 9329 P.A.Ferrari , L.R.G.Fontes
 Shock fluctuations in the asymmetric simple exclusion process
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Feb 11, 93

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Abstract. 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, Kipnis and Saada
(1991) have shown that if the initial measure is $\nu_{\rho,\lambda}$, a product
measure with densities $\rho$ and $\lambda$ to the left and right of the origin
respectively, $\rho<\lambda$, then there exists a (microscopic) shock for the system.
A shock is a random
position $X_t$ such that the system as seen from this position at time $t$ has
asymptotic product distributions with densities $\rho$ and $\lambda$ to the left
and right of the origin respectively, uniformly in $t$. We compute the
diffusion coefficient of the shock $D=\lim_{t\to\infty} t^{1}(E(X_t)^2  (EX_t)^2)$ and
find $D=(pq)(\lambda\rho)^{1} (\rho(1\rho)+\lambda(1\lambda))$ as conjectured by
Spohn (1991). We show that in the scale $\sqrt t$ the position of $X_t$ is
determined by the initial distribution of particles in a region of lenght
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 $\rho$ and $\lambda$. 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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