Current fluctuations in the one dimensional Symmetric Exclusion Process with open boundaries

Details Current fluctuations in the one dimensional Symmetric Exclusion Process with open boundaries Current fluctuations in the one dimensional Symmetric Exclusion Process with open boundaries

2003-10-20

arxiv.org/abs/cond-mat/0310453v1

Journal of Statistical Physics 115 (2004) 717

Physics

Condensed Matter

Disordered Systems and Neural Networks

submitted to Journal of Statistical Physics

Scientific paper

10.1023/B:JOSS.0000022379.95508.

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 Yakovets for one dimensional quantum conductors in the metallic regime.

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