Shock fluctuations in the asymmetric simple exclusion process
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چکیده
We consider the one dimensional nearest neighbors asymmetric simple exclusion process with rates q and p for left and right jumps respectively; q < p. Ferrari et al. (1991) have shown that if the initial measure is vp, 4, a product measure with densities p and 2 to the left and right of the origin respectively, p < 2, then there exists a (microscopic) shock for the system. A shock is a random position Xt such that the system as seen from this position at time t has asymptotic product distributions with densities p and 2 to the left and right of the origin respectively, uniformly in t. We compute the diffusion coefficient of the shock D = limt.~ t l ( E ( X t ) 2 -( E X t ) 2) and find D = (p q)(2 p)l(p(1 p) + 2(1 2)) as conjectured by Spohn (1991). We show that in the scale ~ the position of Xt is determined by the initial distribution of particles in a region of length proportional to t. 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 p and 2. 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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تاریخ انتشار 1993