2003/12/27 by P.-E. Roche, Philippe-E. Roche, Bernard Derrida +2 · 1 citation
Mathematics · Physics and Astronomy · #Computer science #Current (fluid) #Higher-order statistics #Mathematics #Mesoscopic physics #Physics #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Skewness #Statistical physics #Statistics #Telecommunications #Theoretical and Computational Physics #cond-mat.mes-hall #cond-mat.stat-mech
paper · pdf · doi:10.1140/epjb/e2005-00087-5
published as European Physical Journal B 43 (2005) 529 · Submitted to Eur. Phys. J. B
arxiv created 2003/12/27 · openalex publication_date 2005/02/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.