Burgers equation with finite particle correction of the asymmetric simple exclusion process derived from the derivative nonlinear Schrödinger equation

2020/05/07 by Yuki Ishiguro, Jun Sato, Ishiguro, Yuki +3
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Cold Atom Physics and Bose-Einstein Condensates #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2005.03715

openalex publication_date 2020/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the dynamics of the asymmetric simple exclusion process (ASEP) on a ring. The ASEP is equivalent to the derivative nonlinear Schrödinger equation (DNLS), which is integrable quantum field theory, in the continuous limit. We derive the Burgers equation with finite particle correction from the DNLS and numerically confirm that the obtained Burgers equation describes the dynamics of the ASEP at small numbers of particles better than the conventional Burgers equation.

Related

• An exactly solvable asymmetric K-exclusion process
• Derivation of the stochastic Burgers equation with Dirichlet boundary conditions from the WASEP
• Spontaneous Breaking of Translational Invariance and Spatial\n Condensation in Stationary States on a Ring: II. The Charged System and the\n Two-component Burgers Equations
• Derivation of viscous Burgers equations from weakly asymmetric exclusion processes
• Asymmetric simple exclusion process on a ring conditioned on enhanced flux