Energy absorption in time-dependent unitary random matrix ensembles: dynamic vs Anderson localization

TL;DR

This paper investigates energy absorption in driven chaotic fermionic systems modeled by unitary random matrices, revealing how quantum interference effects modify classical predictions and suggesting a link to Anderson localization.

Contribution

It calculates the two-loop interference correction to the energy absorption rate and proposes a conjecture connecting periodic driving dynamics to the Anderson model.

Findings

Interference corrections significantly alter classical absorption rates.

In strong localization, absorption decays as W(t) ln(t)/t^2.

A conjecture links periodically-driven random matrices to the Anderson model.

Abstract

We consider energy absorption in an externally driven complex system of noninteracting fermions with the chaotic underlying dynamics described by the unitary random matrices. In the absence of quantum interference the energy absorption rate W(t) can be calculated with the help of the linear-response Kubo formula. We calculate the leading two-loop interference correction to the semiclassical absorption rate for an arbitrary time dependence of the external perturbation. Based on the results for periodic perturbations, we make a conjecture that the dynamics of the periodically-driven random matrices can be mapped onto the one-dimensional Anderson model. We predict that in the regime of strong dynamic localization W(t) ln(t)/t^2 rather than decays exponentially.