Properties of the Quantum Kinetic Equation

A. N. Temchin

Katsunori Mita

The transport properties of the probability fluid are investigated. The transport equation is derived as a generalization of the equation of continuity. This equation is used to examine the properties of the mass flux density, momentum flux density, and kinetic energy flux density of the probability fluid. It is shown that the transport equations of the probability fluid can be represented in a form identical to those of the classical, Eulerian fluid. It is also shown that the transport equations are differential forms of Ehrenfest’s theorem. Local conservation of the mass density and kinetic energy density for the stationary states are examined. Explicit expressions of the mass flux density and kinetic energy flux density are obtained for the 2p state of the hydrogen atom.

Miriam Scharnke, Niclas Schlünzen, M. Bönitz

Time reversal symmetry is a fundamental property of many quantum mechanical systems. The relation between statistical physics and time reversal is subtle and not all statistical theories conserve this particular symmetry, most notably hydrodynamic equations and kinetic equations such as the Boltzmann equation. In this article, it is shown analytically that quantum kinetic generalizations of the Boltzmann equation that are derived using the nonequilibrium Green functions formalism as well as all approximations that stem from Φ-derivable self-energies are time reversal invariant.

V. L. Kon'kov, V. N. Gorshenkov, Е. П. Богданов

Е. П. Богданов, V. N. Gorshenkov, V. L. Kon'kov

Lev I. Ivankiv, Yarema A. Prykarpatsky, В. Г. Самойленко +1 more

We review a non-relativistic current algebra symmetry approach to constructing the Bogolubov generating functional of many-particle distribution functions and apply it to description of invariantly reduced Hamiltonian systems of the Boltzmann type kinetic equations, related to naturally imposed constraints on many-particle correlation functions. As an interesting example of deriving Vlasov type kinetic equations, we considered a quantum-mechanical model of spinless particles with delta-type interaction, having applications for describing so called Benney-type hydrodynamical praticle flows. We also review new results on a special class of dynamical systems of Boltzmann–Bogolubov and Boltzmann–Vlasov type on infinite dimensional functional manifolds modeling kinetic processes in many-particle media. Based on algebraic properties of the canonical quantum symmetry current algebra and its functional representations, we succeeded in dual analysis of the infinite Bogolubov hierarchy of many-particle distribution functions and their Hamiltonian structure. Moreover, we proposed a new approach to invariant reduction of the Bogolubov hierarchy on a suitably chosen correlation function constraint and deduction of the related modified Boltzmann–Bogolubov kinetic equations on a finite set of multi-particle distribution functions. There are also presented results of application of devised methods to describing kinetic properties of a many-particle system with an adsorbent surface, in particular, the corresponding kinetic equation for the occupation density distribution function is derived.