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

B Derrida, B Doucot, P. -E. Roche

Published 2003-10-20Version 1

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.