Statistics of quantum transport in weakly non-ideal chaotic cavities

TL;DR

This paper develops a perturbation theory for electronic transport statistics in chaotic quantum cavities with weakly non-ideal leads, providing explicit formulas for conductance and shot-noise moments.

Contribution

It introduces a systematic perturbation approach using symmetric functions and Selberg integrals for arbitrary channel numbers in chaotic cavities with broken time-reversal symmetry.

Findings

Explicit formulas for average conductance and shot-noise up to second order.

Perturbation theory valid for arbitrary number of channels.

Analysis of higher moments of conductance to leading order.

Abstract

We consider statistics of electronic transport in chaotic cavities where time-reversal symmetry is broken and one of the leads is weakly non-ideal, i.e. it contains tunnel barriers characterized by tunneling probabilities $\Gamma_i$. Using symmetric function expansions and a generalized Selberg integral, we develop a systematic perturbation theory in $1-\Gamma_i$ valid for arbitrary number of channels, and obtain explicit formulas up to second order for the average and variance of the conductance, and for the average shot-noise. Higher moments of the conductance are considered to leading order.