Statistics of time delay in quantum chaotic transport

TL;DR

This paper investigates the statistical properties of the time delay matrix in quantum chaotic transport without time-reversal symmetry, using random matrix theory and semiclassical methods to derive and compare key statistical results.

Contribution

It provides exact random matrix results and semiclassical perturbation series for the time delay matrix, demonstrating their agreement for various statistical properties.

Findings

Exact average values of polynomial functions of Q obtained

Semiclassical perturbation series derived for energy-dependent correlations

Agreement shown between random matrix theory and semiclassical results

Abstract

We study the statistical properties of the time delay matrix $Q$ in the context of quantum transport through a chaotic cavity, in the absence of time-reversal invariance. First, we approach the problem from the point of view of random matrix theory, and obtain exact results that provide the average value of any polynomial function of $Q$. We then consider the problem from the point of view of the semiclassical approximation, obtaining the entire perturbation series for some energy-dependent correlation functions. Using these correlation functions, we show agreement between the random matrix and the semiclassical approaches for several statistical properties.