Mesoscopic Full Counting Statistics and Exclusion models

TL;DR

This paper calculates current fluctuation distributions in classical exclusion models, showing they replicate quantum mesoscopic conductors' statistics and deriving key quantities like shot noise and skewness.

Contribution

It introduces a simplified eigenvalue approach to full counting statistics in exclusion models, applicable to various conductors and including higher-order fluctuations.

Findings

Distribution matches quantum formalism even in small classical systems

Eigenvalue method simplifies calculation of full counting statistics

Results include shot noise, skewness, and higher cumulants for multiple conductors

Abstract

We calculate the distribution of current fluctuations in two simple exclusion models. Although these models are classical, we recover even for small systems such as a simple or a double barrier, the same distibution of current as given by traditionnal formalisms for quantum mesoscopic conductors. Due to their simplicity, the full counting statistics in exclusion models can be reduced to the calculation of the largest eigenvalue of a matrix, the size of which is the number of internal configurations of the system. As examples, we derive the shot noise power and higher order statistics of current fluctuations (skewness, full counting statistics, ....) of various conductors, including multiple barriers, diffusive islands between tunnel barriers and diffusive media. A special attention is dedicated to the third cumulant, which experimental measurability has been demonstrated lately.