Systematic approach to statistics of conductance and shot-noise in chaotic cavities

TL;DR

This paper introduces a new random matrix theory-based method to compute conductance and shot-noise moments in chaotic quantum cavities, providing explicit asymptotics and distribution functions for systems with varying channel numbers.

Contribution

It develops a novel approach combining Selberg integrals and symmetric functions to analyze conductance and shot-noise in chaotic cavities for arbitrary channel counts.

Findings

Derived explicit formulas for moments and cumulants of conductance and shot-noise.

Established asymptotic behavior of cumulants in large-channel limit.

Provided Pfaffian representation for distribution functions and analyzed their edge behavior.

Abstract

Applying random matrix theory to quantum transport in chaotic cavities, we develop a novel approach to computation of the moments of the conductance and shot-noise (including their joint moments) of arbitrary order and at any number of open channels. The method is based on the Selberg integral theory combined with the theory of symmetric functions and is applicable equally well for systems with and without time-reversal symmetry. We also compute higher-order cumulants and perform their detailed analysis. In particular, we establish an explicit form of the leading asymptotic of the cumulants in the limit of the large channel numbers. We derive further a general Pfaffian representation for the corresponding distribution functions. The Edgeworth expansion based on the first four cumulants is found to reproduce fairly accurately the distribution functions in the bulk even for a small number of channels. As the latter increases, the distributions become Gaussian-like in the bulk but are always characterized by a power-law dependence near their edges of support. Such asymptotics are determined exactly up to linear order in distances from the edges, including the corresponding constants.