Semiclassical calculation of time delay statistics in chaotic quantum scattering

TL;DR

This paper develops a semiclassical method to calculate the statistical moments of the Wigner--Smith time delay matrix in chaotic quantum scattering, linking classical dynamics with quantum properties.

Contribution

It introduces a matrix integral approach to compute all moments of the time delay matrix for systems with chaotic dynamics, valid for broken time reversal symmetry.

Findings

Results depend only on classical dwell time and number of channels

Agreement with random matrix theory confirmed in special cases

Provides a combinatorial identity related to the theory

Abstract

We present a semiclassical calculation, based on classical action correlations implemented by means of a matrix integral, of all moments of the Wigner--Smith time delay matrix, $Q$, in the context of quantum scattering through systems with chaotic dynamics. Our results are valid for broken time reversal symmetry and depend only on the classical dwell time and the number of open channels, $M$, which is arbitrary. Agreement with corresponding random matrix theory reduces to an identity involving some combinatorial concepts, which can be proved in special cases.