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Exact Confirmation of 1D Nonlinear Fluctuating Hydrodynamics for a Two-Species Exclusion Process

Zeying Chen, Jan de Gier, Iori Hiki, and Tomohiro Sasamoto
Phys. Rev. Lett. 120, 240601 – Published 15 June 2018

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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  • Received 26 March 2018
  • Revised 28 April 2018

DOI:https://doi.org/10.1103/PhysRevLett.120.240601

© 2018 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Zeying Chen§ and Jan de Gier

  • ARC Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS), School of Mathematics and Statistics, The University of Melbourne, Melbourne, Victoria 3010, Australia

Iori Hiki and Tomohiro Sasamoto*

  • Department of Physics, Tokyo Institute of Technology, Ookayama 2-12-1, Tokyo 152-8551, Japan

  • §zeyingc@student.unimelb.edu.au
  • jdgier@unimelb.edu.au
  • hiki.i@stat.phys.titech.ac.jp
  • *Corresponding author. sasamoto@phys.titech.ac.jp

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Issue

Vol. 120, Iss. 24 — 15 June 2018

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