Quantum master equation for a system of identical particles

TL;DR

This paper derives a quantum master equation for identical particles in an open system, revealing multiple equilibrium solutions and anisotropic distributions due to interactions, with implications for electron behavior in metals.

Contribution

It introduces a kinetic equation for the density matrix of identical particles, including interaction effects and anisotropic distributions, within a mean-field approximation.

Findings

Multiple solutions for electron distribution in metals.

Existence of anisotropic distribution solutions.

Distribution function's multivalence in wave vector space.

Abstract

We consider an open quantum many-particle system in which there are dissipative processes. The evolution of this system is described by a kinetic equation for the density matrix. From the equation describing a random Markov process in this system, we obtain an equation for the single-particle statistical operator. This equation describes the evolution of a system of identical particles in a mean-field approximation. The equation for interacting particles in thermodynamic equilibrium was obtained. The distribution function of a system of interacting electrons in metals has multivalence in a certain region of wave vectors. Among many solutions one is isotropic. Other solutions have the anisotropy of the electron distribution over the wave vectors. The anisotropy arises as a result of repulsion and attraction between electrons.