Exact Confirmation of 1D Nonlinear Fluctuating Hydrodynamics for a Two-Species Exclusion Process
Zeying Chen, Jan de Ger, Iori Hiki, Tomohiro Sasamoto
Physical Review Letters | AMER PHYSICAL SOC | Published : 2018
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.
Awarded by National Science Foundation
Awarded by JSPS KAKENHI
The authors are grateful to M. Wheeler for suggesting an idea leading to the formula in Eq. (5) and to P. L. Ferrari, I. Kostov, and H. Spohn for discussions. This work was initiated at KITP Santa Barbara during the program New approaches to non-equilibrium and random systems: KPZ integrability, universality, applications and experiments, which was supported in part by the National Science Foundation under Grant No. NSF PHY11-25915. Part of this work was performed during a stay of all authors at the MATRIX mathematical research institute in Australia during the program Non-equilibrium systems and special functions. J. dG. and Z. C. gratefully acknowledge support from the Australian Research Council. The work of T. S. is supported by JSPS KAKENHI Grants No. JP25103004, No. JP15K05203, No. JP16H06338, No. JP18H03672, and No. JP18H01141.