Theoretical Treatment of Nonstationary Scattering by Phonons and Polaritons Part I. Derivation of the Basic Equations

The equations of motion of a two-level system and a harmonic oscillator coupled to a dissipative system are discussed; the dissipative system is assumed to consist of a large number of radiation oscillators. Special equations for the determination of the correlation functions of the fluctuation forces are derived under the condition of large time values, for which the atomic system has “forgotten” its initial state. The expectation values of the correlation functions are connected with the damping constant and the population operator of the excited state of the atomic system is in thermal equilibrium. Taking into account the influence of the coherent radiation field on the atomic system, the basic equations for the treatment of the nonstationary Raman scattering by polaritons are derived; the temporal range of validity is discussed. Using a time-dependent “variable” Fourier transformation, the nonstationary time- and spacedependent spectral densities are related to the correlation functions of the fields; here the Wiener-Khintchine theorem is applied in a nonstationary form. The limiting cases of the stationary scattering process as well as the usually introduced correlators of the slowly varying amplitudes are discussed.     

Spatiotemporal characteristics of laser emission. I

The first chapter describes the general premises of the electrodynamic theory of the laser as a nonstationary nonlinear oscillatory system with spatially distributed parameters. Maxwell's equations are used to derive an equation for the complex amplitude of the electromagnetic field in a cavity filled with transversely inhomogeneous active medium. The self-conssitent analysis includes a simultaneous solution of the equations for the field and for the inverted population. In the second chapter, electrodynamic theory is applied to injection and electron-beampumped semiconductor lasers. The threshold characteristics, the field structure in the near and far zones, the lasing regimes of semiconductor lasers, and the influence of nonlinearity of the refractive index are considered.Division of Quantum Radiophysics, Lebedev Physics Institute. Translated from Preprint No. 33, Lebedev Physics Institute, Moscow, 1990.     

Equations of two-fluid hydrodynamics in the Hubbard model

A set of equations is obtained using stationary and nonstationary superconductivity theories in terms of the Hubbard model. The equations near T _c and for a weak magnetic field have the general form of superconductivity equations with a strongly anisotropic Fermi surface. Calculations are performed using a kinetic equation for quasiparticles. The low-temperature collective excitations in a superconductor are studied. An explicit relationship for the temperature dependence of second sound is obtained.     

Five-domensional, nonstationary cosmological solutions with rotation

Two nonstationary cosmological solutions of the five-dimensional Einstein equations are found for different metrics. In one case the sources of the gravitational field are an anisotropic fluid and a radiation field, while in the other case they are an anisotropic fluid, a radiation field, and a heat flux. Perm' State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 25–28, September, 1997.     

General Formulation for the Ponderomotive Force in a Warm Two Fluid Magnetized Plasma

A general expression for the ponderomotive force in a warm, inhomogeneous, nonstationary, magnetized and collisionless two fluid plasma in the presence of electromagnetic field is obtained. We start with two fluid equations viz. continuity, momentum equations and Maxwell's equation. Expanding the physical quantities in terms of a high frequency part and a slowly varying part and averaging the quantities over one period of the high frequency, we have obtained the expression for the ponderomotive force. The results are compared with the results of earlier workers under different approximations.     

Method of Coupled Waves in the Theory of Excitation of Waveguides by High-Frequency Currents with Slowly Varying Amplitudes

Based on the method of coupled waves, we propose nonstationary equations describing excitation of waveguides in which the energy distribution in wave packets varies due to mutual transformation of the coupled waves. We obtain a universal expression relating the dispersion of a waveguide mode to the frequency dependence of its field, i.e., to a change in the field structure of the mode during a pulse. To illustrate the proposed procedure of constructing nonstationary equations, we apply it to the well-known case of excitation of plane-wave packets by electric currents in a homogeneous isotropic medium with time dispersion.__________Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 3, pp. 198–06, March 2005.     

Nonstationary self-consistent model for an ensemble in the self-field

The behavior of a nonstationary system of charged particles interacting with the self-field is studied using integrals of motion for nonstationary systems. Numerical solutions are obtained for the sets of equations describing the characteristics of a system of particles. A nonstationary self-consistent quantum system is also analyzed. The proposed model can be useful for investigating the acceleration of charged particles by the self-field.     

Numerical investigation of atomic dynamics in strong ultrashort laser pulses

The algorithms for the numerical solution of the stationary and nonstationary Schrödinger equations that allow the analysis of the dynamics of single-electron atoms in the presence of an external strong linearly polarized electromagnetic field in the dipole approximation are presented. Several examples of the simulation of atomic dynamics in the presence of high-intensity laser fields are considered to illustrate the possibilities of the proposed algorithms.     

Nonlinear dynamic structure rearrangement of vortexlike domain walls in magnetic films with in-plane anisotropy

The nonlinear dynamic behavior of vortexlike domain walls in magnetic uniaxial films having an in-plane anisotropy was investigated within a rigorous micromagnetic approach in the framework of a two-dimensional magnetization distribution by numerically solving the Landau–Lifshitz equations (with the Gilbert damping parameter) with allowance for all the main interactions, including the dipole–dipole one. The studies were carried out on magnetic soft films with an anisotropy axis lying in their plane in a dc magnetic field parallel to an easy axis and a pulsed magnetic field normal to it. New possibilities for controlling the nonlinear dynamic rearrangement of the internal structure of domain walls and their velocities in fields both above and below the critical field are established. The wall motion in the field above the critical one is nonstationary.     

New exact solutions of the Dirac equation

The search for new exact solutions to the Dirac and Klein-Gordon equations initiated in [1] is continued. New solutions are found for axisymmetric fields and one type of nonstationary field of special configuration. The basic notation and system of units of [1] are retained.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 10–16, April, 1980.     

Kinetics of ions in a neutral gas upon abrupt application of an electric field. I. CEM model

A new method for calculating matrix elements of the collision integral is used for solving problems of the mobility of ions against the background of atoms and for constructing the distribution functions for ions upon an abrupt application of an electric field. It is shown how the stationary distribution function can be constructed using the nonstationary moments method in the case when the stationary moments method is completely inapplicable. The solution to the nonstationary problem for the CEM model corresponding to resonant charge exchange with a constant collision frequency, which is constructed analytically, is used for analyzing the limits of applicability of the nonstationary moments method.     

Imitation of matter by a scalar field in five-dimensional Kaluza-Klein theory

The interpretation of the scalar field ={ie96-1} in the five-dimensional variant of Kaluza-Klein theory is considered. It is proposed that the scalar field be considered as the generalized potential of four material velocities. It can be shown that with additional limitations on the scalar field the right side of the split five-dimensional Einstein equations transform to a hydrodynamic energy-momentum tensor for an ideal liquid with a limited set of equations of state. Concrete five-dimensional metrics, which are obligatorily nonstationary, are analyzed from this viewpoint.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 111–117, January, 1995.     

ANGEL program: Solution of large systems of linear differential equations describing nonstationary processes using CUDA technology

This paper presents the formulation of the problem and the methodical approach for solving large systems of linear differential equations describing nonstationary processes with the use of CUDA technology; this approach is implemented in the ANGEL program. Results for a test problem on transport of radioactive products over loops of a nuclear power plant are given. The possibilities for the use of the ANGEL program for solving various problems that simulate arbitrary nonstationary processes are discussed.     

Approximate Gaussian representation of evolution equations I. Single degree of freedom nonlinear equations

We have developed a generalization of the method of statistical linearization to enable us to describe transient and other nonstationary phenomena obeying stochastic nonlinear differential equations. This approximation technique provides an optimal Gaussian representation with time-dependent parameters. The algorithm specifies a set of ordinary differential equations for the Gaussian parameters in terms of the time-dependent average nonlinearities. We apply the general formalism developed herein for single degree of freedom dissipative systems to a particular example.     

Linear nonstationary optical dimensional resonances in atomic nanostructures

The existence of linear nonstationary optical resonances in a diatomic nanostructural object with a dipole-dipole atomic interaction has been proved. A new solution to the joint system of modified Bloch optical equations and nonlocal field equations is obtained for time intervals much shorter than the times of phase and energy relaxation. Formulas for effective polarizabilities of the object’s atoms, which have a set of dimensional resonances, are derived. The frequencies of these resonances significantly differ from the eigenfrequencies of the object’s atoms, and their properties depend on the interatomic distance, light-pulse duration, initial atomic inversions, and the orientation of the object’s axis relative to the direction of incidence of the external light wave.     

Separation of variables in the Klein-Gordon equations. II

Two kinds of external nonstationary electromagnetic fields are found containing arbitrary functions which admit of total separation of variables in the Klein-Gordon equations by using two differential symmetry operators and one second order operator. Curvilinear coordinates are presented in which the variables are divided, and equations are written down in the separated variables.Translated from Izvestiya VUZ, Fizika, No. 12, pp. 45–52, December, 1973.     

Anomalous suppression of the probability of resonance interaction of electrons with an rf field in asymmetric double-barrier structures on account of plasma oscillations

An analytical self-consistent solution of the nonstationary Schrödinger and Poisson equations describing the resonance interaction of electrons with a radio-frequency (rf) field has been found for asymmetric resonance-tunneling structures with high, thin barriers. It is shown that plasma oscillations limit the probability of transitions between neighboring levels and suppress anomalously strongly transitions in which the level number changes by more than 1 (by tens and hundreds of times compared with transitions between neighboring levels).     

Yang-Mills fields of nonstationary spherical objects with big charges

We study the nonlinear electrodynamics suggested in our paper in [Russ. J. Math. Phys. 12 (3), 379–385 (2005)] by using the Yang-Mills equations. This theory is intended to describe strong fields generated by objects with large electric charges. For nonstationary sources with spherical symmetry, we find formulas for the electric field strengths. This solution generalizes our previous result related to the stationary case. The corresponding formulas for nonlinear electric fields are used to explain some puzzling properties of the Earth atmosphere.     

Boundary regularity for the Navier-Stokes equations in a half-space

Weak solutions to the nonstationary Navier-Stokes equations in a half-space are locally bounded at the boundary except for a closed set with finite one-dimensional Hausdorff measure.This research was supported in part by the National Science Foundation Grant MCS-81-02737     

Quantum-hydrodynamic approach to the problem of electron exchange between atomic particles and nanosystems

The application of quantum-hydrodynamic methods for solving the problem of electron exchange between atomic particles and solid surfaces, and nanosystems has been examined. The derivation of a system of equations that is alternative to the nonstationary Schrödinger equation is given to describe the dynamics of electronic processes with variable charge and current densities. A comparison of results of solving the nonstationary Schrödinger equation and the quantum-hydrodynamic system of equations shows that both approaches give a good coincidence. The numerical solution to the system of quantum-hydrodynamic equations has a number of advantages, because it does not lead to oscillations at the boundary of the computational mesh and nor to the problem of exponential growth in numerical complexity for many-electron systems.