. I. Shafarevich
      Pages: 244 - 250
      Abstract: Abstract From the point of view of applications to quantum mechanics, it is natural to pose a question concerning the distribution of energy of localized solutions of a nonstationary Schrödinger equation over the graph (in other words, the probability to find a quantum particle in a given area). This problem is apparently very complicated for general graphs, because the energy distribution is much more sensitive to the form of boundary conditions and to the initial state than the asymptotic behavior of the number of localized functions. Below, we present initial results concerning the distribution of energy in the case of symmetric quantum graphs (this means that the Schrödinger operators on different edges have the same structure). For general local self-adjoint boundary conditions, we describe the process of onestep scattering of the localized solutions and obtain a simple general result of the distribution of energy. Some special cases and specific examples are discussed.
      PubDate: 2016-04-01
      DOI: 10.1134/s1061920816020096
      Issue No: Vol. 23, No. 2 (2016)
  • On rational functions of first-class complexity
    • Authors: M. Stepanova
      Pages: 251 - 256
      Abstract: Abstract It is proved that, for every rational function of two variables P(x, y) of analytic complexity one, there is either a representation of the form f(a(x) + b(y)) or a representation of the form f(a(x)b(y)), where f(x), a(x), b(x) are nonconstant rational functions of a single variable. Here, if P(x, y) is a polynomial, then f(x), a(x), and b(x) are nonconstant polynomials of a single variable.
      PubDate: 2016-04-01
      DOI: 10.1134/s1061920816020102
      Issue No: Vol. 23, No. 2 (2016)
  • Bloch principle for elliptic differential operators with periodic
    • Authors: V. V. Zhikov; S. E. Pastukhova
      Pages: 257 - 277
      Abstract: Abstract Differential operators corresponding to elliptic equations of divergent type with 1-periodic coefficients are considered. The equations are put in Sobolev spaces with an arbitrary 1-periodic Borel measure on the entire space R d . In the study of the spectrum of operators of this kind, the Bloch principle is of fundamental importance. According to this principle, all points of the desired spectrum are obtained when studying the equation on the unit cube with quasiperiodic boundary conditions. The proof of the Bloch principle for problems in the above formulation is proved, in several versions of the principle. Examples of the application of the principle to finding the spectrum of specific operators, for example, for the Laplacian in a weighted space or on a singular structure of lattice type.
      PubDate: 2016-04-01
      DOI: 10.1134/s1061920816020114
      Issue No: Vol. 23, No. 2 (2016)
  • Thermodynamics, idempotent analysis, and tropical geometry as a return to
    • Authors: V. P. Maslov
      Pages: 278 - 280
      PubDate: 2016-04-01
      DOI: 10.1134/s1061920816020126
      Issue No: Vol. 23, No. 2 (2016)
  • Absence of two Paley–Wiener properties for semisimple Lie groups of
           real rank one
    • Authors: A. I. Shtern
      Pages: 281 - 282
      Abstract: Abstract The weak Paley–Wiener property and the topological Paley–Wiener property for connected semisimple Lie groups of real rank one with finite center are discussed.
      PubDate: 2016-04-01
      DOI: 10.1134/s1061920816020138
      Issue No: Vol. 23, No. 2 (2016)
  • Creation of spectral bands for a periodic domain with small windows
    • Authors: D. I. Borisov
      Pages: 19 - 34
      Abstract: Abstract We consider a Schrödinger operator in a periodic system of strip-like domains coupled by small windows. As the windows close, the domain decouples into an infinite series of identical domains. The operator similar to the original one, and defined on one copy of these identical domains, has an essential spectrum. We show that once there is a virtual level at the threshold of this essential spectrum, the windows turn this virtual level into the spectral bands for the original operator. We study the structure and the asymptotic behavior of these bands.
      PubDate: 2016-01-01
      DOI: 10.1134/s1061920816010027
      Issue No: Vol. 23, No. 1 (2016)
  • Stability of the autoresonance in a dissipative system
    • Authors: L. A. Kalyakin
      Pages: 77 - 87
      Abstract: Abstract The autoresonance problem is to distinguish solutions with unboundedly increasing amplitude for model equations of principal resonance. At the level of formal constructions, the problem is solved by constructing an asymptotic solution in the form of a power series with constant coefficients. As is known, such a series represents the asymptotic behavior of the exact solution. However, for this solution to be related to the description of a physical phenomenon, the stability of the solution is required both with respect to perturbations of the initial data and with respect to the relatively constantly acting perturbations. These two properties are established using the Lyapunov function.
      PubDate: 2016-01-01
      DOI: 10.1134/s1061920816010052
      Issue No: Vol. 23, No. 1 (2016)
  • A note on nonlinear Changhee differential equations
    • Authors: T. Kim; D. S. Kim
      Pages: 88 - 92
      Abstract: Abstract In this paper, we study nonlinear Changhee differential equations and derive some new and explicit identities of Changhee and Euler numbers from those nonlinear differential equations.
      PubDate: 2016-01-01
      DOI: 10.1134/s1061920816010064
      Issue No: Vol. 23, No. 1 (2016)
  • Asymptotic stability of stationary states in the wave equation coupled to
           a nonrelativistic particle
    • Authors: E. A. Kopylova; A. I. Komech
      Pages: 93 - 100
      Abstract: Abstract We consider the Hamiltonian system consisting of a scalar wave field and a single particle coupled in a translation invariant manner. The point particle is subjected to an external potential. The stationary solutions of the system are a Coulomb type wave field centered at those particle positions for which the external force vanishes. It is assumed that the charge density satisfies the Wiener condition, which is a version of the “Fermi Golden Rule.” We prove that in the large time approximation, any finite energy solution, with the initial state close to the some stable stationary solution, is a sum of this stationary solution and a dispersive wave which is a solution of the free wave equation.
      PubDate: 2016-01-01
      DOI: 10.1134/s1061920816010076
      Issue No: Vol. 23, No. 1 (2016)
  • Freudenthal–Weil theorem for pro-Lie groups
    • Authors: A. I. Shtern
      Pages: 115 - 117
      Abstract: Abstract An analog of the Freudenthal–Weil theorem holds for the discontinuous homomorphisms of a connected pro-Lie group into a compact group if and only if the radical of the pro-Lie group is amenable.
      PubDate: 2016-01-01
      DOI: 10.1134/s106192081601009x
      Issue No: Vol. 23, No. 1 (2016)
  • A simple probabilistic model of ideal gases
    • Authors: A. B. Sossinsky
      Pages: 118 - 123
      Abstract: Abstract We describe a discrete 3D model of ideal gas based on the idea that, on the microscopic level, the particles move randomly (as in ASEP models), instead of obeying Newton’s laws as prescribed by Boltzmann.
      PubDate: 2016-01-01
      DOI: 10.1134/s1061920816010106
      Issue No: Vol. 23, No. 1 (2016)
  • On solutions of the mixed Dirichlet–Navier problem for the polyharmonic
           equation in exterior domains
    • Authors: O. A. Matevosyan
      Pages: 135 - 138
      Abstract: Abstract We study the unique solvability of the mixed Dirichlet–Navier problem for the polyharmonic equation in exterior domains under the assumption that a generalized solution of this problem has a bounded Dirichlet integral with weight x a . Depending on the value of the parameter a, we prove a uniqueness theorem or present exact formulas for the dimension of the solution space of the mixed Dirichlet–Navier problem in the exterior of a compact set.
      PubDate: 2016-01-01
      DOI: 10.1134/s106192081601012x
      Issue No: Vol. 23, No. 1 (2016)
School of Mathematical and Computer Sciences
Heriot-Watt University
Edinburgh, EH14 4AS, UK
Tel: +00 44 (0)131 4513762
Fax: +00 44 (0)131 4513327
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