- Dr. Marcos Rigol - Penn State University
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 .
References:  K. Mallayya, MR, and W. De Roeck, Prethermalization and Thermalization in Isolated Quantum Systems, Phys. Rev. X 9, 021027 (2019).  K. Mallayya and MR, Heating Rates in Periodically Driven Strongly Interacting Quantum Many-Body Systems, Phys. Rev. Lett. 123, 240603 (2019).  T. LeBlond, K. Mallayya, L. Vidmar, and MR, Entanglement and matrix elements of observables in interacting integrable systems, Phys. Rev. E 100, 062134 (2019).
dr. Iacopo Carusotto