Current Fluctuations of the One Dimensional Symmetric Simple Exclusion Process with Step Initial Condition

Bernard Derrida; Antoine Gerschenfeld

doi:10.1007/s10955-009-9772-7

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arXiv · 0902.2364

Current Fluctuations of the One Dimensional Symmetric Simple Exclusion Process with Step Initial Condition

Bernard Derrida·Antoine Gerschenfeld

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Abstract

For the symmetric simple exclusion process on an infinite line, we calculate exactly the fluctuations of the integrated current $Q_t$ during time $t$ through the origin when, in the initial condition, the sites are occupied with density $\rho_a$ on the negative axis and with density $\rho_b$ on the positive axis. All the cumulants of $Q_t$ grow like $\sqrt{t}$. In the range where $Q_t \sim \sqrt{t}$, the decay $\exp [-Q_t^3/t]$ of the distribution of $Q_t$ is non-Gaussian. Our results are obtained using the Bethe ansatz and several identities recently derived by Tracy and Widom for exclusion processes on the infinite line.

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Bernard Derrida, Antoine Gerschenfeld. 2009-02-13. Current Fluctuations of the One Dimensional Symmetric Simple Exclusion Process with Step Initial Condition. https://doi.org/10.1007/s10955-009-9772-7

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