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

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 $σ-$model and can be applied when the use of orthogonal polynomials is problematic.