Typical relaxation of perturbed quantum many-body systems

Abstract

We substantially extend our relaxation theory for perturbed many-body quantum systems from ((2020) Phys. Rev. Lett. 124 120602) by establishing an analytical prediction for the time-dependent observable expectation values which depends on only two characteristic parameters of the perturbation operator: its overall strength and its range or band width. Compared to the previous theory, a significantly larger range of perturbation strengths is covered. The results are obtained within a typicality framework by solving the pertinent random matrix problem exactly for a certain class of banded perturbations and by demonstrating the (approximative) universality of these solutions, which allows us to adopt them to considerably more general classes of perturbations. We also verify the prediction by comparison with several numerical examples.

Nontrivial damping of quantum many-body dynamics

“…This ratio is a nontrivial function and does not coincide with the damping in the interaction picture. approach correctly captures the "standard" case of exponential damping of J (t )J , in agreement with typicality and random-matrix considerations [24][25][26].…”

“…( 10) simply carries over to the Schrödinger picture, and the relaxation dynamics of J (t )J ε>0 may exhibit nontrivial behavior that is distinct from typicality predictions in Refs. [24,25].…”

“…A particularly intriguing and omnipresent question in physics is how the dynamics of a given quantum system is affected by the presence of a perturbation [12,[22][23][24][25][26], i.e., scenarios where the Hamiltonian H of the full system can be written as…”

“…Given a quantum system with many degrees of freedom, the impact of a perturbation can clearly be manifold. It is therefore quite remarkable that a series of recent works predicts that, in the overwhelming majority of cases, the reference dynamics is just damped by a simple function [24,25], e.g., exponentially as expected from Fermi's golden rule [26,37,38]. In essence, these works rely on random-matrix theory as V is modeled by (an ensemble of) random matrices with respect to the eigenstates of H 0 [24], as well as on the concept of typicality [39][40][41][42], as a given perturbation is shown to behave very similarly to the ensemble average.…”

Typicality of nonequilibrium (quasi-)steady currents

“…[1,[6][7][8][9][10]. Meanwhile, the attention on the foundation of statistical mechanics has led to the development of the notion of typicality [2,[11][12][13], within canonical formalism [14,15] and for unitary dynamical processes [12,16] with more specific scenarios such as prethermalization [17] and perturbation [18,19]. For example, dynamical typicality states that pure states with the same initial expectation value for some observables will likely have similar expectation values at any later time [12,16].…”