Random-matrix approach to time-dependent forcing in many-body quantum systems

TL;DR

This paper advances a nonlinear response theory based on random-matrix methods to analyze how many-body quantum systems react to time-dependent parameters, with applications to quantum computing and simulation.

Contribution

It develops analytical approximations for the response function under various driving regimes, extending the theory's applicability to out-of-equilibrium quantum systems.

Findings

Derived response function approximations for fast and strong driving

Predicted system behavior under finite-time quenches

Validated predictions with numerical examples

Abstract

Changing some of its parameters over time is a paradigmatic way of driving an otherwise isolated many-body quantum system out of equilibrium, and a vital ingredient for building quantum computers and simulators. Here, we further develop a recently proposed nonlinear response theory which is based on typicality and random-matrix methods, and which is applicable to a wide variety of such parametrically perturbed systems in and out of equilibrium: We derive analytical approximations of the characteristic response function for the two limiting cases of fast driving and of strong and short-ranged-in-energy driving. Furthermore, we work out implications and predictions for common applications, including finite-time quenches and time-dependent forcing that breaks conservation laws of the underlying undriven system. Finally, we verify all predictions by numerical examples and discuss the theory's scope and limitations.