Current fluctuations in the one-dimensional symmetric exclusion process with open boundaries

We calculate the first four cumulants of the integrated current of the one dimensional symmetric simple exclusion process of $N$ sites with open boundary conditions. For large system size $N$, the generating function of the integrated current depends on the densities $\rho_a$ and $\rho_b$ of the two...

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Bibliographic Details
Published in:Journal of statistical physics 2004-05, Vol.115 (3-4), p.717-748
Main Authors: DERRIDA, B, DOUCOT, B, ROCHE, P.-E
Format: Article
Language:English
Subjects:
Condensed Matter
Disordered Systems and Neural Networks
Exact sciences and technology
Mesoscopic Systems and Quantum Hall Effect
Other
Physics
Statistical Mechanics
Statistical physics, thermodynamics, and nonlinear dynamical systems
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Summary:We calculate the first four cumulants of the integrated current of the one dimensional symmetric simple exclusion process of $N$ sites with open boundary conditions. For large system size $N$, the generating function of the integrated current depends on the densities $\rho_a$ and $\rho_b$ of the two reservoirs and on the fugacity $z$, the parameter conjugated to the integrated current, through a single parameter.Based on our expressions for these first four cumulants, we make a conjecture which leads to a prediction for all the higher cumulants.In the case $\rho_a=1$ and $\rho_b=0$, our conjecture gives the same universal distribution as the one obtained by Lee, Levitov and Yakovetsfor one dimensional quantum conductors in the metallic regime.
ISSN:0022-4715
1572-9613
DOI:10.1023/b:joss.0000022379.95508.b2