Prethermalization and Thermalization in Generic Isolated Quantum Systems

Prethermalization has been extensively studied in systems close to integrability. We propose a more general, yet simpler, setup for this phenomenon. We consider a -possibly nonintegrable- reference dynamics, weakly perturbed so that the perturbation violates at least one conservation law of the reference dynamics. We argue then that the evolution of the system proceeds via intermediate (generalized) equilibrium states of the reference dynamics. The motion on the manifold of equilibrium states is governed by an autonomous equation, flowing towards global equilibrium in a time of order g², with g the perturbation strength. We also describe the leading corrections to the time-dependent reference equilibrium state, in general of order g. The theory is well-confirmed by numerical calculations relying on the numerical linked cluster expansion.