Statistics of conductance and shot-noise power for chaotic cavities

TL;DR

This paper provides an analytical study of the statistical properties of conductance and shot-noise power in chaotic cavities, deriving explicit formulas for their distributions and cumulants for arbitrary channel numbers and symmetry classes.

Contribution

It introduces a novel analytical approach using Selberg's integral to compute cumulants and distributions of conductance and shot-noise in chaotic cavities with arbitrary parameters.

Findings

Derived explicit formulas for conductance and shot-noise distributions.

Calculated the first four cumulants of conductance and two of shot-noise.

Confirmed analytical results with numerical simulations.

Abstract

We report on an analytical study of the statistics of conductance, $g$, and shot-noise power, $p$, for a chaotic cavity with arbitrary numbers $N_{1,2}$ of channels in two leads and symmetry parameter $\beta = 1,2,4$. With the theory of Selberg's integral the first four cumulants of $g$ and first two cumulants of $p$ are calculated explicitly. We give analytical expressions for the conductance and shot-noise distributions and determine their exact asymptotics near the edges up to linear order in distances from the edges. For $0<g<1$ a power law for the conductance distribution is exact. All results are also consistent with numerical simulations.