Non-Equilibrium Many-Body Dynamics Following A Quantum Quench

TL;DR

This paper investigates the non-equilibrium dynamics of many-body quantum systems after a quench, using random matrix models to describe the transition from integrability to chaos, with analytical and numerical insights into relaxation processes.

Contribution

It introduces a spectral variance-based analytical framework for describing relaxation dynamics in many-body systems modeled by EGOE random matrices, bridging integrability and chaos.

Findings

Analytical results agree well with numerical simulations.

Spectral variances effectively describe relaxation dynamics.

Model captures crossover from integrability to chaos.

Abstract

We study analytically and numerically the non-equilibrium dynamics of an isolated interacting many-body quantum system following a random quench. We model the system Hamiltonian by Embedded Gaussian Orthogonal Ensemble (EGOE) of random matrices with one plus few-body interactions for fermions. EGOE are paradigmatic models to study the crossover from integrability to chaos in interacting many-body quantum systems. We obtain a generic formulation, based on spectral variances, for describing relaxation dynamics of survival probabilities as a function of rank of interactions. Our analytical results are in good agreement with numerics.