Eur. Phys. J. B 43, 529-541 (2005)
https://doi.org/10.1140/epjb/e2005-00087-5

Mesoscopic full counting statistics and exclusion models

¹ Centre de Recherches sur les Très Basses Températures, Laboratoire du CNRS, associé à l'Université Joseph Fourier, 25 avenue des Martyrs, 38042 Grenoble Cedex 9, France
² Laboratoire Pierre Aigrain, École Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 05, France
³ Laboratoire de Physique Statistique, École Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 05, France
⁴ Laboratoire de Physique Théorique et des Hautes Énergies, Université Denis Diderot, 4 place Jussieu, 75252 Paris Cedex 05, France

Corresponding author: ^a per@grenoble.cnrs.fr

Received: 23 December 2003
Revised: 6 December 2004
Published online: 30 March 2005

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 traditional 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.