Statistics of quantum transport in chaotic cavities with broken time-reversal symmetry

TL;DR

This paper derives exact statistical properties of quantum transport in chaotic cavities with broken time-reversal symmetry, providing explicit formulas for charge cumulants and conductance moments for any number of channels.

Contribution

It presents explicit closed-form expressions for the average, variance, and higher cumulants of quantum transport traces in chaotic cavities with broken time-reversal symmetry, valid for any number of channels.

Findings

Explicit formulas for average and variance of transport traces

Exact charge cumulants of all orders

Moments of conductance for arbitrary channels

Abstract

The statistical properties of quantum transport through a chaotic cavity are encoded in the traces $\T={\rm Tr}(tt^\dag)^n$, where $t$ is the transmission matrix. Within the Random Matrix Theory approach, these traces are random variables whose probability distribution depends on the symmetries of the system. For the case of broken time-reversal symmetry, we present explicit closed expressions for the average value and for the variance of $\T$ for all $n$. In particular, this provides the charge cumulants $\Q$ of all orders. We also compute the moments $<g^n>$ of the conductance $g=\mathcal{T}_1$. All the results obtained are exact, {\it i.e.} they are valid for arbitrary numbers of open channels.