Quantum-statistical kinetic equations

D. Ya. Petrina

William C. Schieve, Lawrence Paul Horwitz

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.

Herbert E. Spohn

Давид Николаевич Клышко, Yuri Sviridov

This chapter provides a recipe for passing from the classical equations of motion to quantum equations. It discusses the relation between observed and calculated quantities. The chapter explains the convenient Dirac notation and a geometric interpretation of quantum mechanics. It deals with an important law of statistical physics known as the fluctuation-dissipation theorem (FDT). It describes the notions of relaxation and the thermostat and derives the simplest kinetic equation, which differs from dynamic equations in that it allows for an interaction with the thermostat. It should be emphasized that, unlike a FDT, the solution of a kinetic equation defines all the moments of a nonequilibrium system, including its susceptibility—the ratio of the first moment to the force. In principle, then, a kinetic equation describes the change of all the statistical properties of a system under the influence of the thermostat and external forces.

Paul C. Martin