Distribution of Scattering Matrix Elements in Quantum Chaotic Scattering

TL;DR

This paper provides an exact analytical solution for the distribution of off-diagonal elements in the scattering matrix of quantum chaotic systems, validated by microwave billiard experiments, advancing understanding of universal scattering properties.

Contribution

It introduces a new supersymmetry-based method to compute the distribution of off-diagonal scattering matrix elements in chaotic systems with and without time-reversal symmetry.

Findings

Exact distribution formulas derived for off-diagonal elements.

Validation with microwave billiard experimental data.

Applicable to systems with preserved and violated time-reversal invariance.

Abstract

Scattering is an important phenomenon which is observed in systems ranging from the micro- to macroscale. In the context of nuclear reaction theory the Heidelberg approach was proposed and later demonstrated to be applicable to many chaotic scattering systems. To model the universal properties, stochasticity is introduced to the scattering matrix on the level of the Hamiltonian by using random matrices. A long-standing problem was the computation of the distribution of the off-diagonal scattering-matrix elements. We report here an exact solution to this problem and present analytical results for systems with preserved and with violated time-reversal invariance. Our derivation is based on a new variant of the supersymmetry method. We also validate our results with scattering data obtained from experiments with microwave billiards.