Investigation of classical, relativistic and quantum kinetic equations, examination of their properties and regions of applicability for various physical systems. The Post-Galilean statistical mechanics and hydrodynamics in Lagrange and Hamilton variables has been constructed for the systems with retardation of interaction with the use of correct investigation of Legendre transformation. The general linear quantization is consructed for the Post-Galilean dynamical systems. The density matrix and Wigner function were examined in the neighborhood of Lagrangian singular points. The class of two-dimensional integrable dynamical systems is constructed and linearly quantized. Only for Weil quantization there exist one of the representatives, which remains integrable in quantum case. The class of polynomial Hamiltonians, modelling the scattering processes in problems of quantum optics, has been classified with respect to linear conservation laws in terms of number operators. The non-classical special polynomials were introduced for precise asymtotic spectrum analysis. The generalized coherence states representation is constructed for non-classical commutation relations. The existence of covariant symbols of vectors and operators has been proved for this representation. The kinetic equations method is applied to the cocial systems, for the problems of demography, economy and ecology. The non-linear models of evolution of non-uniform populations were constructed and theoretically and numerically examined for the assimilation task. In particularly, the long-time prediction of demography situation in Russia is constructed.
Main publications:
Quantum BBGKY Hierarchies and Wigner Equation in Postgalilean Approximation (with I. P.Pavlotsky) // Physica A, 158 (1989), 607–618.
Equilibrium Postgalilean BBGKY Hierarchies (with I. P. Pavlotsky) // Dokl. Akad. Nauk SSSR, 304 (1989), 329–332.
Special Polynomials in Problems of Quantum Optics (with V. V. Vedenyapin) // Modern Physics Letters B, 9, no. 5 (1995), 291–298.
Conservation laws for Polynomial Quantum Hamiltonians (with O. V. Mingalev and V. V. Vedenyapin) // Physics Letters A, 223 (1996), 246–250.
