Fidelity and level correlations in the transition from regularity to chaos

TL;DR

This paper analytically compares the effects of chaotic perturbations on regular and chaotic quantum systems, revealing that regular systems are more susceptible to random perturbations than chaotic ones.

Contribution

It provides an exact calculation of fidelity amplitude and energy-energy correlations for regular systems under chaotic perturbations, highlighting their equivalence on average.

Findings

Mean fidelity amplitude equals parametric energy-energy correlations in regular systems.

Regular systems show greater susceptibility to random perturbations than chaotic systems.

Analytical results support the transition understanding from regularity to chaos.

Abstract

Mean fidelity amplitude and parametric energy--energy correlations are calculated exactly for a regular system, which is subject to a chaotic random perturbation. It turns out that in this particular case under the average both quantities are identical. The result is compared with the susceptibility of chaotic systems against random perturbations. Regular systems are more susceptible against random perturbations than chaotic ones.