Physics

Matrix Description of Multicoupled Oscillatory Systems Based on Tridiagonal Matrixes

Authors: Hohlov A. V.

The matrix description of multicoupled oscillatory systems is presented on the base of tridiagonal matrixes with dominating diagonale elements. The eigenfrequencies of a band-pass filter one calculated for the input node of a differential-gated radiopolarimeter.

Integral Equations for Photonic Crystal Fibers

Authors: Davidovich M. V., Stephuk J. V.

The integral and integrodifferential equations for photonic crystal waveguides (fibers) have been obtained both for finite and infinite dimensions of quasiperiodic dielectric coverings. Previously the equations for two-dimensional periodic photonic crystals with magnetodielectric and metallic periodic inclusions have been considered. The corresponding numerical results are presented.

Dynamical Chaos In Quantum Systems

Authors: Lazerson A. G., Boykov A. A.

Complex dynamics of a quantum periodically driven square well is considered. It is shown that analysis of its ensemble average energy time series provides an identification of its dynamics to be either regular or chaotic. It has been found that enhancement of the driving force causes the energy spectrum to look like a spectrum of some random process, which may be identified as the signature of chaos in a quantum system. 

An Explicit Solutions of the Maxwell-Einstein Equations

Authors: Zayko Y. N.

This article concerns the effect of gravitation field of the spherical electro-magnetic wave (EMW) on its propagation in vacuum. For this it was received a solution of the coupled Maxwell-Einstein equations. The expression for metric is supposed to be just the same as in wellknown Schwarzschild problem for gravitation field at the vicinity of point mass with additional dependence on polar angle 9. The equations for radial and angular parts of EMW fields of ТЕ- and TM-types are received. Their various solutions are Investigated.

Exactly Solvable Model of Instantaneously Switched-On Field In the Kinetics of Vacuum Particle Creation

Authors: Blaschke D. B., Dmitriev V. V., Smolyansky P. I., Smolyansky S. A., Chertilin A. V.
Exact solutions of the nonperturbative kinetic equations for the description of fermion and boson pair creation in the vacuum are obtained for the case of a linearly polarized instantaneously switched-on electric field. The corresponding momentum distributions are nonintegrable, The renormalized distribution functions are also found. The obtained results can be used as estimates for upper limits of different vacuum pair creation effects in the more realistic case of short electric field pulses.

Non-Markovian Quantum Relaxation and Theory of Spectral Lines Width

Authors: Gorokhov A. V., Semin V. V.

The quantum equation of relaxation with non-Markovian terms in the approximation of short-time memory is derived. The correlation functions for a single two-level atom and system of two dipole-dipole interaction of atoms in the external regular fields and the contour of the radiation lines are calculated. Accounting Non-Markovian effects leads to a more vivid expression of dipole-dipole interaction.

Coherent States and Mode Dynamics in Kerr Nonlinear Medium

Authors: Barsov A. S., Gorokhov A. V.

Dynamics of three photonic modes in the theory of parametric amplifier in the medium, taking into account the Kerr nonlinearity, can be studied using the dynamical group WSp (6, R). For a degenerate parametric amplification with classical pump the description is reduced to the dynamics of coherent states of SU(1,1) group. The time dependence of average numbers of photons and squeezing are calculated. It is shown that the «switching-on» of the Kerr nonlinearity leads to suppression of the parametric amplification.

Superextensions of Landau Models

Authors: Ivanov E. A.

The paper is a review of recent works on superextensions of the model of non-relativistic quantum charged particle moving in a homogeneous magnetic field on the plane R2 (Landau model), and a model of the particle in the field of Dirac monopole on the sphere S2: SU(2)11/(1) (Haldane model). We consider the models on the supersphere Sl/(2|1)/l/(1|1), superflag SU(2|1)/[l/(1)xl/(1)] and their planar limits, based upon a geometric interpretation of these models and their bosonic proptotypes as d=1 analogs of nonlinear sigma models of the Wess-Zumino-Novikov-Witten type.

SN and СМВ Data and Higgs Particle Mass in a Scale-Invariant Gravitation Theory

Authors: Pervushin V. N.

In a Scale-Invariant Gravitation Theory, it was shown that both CMB data and SN ones testify to an ordinary cosmological quantum vacuum creation of the Universe together with the W-, Z-vector bosons and the Higgs particles. The initial momentum of the evolution, given by the kinetic energy of an additional scalar field, the Standard Model mass spectrum determine the CMB temperature and its fluctuation spectrum, if the Higgs particle mass is in the region of about 118 GeV.

On Solving the Low-Dimensional Boundary Value Problems of Quantum Mechanics by Kantorovich Method - Reduction to Ordinary Differential Equations

Authors: Derbov V. L., Serov V. V., Vinitsky S. l., Gusev A. A., Chuluunbaatar O., Kazaryan E. M., Sarkisyan A. A.

The calculation scheme for solving the elliptic boundary problem by Kantorovich method for impurity states in models of quantum dots, wires and wells in the effective mass approximation with parabolic confinement potential of harmonic oscillator and infinitely-high walls is presented.

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