MICROSCOPIC COEFFICIENTS FOR THE QUANTUM MASTER EQUATION OF A FERMI SYSTEM

Abstract

In a previous paper, we derived a master equation for fermions, of Lindblad's form, with coefficients depending on microscopic quantities. In this paper, we study the properties of the dissipative coefficients taking into account the explicit expressions of: (a) the matrix elements of the dissipative potential, evaluated from the condition that, essentially, this potential induces transitions among the system eigenstates without significantly modifying these states, (b) the densities of the environment states according to the Thomas–Fermi model, and (c) the occupation probabilities of these states taken as a Fermi–Dirac distribution. The matrix of these coefficients correctly describes the system dynamics: (a) for a normal, Fermi–Dirac distribution of the environment population, the decays dominate the excitation processes; (b) for an inverted (exotic) distribution of this population, specific to a clustering state, the excitation processes are dominant.