Quantum transport in chaotic cavities with tunnel barriers

TL;DR

This paper develops a non-perturbative semiclassical method to compute quantum transport moments in chaotic cavities with tunnel barriers, accounting for small channel numbers and non-perturbative effects.

Contribution

It introduces a new explicit power series approach in barrier reflectivity, handling small channel numbers and non-perturbative terms in quantum chaos transport calculations.

Findings

Derived explicit power series expressions for transport moments.

Accounted for non-perturbative effects previously inaccessible.

Extended the method to systems with multiple leads.

Abstract

We bring together the semiclassical approximation, matrix integrals and the theory of symmetric polynomials in order to solve a long standing problem in the field of quantum chaos: to compute transport moments when tunnel barriers are present and the number of open channels, $M$, is small. In contrast to previous approaches, ours is non-perturbative in $M$; instead, we arrive at an explicit expression in the form of a power series in the barrier's reflectivity, whose coefficients are rational functions of $M$. For general moments we must require that the barriers are equal and time reversal symmetry is broken, but for conductance we treat the general situation. Our method accounts for exponentially small non-perturbative terms that were not accessible to previous semiclassical approaches. We also show how to include more than two leads in the system.