Magnetic interactions in a classical system of charged particles with intrinsic magnetic moments

A classical, quasirelativistic Hamiltonian is found for a system of charged particles with intrinsic magnetic moments. It represents a generalization of the Darwin Hamiltonian and is the classical analog of the Breit Hamiltonian.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 73–76, November, 1973.     

Susceptibility of a three-level V-type quantum system in a bichromatic field

A theory of interaction of a three-level V-type quantum system with a bichromatic field of two waves, one of which is weak, has been developed. It is suggested that the upper two levels of this system are closely spaced and, therefore, both waves interact simultaneously with both allowed transitions. An expression for nonlinear macroscopic polarization of the V-system has been obtained by the density-matrix method.__________Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 1, pp. 67–71, January–February, 2005.     

Group-theoretic approach to the construction of relativistic lagrangian mechanics of a system of particles

Mathematical aspects of the Lagrangian formalism of relativistic mechanics of a system of interacting particles are considered. A geometric definition of a form of relativistic dynamics possessing the spacelike or isotropic foliation of Minkowski space is introduced. A realization of the Lie algebra of the Poincaré group by means of Lie-Bäcklund vector fields on a general jet continuation of the configuration space is constructed. Invariance conditions of Lagrangian relativistic mechanics are formulated and investigated; the characteristic features of this formalism, which arises as a consequence of the demands of Poincaré invariance, are described.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 11, pp. 1516–1521, November, 1991.     

Survival Analysis of Latvian Population Using Tchebyshev's Polynomials

Several laws have been used in history to characterize mortality. Some of them are rather simple, like Gompertz's law, or quite complicated, like Heligman and Pollard's law. But no law fits very well for all countries and in all time intervals. A similar situation exists in Latvia too. Therefore the main idea of this paper was not to find concrete mortality law but to find its approximation by Fourier and Tchebyshev's series to use an appropriate number of terms. Experimentally, was found that good approximation can be reached using nine terms. Further behavior of constants with the aim of projecting them, was investigated in relation to the approximation of mortality law by the Fourier–Tchebyshev series for a large range of data (1973–1997).     

Experimental and numerical study of self-induced transparency in a neon absorber

Self-induced transparency on the neon transition 2s ₂(J=1)–2p ₄(J=2) is studied both experimentally by investigating the propagation of 3-nsec laser pulses at 1.15 µm in an absorber discharge and theoretically by a numerical integration of Bloch's equations and the wave equation.—The application of linearly and circularly polarized light corresponds to the interaction with a quasi-nondegenerate and degenerate transition, respectively. Pulse shapes, delays, and transmittancevs. input peak intensity are found in quantitative agreement with the calculated data. While with linear light polarization all SIT characteristics clearly appear, with circular polarization the pulse break-up and the oscillation of transmittance due to optical nutations are washed out.—The homogeneous linewidth derived from pulse delay data agrees with the value from conventional measurements. The results prove SIT useful as a quantitative spectroscopic method.     

Dispersion of a three-level quantum system in a bichromatic field

We consider aspects of the interaction between a V-type three-level quantum system and the bichromatic field of two waves, one of which is assumed to be weak. We trace the dynamics of splitting into individual components for the spectral contours of the absorption coefficient (gain) for the signal wave. We discuss the effect of amplification of the signal wave for its frequency-degenerate two-wave interaction with pumping, when the field frequency is tuned to the “zero dispersion” point. We determine the conditions with respect to the concentration of resonant atoms and the spectral regions of the frequencies of the interacting waves for which, in order to correctly describe the effects under consideration, we need to take into account the effect of pumping and the signal in both dipole-allowed transitions of an ensemble of V type three-level quantum systems. We present the results of numerical calculations of the imaginary and real parts of the susceptibility of the resonant medium at the frequency of the signal wave, as a function of the parameters for the high-power radiation and resonant transitions of the quantum V system. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 5, pp. 631–636, September–October, 2007.     

Approximately relativistic center-of-mass variables for a system of two interacting particles

A canonical transformation is found that enables one in the first quasirelativistic approximation (which takes into account orders c^–2) to separate the internal motion in a classical system of two particles from its motion as a whole in the case of arbitrary interaction between the particles.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 49–53, October, 1980.