Derivation in a nonequilibrium ensemble formalism of a far-reaching generalization of a quantum Boltzmann theory

Abstract

Within the framework of the nonequilibrium statistical ensemble formalism provided by the nonequilibrium statistical operator method, we derive a quantum Boltzmann-style transport theory of a broad scope. This is done by choosing the single- and two-particle dynamical density operators as the basic informational–statistical variables. The equations of evolution for their average values over the nonequilibrium ensemble, the nonequilibrium-reduced Dirac–Landau–Bogoliubov-type density matrices, are obtained. From the resulting generalized nonlinear quantum transport theory, after resorting to perturbative-like expansions, a far-reaching generalization of Boltzmann equation for the single-particle distribution function is derived. A type of traditional Boltzmann equation follows after using stringent approximations, whose limits of validity are evaluated.