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

We study the time scales involved in the relaxation process of isolated quantum many-body systems. Using experimental observables and a realistic many-body quantum model, we unveil three different time scales: a very short time that characterizes the early fast decay of the initial state, and two much longer times that increase exponentially with system size. These are the Thouless time, t_Th, and the relaxation time, t_R. The Thouless time refers to the point beyond which the dynamics acquire universal features, and relaxation happens when the evolution reaches a stationary state. We show that in chaotic systems, t_Th<<t_R, while for systems approaching a many-body localized phase, t_Th tends to t_R. We also compare these results with those for random matrices, and study how self-averaging properties depend on time scales.