Nonlinear statistics of quantum transport in chaotic cavities

TL;DR

This paper uses random matrix theory and Selberg's integral to analytically derive moments and statistical properties of quantum transport in chaotic cavities, revealing universal behaviors in shot-noise fluctuations.

Contribution

It provides explicit formulas for moments, skewness, kurtosis, and shot-noise variance in chaotic cavities with arbitrary channel numbers, extending understanding of quantum transport statistics.

Findings

Exact expressions for conductance and charge skewness and kurtosis.

Shot-noise variance approaches a universal value for large channel numbers.

Results are valid for any number of propagating channels.

Abstract

In the framework of the random matrix approach, we apply the theory of Selberg's integral to problems of quantum transport in chaotic cavities. All the moments of transmission eigenvalues are calculated analytically up to the fourth order. As a result, we derive exact explicit expressions for the skewness and kurtosis of the conductance and transmitted charge as well as for the variance of the shot-noise power in chaotic cavities. The obtained results are generally valid at arbitrary numbers of propagating channels in the two attached leads. In the particular limit of large (and equal) channel numbers, the shot-noise variance attends the universal value 1/(64\beta) that determines a universal Gaussian statistics of shot-noise fluctuations in this case.