Shock fluctuations in the asymmetric simple exclusion process |
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Authors: | P. A. Ferrari L. R. G. Fontes |
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Affiliation: | (1) Instituto de Matemática e Estatística, Universidade de São Paulo, Cx. Postal 20570, 01452-010 São Paulo, SP, Brasil |
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Abstract: | Summary We consider the one dimensional nearest neighbors asymmetric simple exclusion process with ratesq andp for left and right jumps respectively;q<p. Ferrari et al. (1991) have shown that if the initial measure isv,, a product measure with densities and to the left and right of the origin respectively, <, then there exists a (microscopic) shock for the system. A shock is a random positionXt such that the system as seen from this position at timet has asymptotic product distributions with densities and to the left and right of the origin respectively, uniformly int. We compute the diffusion coefficient of the shockD=limtt–1(E(Xt)2–(EXt)2) and findD=(p–q)(–)–1((1–)+(1–)) as conjectured by Spohn (1991). We show that in the scale the position ofXt is determined by the initial distribution of particles in a region of length proportional tot. We prove that the distribution of the process at the average position of the shock converges to a fair mixture of the product measures with densities and . This is the so called dynamical phase transition. Under shock initial conditions we show how the density fluctuation fields depend on the initial configuration. |
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Keywords: | 60K35 82C22 82C24 82C41 |
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