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

Abstract

In a disordered system, a quantity is self-averaging when the ratio between its variance over disorder realizations and the square of its mean decreases as the system size increases. Here, we consider a chaotic disordered many-body quantum system out of equilibrium and identify which quantities are self-averaging and at which time scales. This is done by analyzing their distributions over disorder realizations. 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, on the other hand, are obtained for both self-averaging and non-self-averaging quantities. We also show that semi-analytical results for the self-averaging behavior of one quantity can be achieved from the knowledge of the distribution of another related quantity. This strategy circumvents numerical limitations on the sizes of the systems that we can deal with.