Breit-Wigner width and participation ratio in finite interacting Fermi systems

TL;DR

This paper investigates how the Breit-Wigner width and participation ratio in finite interacting Fermi systems depend on interaction strength and energy excitation, especially during the transition from Poisson to Wigner-Dyson statistics.

Contribution

It provides a detailed analysis of the relationship between interaction strength, energy excitation, and spectral statistics in many-body Fermi systems, highlighting the crossover behavior.

Findings

Eigenstates become highly mixed at U > Uc.

Poisson-like statistics can occur with large IPR even below Uc.

Transition from Poisson to Wigner-Dyson statistics is characterized by changes in IPR and spectral correlations.

Abstract

For many-body Fermi systems we determine the dependence of the Breit-Wigner width and inverse participation ratio (IPR) on interaction strength U > Uc and energy excitation dE > dE_ch when a crossover from Poisson to Wigner-Dyson P(s)-statistics takes place. At U > Uc the eigenstates are composed of a large number of noninteracting states and even for U < Uc there is a regime where P(s) is close to the Poisson distribution but IPR >> 1.