A microscopic theory of one-body dissipation

Abstract

Zwanzig's projection operator method is applied to the equation of motion for the single-particle reduced density matrix of a many-fermion system. An approximate equation obeyed by the projected part is derived for the case the collision integral is treated in the Born Collision Approximation. The form of Balian and Vénéroni's equation is shown to be a Markovian limit of the resulting equation, if the Born collision term is neglected. Specializing the projection operator to give the diagonal elements of the single-particle density matrix in appropriately chosen fixed bases we obtain genealized “Master Equations” which are then compared to the equation of motion for the occupation probabilities of the natural single-particle states of the system. From the analysis we conclude that, microscopically, the so-called one-body dissipation mechanism introduced by Blocki et al. ( Ann. Phys. (N.Y.) 113 (1978), 330) is a mean-field effect which appears whenever a contracted single-particle description of a many-particle system is employed.