Prethermalization, thermalization, and Fermi's golden rule in quantum many-body systems

Abstract

We study the prethermalization and thermalization dynamics of local observables in weakly perturbed nonintegrable systems, with Hamiltonians of the form Ĥ0 + g V , where Ĥ0 is nonintegrable and g V is a perturbation. We explore the dynamics of far from equilibrium initial states in the thermodynamic limit using a numerical linked cluster expansion (NLCE), and in finite systems with periodic boundaries using exact diagonalization. We argue that generic observables exhibit a twostep relaxation process, with a fast prethermal dynamics followed by a slow thermalizing one, only if the perturbation breaks a conserved quantity of Ĥ0 and if the value of the conserved quantity in the initial state is O(1) different from the one after thermalization. We show that the slow thermalizing dynamics is characterized by a rate ∝ g 2 , which can be accurately determined using a Fermi golden rule (FGR) equation.

Typicality of nonequilibrium (quasi-)steady currents

“…For weak coupling between the two chains one thus expects a slow "prethermalizationlike" dynamics, where the prethermal state actually ap-proaches a nonequilibrium steady state. Finally, we numerically show that the relaxation dynamics is proportional to the square of the coupling between the chains, and inversely proportional to their length, which can be derived within the prethermalization paradigm [30,31]. We thus expect, in the thermodynamic limit, that the current will exist indefinitely.…”

“…In our case the conserved quantity is the energy of each bath, which is broken by the coupling between them. This dynamical correspondence with prethermalization is strengthened by the γ 2 relaxation rate [30,31].…”

“…Within the thermalization dynamics, the system may experience prethermalization [25][26][27][28][29][30][31]. A key signature of this phenomenon is a separation of timescales during the relaxation, for instance, a fast initial dynamics in which the system relaxes to an intermediate (often called prethermal) state, and a slower relaxation toward the true thermal state.…”