Reducing dynamical fluctuations and enforcing self-averaging by opening many-body quantum systems

TL;DR

This paper studies how opening many-body quantum systems to a dephasing environment can reduce fluctuations and promote self-averaging, with implications for understanding criticality and chaos in quantum dynamics.

Contribution

It demonstrates that opening systems generally reduces fluctuations, but self-averaging is only achieved away from critical points, providing new insights into quantum chaos and phase transitions.

Findings

Fluctuations are reduced when systems are opened to dephasing environments.

Self-averaging occurs in random matrix models away from critical points.

In spin models, self-averaging is limited to the chaotic regime.

Abstract

We investigate how the dynamical fluctuations of many-body quantum systems out of equilibrium can be mitigated when they are opened to a dephasing environment. We consider the survival probability (spectral form factor with a filter) evolving under different kinds of random matrices and under a spin-1/2 model with weak and strong disorder. In isolated many-body quantum systems, the survival probability is non-self-averaging at any timescale, that is, the relative variance of its fluctuations does not decrease with system size. By opening the system, we find that the fluctuations are always reduced, but self-averaging can only be ensured away from critical points. Self-averaging is achieved for the long-time dynamics of full random matrices, power-law banded random matrices deep in the delocalized phase, and the Rosenzweig-Porter ensemble in all the phases except at the delocalization-localization transition point. For the spin model, the survival probability becomes self-averaging only in the chaotic regime provided the initial states are in the middle of the spectrum. Overall, a strongly non-self-averaging survival probability in open systems is an indicator of criticality.