Shocks in asymmetric one-dimensional exclusion processes

P.A. Ferrari and L. R. G. Fontes

We review recent results concerning the local structure of the shocks in the one dimensional nearest neighbors totally asymmetric simple exclusion process. A microscopic shock is a random position X_t such that the system as seen from this position at time t has a stationary distribution which is equivalent to the product measure with densities \rho and \la to the left and right of the origin respectively. The diffusion coefficient of the shock D=\limt t^{-1}(E(X_t)^2 - (EX_t)^2) has been found to be D=(\la-\rho)^{-1} (\rho(1-\rho)+\la(1-\la)). 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. 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 \la. This is the so called dynamical phase transition. Under shock initial conditions the density fluctuation fields depend on the initial configuration. The results are a little weaker in the asymmetric case, when jumps to the left are also allowed. Key words: Asymmetric simple exclusion. Shock fluctuations. Central limit theorem. Dynamical phase transition. Density fluctuation fields.}}}}

Last modified: Tue Aug 20 10:19:17 GMT-0300 1996