Exact confirmation of 1D nonlinear fluctuating hydrodynamics for a two-species exclusion process

Zeying Chen; Jan de Gier; Iori Hiki; Tomohiro Sasamoto

doi:10.1103/physrevlett.120.240601

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arXiv · 1803.06829

Exact confirmation of 1D nonlinear fluctuating hydrodynamics for a two-species exclusion process

Zeying Chen·Jan de Gier·Iori Hiki·Tomohiro Sasamoto

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Abstract

We consider current statistics for a two species exclusion process of particles hopping in opposite directions on a one-dimensional lattice. We derive an exact formula for the Green's function as well as for a joint current distribution of the model, and study its long time behavior. For a step type initial condition, we show that the limiting distribution is a product of the Gaussian and the GUE Tracy-Widom distribution. This is the first analytic confirmation for a multi-component system of a prediction from the recently proposed non-linear fluctuating hydrodynamics for one dimensional systems.

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Zeying Chen, Jan de Gier, Iori Hiki, Tomohiro Sasamoto. 2018-03-19. Exact confirmation of 1D nonlinear fluctuating hydrodynamics for a two-species exclusion process. https://doi.org/10.1103/physrevlett.120.240601

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