Marcos Rigol: Prethermalization and thermalization in isolated quantum systems

Title: Prethermalization and thermalization in isolated quantum systems

Abstract: Prethermalization has been extensively studied in systems close to integrability. We present a more general, yet conceptually simpler, setup for this phenomenon. We consider a--possibly nonintegrable--reference dynamics, weakly perturbed so that the perturbation breaks at least one conservation law. We argue that the evolution of such a system proceeds via intermediate (generalized) equilibrium states of the unperturbed Hamiltonian, which flow towards global equilibrium in a time of order 1/g^2, where g is the perturbation strength. We test our analytic predictions in the context of quantum quenches and show that the relaxation rates are indeed given by a generalized Fermi's golden rule, while the leading correction to the intermediate equilibrium states is in general of order g. We then discuss the applicability of the generalized Fermi's golden rule to heating in periodically driven strongly interacting systems, in which the drive breaks energy conservation. We show that heating rates allow one to probe the smooth function that characterizes the off-diagonal matrix elements of the drive operator in the eigenbasis of the static Hamiltonian, both for nonintegrable and (remarkably) integrable Hamiltonians.