Computer simulation of shock waves in the completely asymmetric simple exclusion process
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}{...
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Published in | Journal of statistical physics Vol. 55; no. 3-4; pp. 611 - 623 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
Heidelberg
Springer
01.05.1989
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Subjects | |
Online Access | Get full text |
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Summary: | 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} |
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ISSN: | 0022-4715 1572-9613 |
DOI: | 10.1007/bf01041600 |