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

B. Derrida (1, 2) , Benoît Douçot (3) , Philippe-Emmanuel Roche (4)

1 LPS - Laboratoire de Physique Statistique de l'ENS
2 Isaac Newton Institute
3 LPTHE - Laboratoire de Physique Théorique et Hautes Energies
4 CRTBT - Centre de Recherches sur les Très Basses Températures

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.

Mots clés: shot noise; open system; Symmetric Simple Exclusion Process; current fluctuations; ruin problems; diffusive medium; full counting statistics; stationary nonequilibrium state; Large deviations

Domaines: Autre [cond-mat.other]; Mécanique statistique [cond-mat.stat-mech]; Systèmes désordonnés et réseaux de neurones [cond-mat.dis-nn]; Systèmes mésoscopiques et effet Hall quantique [cond-mat.mes-hall]

B. Derrida, Benoît Douçot, Philippe-Emmanuel Roche. Current fluctuations in the one dimensional Symmetric Exclusion Process with open boundaries. Journal of Statistical Physics, 2004, 115, pp.717. ⟨10.1023/B:JOSS.0000022379.95508.b2⟩. ⟨hal-00000763⟩