Semiclassical treatment of quantum chaotic transport with a tunnel barrier

TL;DR

This paper develops a semiclassical matrix model to analyze quantum chaotic transport with a tunnel barrier, providing results valid for any number of channels and comparing favorably with random matrix theory.

Contribution

It introduces a semiclassical matrix model for quantum chaotic transport with a tunnel barrier, valid for arbitrary channel numbers, and simplifies the calculation of transport moments.

Findings

Transport moments expressed as power series in reflection probability

Results are valid in the quantum regime, not just for large channel numbers

Model predictions agree with random matrix theory where tested

Abstract

We consider the problem of a semiclassical description of quantum chaotic transport, when a tunnel barrier is present in one of the leads. Using a semiclassical approach formulated in terms of a matrix model, we obtain transport moments as power series in the reflection probability of the barrier, whose coefficients are rational functions of the number of open channels M. Our results are therefore valid in the quantum regime and not only when $M\gg 1$. The expressions we arrive at are not identical with the corresponding predictions from random matrix theory, but are in fact much simpler. Both theories agree as far as we can test.