Distribution of occupation numbers in finite Fermi-systems and role of interaction in chaos and thermalization

TL;DR

This paper introduces a new, more accurate method for calculating occupation numbers in finite interacting Fermi systems, revealing how interactions influence thermalization and chaos, confirmed through numerical experiments.

Contribution

A novel method for calculating occupation numbers that surpasses the canonical distribution approach and accounts for interaction effects in finite Fermi systems.

Findings

The new method aligns with Fermi-Dirac distribution in large systems.

Interactions effectively increase the system's temperature.

Numerical experiments confirm the theoretical criteria for chaos and equilibrium.

Abstract

New method is developed for calculation of single-particle occupation numbers in finite Fermi systems of interacting particles. It is more accurate than the canonical distribution method and gives the Fermi-Dirac distribution in the limit of large number of particles. It is shown that statistical effects of the interaction are absorbed by an increase of the effective temperature. Criteria for quantum chaos and statistical equilibrium are considered. All results are confirmed by numerical experiments in the two-body random interaction model.