Distributions of Conductance and Shot Noise and Associated Phase Transitions

TL;DR

This paper analytically derives the full distributions of conductance and shot noise in a chaotic cavity with large N, revealing phase transitions that cause non-Gaussian tails and singularities at distribution junctions.

Contribution

It introduces a novel analytical approach to characterize the full distributions of conductance and shot noise, uncovering phase transitions in the Coulomb gas analogy.

Findings

Distribution exhibits Gaussian core with non-Gaussian tails.

Weak singularity at the Gaussian-non-Gaussian transition point.

Identification of phase transitions in the Coulomb gas model.

Abstract

For a chaotic cavity with two indentical leads each supporting N channels, we compute analytically, for large N, the full distribution of the conductance and the shot noise power and show that in both cases there is a central Gaussian region flanked on both sides by non-Gaussian tails. The distribution is weakly singular at the junction of Gaussian and non-Gaussian regimes, a direct consequence of two phase transitions in an associated Coulomb gas problem.