Effect of a tunnel barrier on time delay statistics

TL;DR

This paper introduces a semiclassical method to analyze how tunnel barriers affect time delay statistics in quantum chaotic systems with broken time-reversal symmetry, providing both asymptotic series and conjectured exact formulas.

Contribution

It presents a novel semiclassical framework for time delay statistics considering tunnel barriers, including asymptotic series and conjectured exact expressions.

Findings

Asymptotic series in barrier reflectivity with rational coefficients

Conjectured exact formulas valid for all reflectivity and channel numbers

Numerical verification of specific statistical moments

Abstract

We develop a semiclassical approach for the statistics of the time delay in quantum chaotic systems in the presence of a tunnel barrier, for broken time-reversal symmetry. Results are obtained as asymptotic series in powers of the reflectivity of the barrier, with coefficients that are rational functions of the channel number. Exact expressions, valid for arbitrary reflectivity and channel number, are conjectured and numerically verified for specific families of statistical moments.