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Updated: Feb 8, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Exact Confirmation of 1D Nonlinear Fluctuating Hydrodynamics for a Two-Species Exclusion Process
Zeying Chen1, Jan de Gier1, Iori Hiki2
1ARC Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS), School of Mathematics and Statistics, The University of Melbourne, Melbourne, Victoria 3010, Australia.
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 Gaussian unitary ensemble Tracy-Widom distributions. This is the first analytic confirmation for a multicomponent system of a prediction from the recently proposed nonlinear fluctuating hydrodynamics for one-dimensional systems.
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