Non-perturbative response: chaos versus disorder

TL;DR

This paper investigates the non-perturbative response in quantized chaotic systems, comparing it to disordered systems, and finds surprising semiclassical correspondence through numerical analysis.

Contribution

It reveals the existence of a non-perturbative response effect in chaotic systems, similar to disordered systems, supported by numerical evidence and semiclassical analysis.

Findings

Disordered systems exhibit a strong non-perturbative response.

Chaotic systems show an unexpected semiclassical correspondence.

Numerical results suggest a possible weak non-perturbative effect in chaotic systems.

Abstract

Quantized chaotic systems are generically characterized by two energy scales: the mean level spacing $\Delta$, and the bandwidth $\Delta_b\propto\hbar$. This implies that with respect to driving such systems have an adiabatic, a perturbative, and a non-perturbative regimes. A "strong" quantal non-perturbative response effect is found for {\em disordered} systems that are described by random matrix theory models. Is there a similar effect for quantized {\em chaotic} systems? Theoretical arguments cannot exclude the existence of a "weak" non-perturbative response effect, but our numerics demonstrate an unexpected degree of semiclassical correspondence.