Computer simulation of shock waves in the completely asymmetric simple exclusion process

• Published in: Journal of statistical physics Vol. 55; no. 3-4; pp. 611 - 623
• Main Authors: BOLDRIGHINI, C, COSIMI, G, FRIGIO, S, GRASSO NUNES, M
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer 01.05.1989
• Subjects: 656002 - Condensed Matter Physics- General Techniques in Condensed Matter- (1987-); 657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics; ASYMMETRY; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPUTERIZED SIMULATION; CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; DIFFERENTIAL EQUATIONS; DIFFUSION; EQUATIONS; EQUILIBRIUM; Exact sciences and technology; Fluctuation phenomena, random processes, noise, and brownian motion; INTERACTIONS; MATHEMATICAL MODELS; MECHANICS; ONE-DIMENSIONAL CALCULATIONS; PARTIAL DIFFERENTIAL EQUATIONS; PARTICLE INTERACTIONS; PARTICLE MODELS; PAULI PRINCIPLE; Physics; QUANTUM MECHANICS; SHOCK WAVES; SIMULATION; STABILITY; STATISTICAL MECHANICS; Statistical physics, thermodynamics, and nonlinear dynamical systems; WAVE PROPAGATION; ZERO-RANGE APPROXIMATION; Scaling law; Computer simulation; Specific gravity; One dimensional model; Critical phenomenon; Drift velocity; Shock wave
• ISSN: 0022-4715; 1572-9613
• DOI: 10.1007/bf01041600

The authors study the evolution of the completely asymmetric simple exclusion process in one dimension, with particles moving only to the right, for initial configurations corresponding to average density {rho}{sub {minus}} ({rho}{sub +}) left (right) of the origin, {rho}{sup {minus}} {<=} {rho}{sub +}. The microscopic shock position is identified by introducing a second-class particle. Results indicate that the shock profile is stable, and that the distribution as seen from the shock position N(t) tends, as time increases, to a limiting distribution, which is locally close to an equilibrium distribution far from the shock. Moreover N(t) = V {times} t, with V = 1 {minus} {rho}{sub {minus}} {minus} {rho}{sub +}, as predicted, and the dispersion of N(t), {sigma}{sup 2}(t), behaves linearly, for not too small values of {rho}{sub +} {minus} {rho}{sup {minus}}, i.e., {sigma}{sup 2}(t) = S {times} t, where S is equal, up to a scaling factor, to the value S{sub WA} predicted in the weakly asymmetric case. For {rho}{sub +} = {rho}{sub {minus}} they find agreement with the conjecture {sigma}{sup 2}(t) = {anti S} {times} t{sup 4/3}