Thouless and Relaxation Time Scales in Many-Body Quantum Systems.

Abstract

Studies of the dynamics of isolated interacting many-body quantum systems are at the forefront of experimental and theoretical physics. A major open question is the identification of the time scales involved in the relaxation process of these systems. Using experimental observables and a realistic interacting many-body quantum system, we unveil three different time scales: a very short time that characterizes the early decay of the initial state and two much longer time scales that increase exponentially with system size. These two are the Thouless time, tTh, and the relaxation time, tR. The Thouless time refers to the point beyond which the dynamics acquires universal features and relaxation happens when the evolution reaches a stationary state. We show that in chaotic systems, tTh ≪ tR, while for systems approaching a many-body localized phase, tTh → tR. Our results are compared with those for random matrices, which corroborates their generality.