Chaotic Scattering on Individual Quantum Graphs

TL;DR

This paper demonstrates that for chaotic scattering on quantum graphs, the semiclassical approximation is exact, and uses advanced mathematical techniques to derive precise correlation functions, aligning with random-matrix theory predictions.

Contribution

It provides an exact analytical framework for quantum chaotic scattering on graphs, confirming the universality of random-matrix results using supersymmetry and saddle-point methods.

Findings

Exact expression for scattering matrix correlations derived

Results agree with random-matrix theory predictions

Conjecture of universal applicability to quantum-chaotic scattering

Abstract

For chaotic scattering on quantum graphs, the semiclassical approximation is exact. We use this fact and employ supersymmetry, the colour-flavour transformation, and the saddle-point approximation to calculate the exact expression for the lowest and asymptotic expressions in the Ericson regime for all higher correlation functions of the scattering matrix. Our results agree with those available from the random-matrix approach to chaotic scattering. We conjecture that our results hold universally for quantum-chaotic scattering.