Construction of linear response theory for classical systems by the nonequilibrium statistical operator method

Moscow Institute of Electronic Engineering. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 80, No. 3, pp. 452–460, September, 1989.     

Nonequilibrium thermofield dynamics and the nonequilibrium statistical operator method

V. A. Steklov Mathematics Institute, USSR Academy of Sciences; Institute of the Physics of Condensed Systems, Ukrainian SSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 88, No. 2, pp. 286–310, August, 1991.     

Statistical hydrodynamics of magnetic fluids. I. the nonequilibrium statistical operator method

The Zubarev nonequilibrium statistical operator is used to describe the generalized hydrodynamic state of a magnetic fluid in an external magnetic field. The magnetic fluid is modeled with “liquid-state” and “magnetic” subsystems described using the classical and quantum statistics methods respectively. Equations of the generalized statistical hydrodynamics for a magnetic fluid in a nonhomogeneous external magnetic field with the Heisenberg spin interaction are derived for “liquid-state” and “magnetic” subsystems characterized by different nonequilibrium temperatures. These equations can be used to describe both the weakly and strongly nonequilibrium states. Some limiting cases are analyzed in which the variables of one of the subsystems can be formally neglected. Translated from Teoreticheskaya i Matematicheskaya Fizika. Vol. 115, No. 1, pp. 132–153, April, 1998.     

Wavelet approximations of a collision operator in kinetic theory

This Note is devoted to the derivation of conservative and entropic fast wavelet approximations for the isotropic Fokker–Planck–Landau collision operator arising in the modeling of charged particles in plasma physics. The present approach combines the advantages of both the finite difference schemes (conservation and entropy) and the spectral methods (accuracy) which are developed in the literature. Furthermore, the wavelet approach provides a fast algorithm for the evaluation of such a collision operator. The present work is a first step to the development of wavelet approximations to more complex collision operators in kinetic theory. To cite this article: X. Antoine, M. Lemou, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Structure of the resolvent of the Schrödinger operator for a system of three charged particles

Modified integral Faddeev equations for a system of three particles with Coulomb interaction are studied. The structure of the kernel of the resolvent on a continuous spectrum in coordinate space is described.     

Distribution of the eigenvalues of the energy operator of a continuous system in quantum statistical mechanics

Theoretical and Mathematical Physics -     

Diffusion limits of the linear boltzmann equation in extended kinetic theory: Weak and strong inelastic collisions

We consider the asymptotic analysis for the linear Boltzmann equation with elastic and inelastic scattering. The physical model describes the motion of test particles propagating by elastic and inelastic collisions through a host medium in the Lorentz gas limit. The background is in thermodynamical equilibrium with only two internal energy levels. We apply the compressed Chapman-Enskog procedure to derive the diffusive-type approximations in the cases of dominant elastic and dominant inelastic collisions. Then we present numerical examples showing the time evolution of the distribution function in some physically relevant cases. In the appendix the successive overrelaxation method is briefly cutlined. Conferenza tenuta il giorno 27 Settembre 1999 da G. Frosali