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

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.