Self-averaging in many-body quantum systems out of equilibrium: Time dependence of distributions

TL;DR

This paper investigates how the distribution types of various quantities in disordered many-body quantum systems influence their self-averaging behavior over time, revealing that distribution shape determines whether a quantity self-averages.

Contribution

It establishes a relationship between distribution types and self-averaging, providing a semi-analytical approach to study this behavior in complex quantum systems.

Findings

Exponential distribution explains lack of self-averaging for survival probability.

Gaussian distributions are associated with both self-averaging and non-self-averaging quantities.

Distribution of one quantity can predict the self-averaging behavior of related quantities.

Abstract

In a disordered system, a quantity is self-averaging when the ratio between its variance for disorder realizations and the square of its mean decreases as the system size increases. Here, we consider a chaotic disordered many-body quantum system and search for a relationship between self-averaging behavior and the properties of the distributions over disorder realizations of various quantities and at different timescales. An exponential distribution, as found for the survival probability at long times, explains its lack of self-averaging, since the mean and the dispersion are equal. Gaussian distributions, however, are obtained for both self-averaging and non-self-averaging quantities. Our studies show also that one can make conclusions about the self-averaging behavior of one quantity based on the distribution of another related quantity. This strategy allows for semianalytical results, and thus circumvents the limitations of numerical scaling analysis, which are restricted to few system sizes.