Full counting statistics of chaotic cavities from classical action correlations

TL;DR

This paper develops a semiclassical approach to calculate the full counting statistics of quantum transport in chaotic cavities, demonstrating agreement with random matrix theory across multiple moments.

Contribution

It introduces a trajectory-based semiclassical method for full counting statistics, extending previous conductance and noise analyses to higher moments.

Findings

Semiclassical results match random matrix theory predictions for all moments.

The method involves correlated classical trajectories for each moment calculation.

Provides a unified framework for quantum transport statistics in chaotic systems.

Abstract

We present a trajectory-based semiclassical calculation of the full counting statistics of quantum transport through chaotic cavities, in the regime of many open channels. Our method to obtain the $m$th moment of the density of transmission eigenvalues requires two correlated sets of $m$ classical trajectories, therefore generalizing previous works on conductance and shot noise. The semiclassical results agree, for all values of $m$, with the corresponding predictions from random matrix theory.