A major open question in studies of nonequilibrium quantum dynamics is the identification of the time scales involved in the relaxation process of isolated quantum systems that have many interacting particles. We demonstrate that long time scales can be analytically found by analyzing dynamical manifestations of spectral correlations. Using this approach, we show that the Thouless time
tTh and the relaxation time
tR increase exponentially with system size. We define
tTh as the time at which the spread of the initial state in the many-body Hilbert space is complete and verify that it agrees with the inverse of the Thouless energy.
tTh marks the point beyond which the dynamics acquire universal features, while relaxation happens later when the evolution reaches a stationary state. In chaotic systems, ${t}_{\text{Th}}\ensuremath{\ll}{t}_{\text{R}}$, while for systems approaching a many-body localized phase, ${t}_{\text{Th}}\ensuremath{\rightarrow}{t}_{\text{R}}$. Our analytical results for
tTh and
tR are obtained for the survival probability, which is a global quantity. We show numerically that the same time scales appear also in the evolution of the spin autocorrelation function, which is an experimental local observable. Our studies are carried out for realistic many-body quantum models. The results are compared with those for random matrices.
We show that steady-state entanglement in open quantum systems is controlled by the phase reference of a phase-sensitive reservoir. Using a covariance-matrix approach for Gaussian-preserving dynamics, we demonstrate that purely local, phase-sensitive dissipation can generate entanglement when combined with coherent coupling. The steady state exhibits a finite entangled region with an optimal squeezing strength that maximizes both the magnitude and thermal robustness of entanglement. We find that coherent coupling does not enhance entanglement monotonically, but instead regulates the conversion of local squeezing into nonlocal correlations. Importantly, the coupling dependence is controlled by the phase reference of the squeezed reservoir: phase-locked (rotating-frame) and laboratory-frame implementations yield qualitatively distinct steady states and entanglement structure. These results establish phase-sensitive reservoir engineering as a controllable route to steady-state entanglement in continuous-variable systems. Steady-state entanglement in phase-sensitive open systems depends explicitly on the reservoir phase reference and is not invariant under changes of that reference.}