Parametric S-matrix fluctuations in quantum theory of chaotic scattering

TL;DR

This paper derives a universal, non-perturbative expression for the autocorrelation of S-matrix elements in quantum chaotic scattering, revealing a new signature of quantum chaos in open systems.

Contribution

It introduces an exact supersymmetry-based formula for S-matrix fluctuations under arbitrary perturbations in quantum chaotic systems.

Findings

Derived a universal autocorrelation function for S-matrix elements.

Identified a new signature of quantum chaos in open systems.

Validated universality through appropriate parameter rescaling.

Abstract

We study the effects of an arbitrary external perturbation in the statistical properties of the S-matrix of quantum chaotic scattering systems in the limit of isolated resonances. We derive, using supersymmetry, an exact non-perturbative expression for the parameter dependent autocorrelator of two S-matrix elements. Universality is obtained by appropriate rescaling of the physical parameters. We propose this universal function as a new signature of quantum chaos in open systems.