Journal of Mathematical Physics

Derivation of the Generalized Boltzmann Equation in Quantum Statistical Mechanics

Tohru Morita

Published Jun 1, 1966• 8 citations

Abstract

The hierarchy of the equations of motion for the reduced density matrices in quantum statistical mechanics is solved and the (cumulant) reduced density matrices at a time t are expressed in terms of those at an earlier time t0. Diagrams are introduced to express the results. With the aid of the technique of partial summations, the general term in the kinetic equation for the one-particle reduced density matrix or the generalized Boltzmann equation in quantum statistical mechanics is obtained. The equation is non-Markovian. A method of reducing the equation to Markovian is sketched.

DOI: 10.1063/1.1704996

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