Cosmological solution in the scalar—tensor theory of gravity

We consider the problem of exact integration of the field equations in the scalar—tensor theory of gravity for the case in which matter is an ideal fluid and the metric for space is given in Robertson—Walker form. We obtain a solution (in quadratures) for an arbitrary equation of state and an arbitrary time-dependent density for matter. Tomsk State Pedagogical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 124–127, January, 1997.     

Interaction of a surface magnetostatic wave with an inhomogeneous granular HTSC medium

In the present paper the dispersion properties of surface magnetostatic waves (SMSWs) propagating in a stratified structure, ferrite film—high-temperature superconducting layer, have been investigated. The problem of SMSW propagation in an inhomogeneous stratified medium has been solved and the dispersion equation has been obtained. In the solution of this problem, the granular nature of the high-temperature superconducting (HTSC) medium and the exposure to a constant magnetization field have been taken into account. Upon exposure to the constant magnetic field the HTSC film becomes an inhomogeneous anisotropic medium with respect to a variable magnetic field. The nonhomogeneous wave equation describing the SMSW field in a granular HTSC medium has been solved by the method of sequential iterations. Corrections for the SMSW velocity and attenuation, calculated with the use of the exact dispersion equation, are significant in comparison with previously obtained approximate values and exceed 20 and 40%, respectively. The method of analyzing electromagnetic fields in inhomogeneous granular high-temperature media can be used to solve some other problems, where spatially inhomogeneous HTSC media are used. Tomsk State University of Control Systems and Radioelectronics. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 45–48, April, 1999.     

Operator representation of the wave function for a charged particle in an external field and its applications

A consistent derivation of the operator form for the solution of the wave equation for a charged particle in an arbitrary external electromagnetic field is presented. The expressions obtained can be used for solving any problems in quantum electrodynamics in external fields in the framework of the semiclassical operator method. The peculiarities of the application of this method are demonstrated for the small-angle elastic scattering of a high-energy photon in an arbitrary localized electric field. The problem is solved for the first time without presuming the central symmetry of the external field potential.     

Symmetry Reduction of (2+1)-Dimensional Lax–Kadomtsev–Petviashvili Equation

The Lax–Kadomtsev–Petviashvili equation is derived from the Lax fifth order equation, which is an important mathematical model in fluid physics and quantum field theory. Symmetry reductions of the Lax–Kadomtsev–Petviashvili equation are studied by the means of the Clarkson–Kruskal direct method and the corresponding reduction equations are solved directly with arbitrary constants and functions.     

数值研究二维含时薛定谔方程

采用二维渐近边界条件,将任意极化激光与原子相互作用的二维含时Schr(o)dinger方程无穷空间初值问题转化为有界空间的初边值问题,近而将截断后的初边值问题离散成线性正则方程组,而后利用辛算法求解正则方程得到含时波函数.最后利用含时波函数求得高次谐波谱,证明二维渐近边界条件和辛算法是合理而有效的.     

Gedämpfter Laserverstärker und Phasenunschärfe

Damped Laser Amplifier and Phase Uncertainty In extension of a paper about the possibility to measure the phase of a microscopic field by linear amplification the damping is introduced in the linear amplifier. For this end the Fokker-Planck equation is solved and a quasiprobability distribution is obtained for an arbitrary initial state. With the help of this distribution the phase uncertainty for the largely amplified field is calculated. It is shown that appreciable damping destroys the result which was obtained for a lossless laser amplifier.     

Irregular dielectric or permeable bodies in an external field

An integral equation is derived for the electrostatic potential ψ that arises when a uniform dielectric body of arbitrary shape is placed in an applied electrostatic field. By expansion of ψ in a certain basic set, the integral equation becomes a set of linear equations for the expansion coefficients, and it is often practical to solve the set by truncation. As a test, the equations are applied to the problem of a spheroid in a uniform field, and they easily yield the standard results that are usually derived by introducing spheroidal harmonics. Either the integral equation or the equivalent linear equations can be solved in an iterative approximation (the analog of the Born approximation) when the dielectric constant of the body is not too far from unity. For bodies that differ from spherical or cylindrical ones by a small parameter λ, perturbation formulae are derived that solve the equations in powers of λ. The problem of a homogeneous permeable body of arbitrary shape in an external magnetostatic field is reducible to the dielectric problem, but in addition an alternate integral equation for the magnetic problem is discussed.     

Calculation of Atomic Structurefor Arbitrary Temperature and Matter Density

Schrödinger wave equation is solved for arbitrary matter density and temperature in the Hartree-Fock-Slater (HFS) self-consistent field method. In order to describe relativistic effects, the mass-velocity, the Darwin and spin-orbit coupling terms are included in the wave equation. Some of our results are compared with experimental data and with other theoretical model, the present results are consistent with experiment better and are close to that of Reference.     

A dynamic model of spherical perturbations in the Friedmann universe. I

A self-consistent set of equations describing the evolution of linear spherically symmetrical perturbations in the Friedmann world is derived for an arbitrary equation of state. A singular part of perturbations corresponding to a massive particle-like source is separated, an evolution equation for calculating the source mass is obtained and solved exactly. An exact solution to evolution equations for perturbations at an arbitrary equation of state is constructed. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 66–76, January, 2008.     

Radiation by relativistic dipoles. III

The classical radiation of a point magnetic moment (a magneton) moving at a constant velocity in an arbitrary direction with respect to the field lines of a uniform magnetic field is analyzed. All characteristics of the radiation agree with the Ternov-Bagrov-Khapaev relativistic quantum thoery of the radiation by a neutron. It is thus demonstrated that the classical model of radiation with spin flip is valid. The correspondence principle in the theory of radiation with spin flip will be discussed in more detail in subsequent papers.V. V. Kuibyshev Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 53–59, January 1994.     

Canonical Quantization of Electromagnetic Field in the Presence of Nonlinear Anisotropic Magnetodielectric Medium with Spatial-Temporal Dispersion

Modeling a nonlinear anisotropic magnetodielectric medium with spatial-temporal dispersion by two continuum collections of three dimensional harmonic oscillators, a fully canonical quantization of the electromagnetic field is demonstrated in the presence of such a medium. Some coupling tensors of various ranks are introduced that couple the magnetodielectric medium with the electromagnetic field. The polarization and magnetization fields of the medium are defined in terms of the coupling tensors and the oscillators modeling the medium. The electric and magnetic susceptibility tensors of the medium are obtained in terms of the coupling tensors. It is shown that the electric field satisfy an integral equation in frequency domain. The integral equation is solved by an iteration method and the electric field is found up to an arbitrary accuracy.     

Nonuniform superconducting ring with dangling side branches

The linearized Ginzburg-Landau equation is solved exactly for a superconducting ring with an arbitrary number of dangling branches and transport currents. It is shown that dangling branches always enhance superconductivity. Finite port lengths couple the injected superfluid velocity to the circulating superfluid velocity which give rise to alternating normal and superconducting regions for certain temperature ranges as the magnetic field is varied.     

Extending the Bethe Ansatz: The Quantum Three-Particle Ring

The quantum problem of three impenetrable particles of arbitrary mass confined to a ring is solved by the Bethe ansatz. The solution of this problem is intimately related to the solution a Helmholtz equation in the interior of an arbitrary acute triangle, a problem thought insoluble by Bethe ansatz methods.     

Post-Newtonian approximation for an accelerated,rotating frame of reference

The field equations of general relativity are solved to post-Newtonian order for a frame of reference having an arbitrary time-dependent, translational acceleration and an arbitrary time-dependent angular velocity. The derivation is based on a new 3+1 decomposition of the Einstein field equations and geodesic equation of motion. The resulting space-time metric and equation of motion contain gravitational terms, inertial terms, and coupled gravitational-inertial terms. These effects are expressed explicitly in terms of the Newtonian potential and standard post-Newtonian scalar and vector potentials. The physical meaning of the formulas derived is illustrated by application to a system of point-like gravitating masses. These results should be useful for the investigation of general relativistic effects in the analysis of real experimental measurements made with respect to a noninertial frame of reference, such as the surface of the rotating earth or an accelerated spacecraft.     

Diffraction of electromagnetic waves by three-dimensional ideally conducting bodies in a magnetodielectric envelope

A numerical method of solving the problem of the diffraction of electromagnetic radiation by structures which are an ideally conducting body of arbitrary shape in a uniform magnetodielectric envelope is proposed. The method is implemented in the form of a program for calculating the components of the diffraction field of structures with different geometrical and electrodynamic parameters. Some results of numerical investigations, carried out to investigate the effect of deviations of the shape of the structure from axisymmetrical on the energy characteristics of the scattered field, are presented. V. D. Kuznetsov Siberian Physicotechnical Institute, Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 47–51, July, 1998.     

An alternative f(R, T) gravity theory and the dark energy problem

Recently, a generalized gravity theory was proposed by Harko et al. where the Lagrangian density is an arbitrary function of the Ricci scalar R and the trace of the stress-energy tensor T, known as F(R,T) gravity. In their derivation of the field equations, they have not considered conservation of the stress-energy tensor. In the present work, we have shown that a part of the arbitrary function f(R,T) can be determined if we take into account of the conservation of stress-energy tensor, although the form of the field equations remain similar. For homogeneous and isotropic model of the universe the field equations are solved and corresponding cosmological aspects has been discussed. Finally, we have studied the energy conditions in this modified gravity theory both generally and a particular case of perfect fluid with constant equation of state.     

Relativistic quantum theory of cyclotron resonance in a medium

The relativistic quantum theory of cyclotron resonance in a medium with arbitrary dispersive properties is presented. The quantum equation of motion for a charged particle in the field of a plane electromagnetic wave and in the uniform magnetic field in a medium is solved in the eikonal approximation. The probabilities of induced multiphoton transitions between the Landau levels in a strong laser field are calculated.     

基于磁荷面分布的舰船磁场预测方法

利用等效源观点, 把钢铁建造的舰船船体视为等效磁荷面分布, 建立了该分布与磁场传感器测量值之间应满足的第一类Fredholm积分方程, 然后利用广义逆矩阵对积分方程离散化后得到的线性方程组进行求解, 并以矩阵条件数来衡量方程组的病态程度, 最后利用求解得到的磁荷分布来预测舰船在空间中任意点上产生的磁场. 数值模拟表明该方法可以准确地识别磁性从而得到精确的磁场预测值. 最后利用一个船模实验验证了本方法. 关键词： 舰船 磁场 磁荷 积分方程     

Transformation of a monochromatic plane wane by the pulse-periodic time modulation of an infinite medium

An exact solution to the problem of the transformation of a monochromatic plane wave by a finite train of equally spaced rectangular pulses of permittivity and conductivity of an infinite medium is considered. The permittivity pulse train is shifted relative to the conductivity pulse train by an arbitrary time. The problem is studied analytically in terms of the second-order Volterra integral equation describing the electromagnetic wave transformation in a medium with time-dependent parameters. The equation is solved using the resolvent technique. Expressions for the amplitude of the transformed electric field component for any time instant at any spatial point are derived and analyzed.