Systematic Analytical Approach to Correlation Functions of Resonances in Quantum Chaotic Scattering

TL;DR

This paper develops a systematic analytical method to derive the joint probability density and correlation functions of resonances in quantum chaotic scattering systems with broken time-reversal symmetry, revealing Ginibre-like statistics for many open channels.

Contribution

It introduces a novel combination of Itzykson-Zuber integration and nonlinear sigma-model techniques to analyze resonance statistics in complex quantum systems.

Findings

Derived explicit n-point correlation functions in the complex plane.

Established Ginibre-like resonance statistics for multiple open channels.

Provided a method applicable when orthogonal polynomial techniques are unsuitable.

Abstract

We solve the problem of resonance statistics in systems with broken time-reversal invariance by deriving the joint probability density of all resonances in the framework of a random matrix approach and calculating explicitly all n-point correlation functions in the complex plane. As a by-product, we establish the Ginibre-like statistics of resonances for many open channels. Our method is a combination of Itzykson-Zuber integration and a variant of nonlinear $\sigma-$model and can be applied when the use of orthogonal polynomials is problematic.