Elastic enhancement factor as a quantum chaos probe

TL;DR

This paper investigates how the elastic enhancement factor can serve as a universal indicator of the internal chaotic or regular dynamics of quantum systems, linking it to time delay variances and Dyson's form factor.

Contribution

It establishes a universal relation between the elastic enhancement factor and the time delay variance, providing a new way to measure internal chaos in quantum systems.

Findings

The elastic enhancement factor is connected to the variance of time delays.

The relation between the enhancement factor and the Dyson form factor is universal.

Enhancement factor can quantify the degree of internal chaos.

Abstract

Recent development of the resonance scattering theory with a transient from the regular to chaotic internal dynamics inspires renewed interest to the problem of the elastic enhancement phenomenon. We reexamine the question what the experimentally observed value of the elastic enhancement factor can tell us about the character of dynamics of the intermediate system. Noting first a remarkable connection of this factor with the time delays variance in the case of the standard Gaussian ensembles we then prove the universal nature of such a relation. This reduces our problem to that of calculation of the Dyson's binary form factor in the whole transition region. By the example of systems with no time-reversal symmetry we then demonstrate that the enhancement can serve as a measure of the degree of internal chaos.