MICROSCOPIC SHOCKS IN ONE-DIMENSIONAL DRIVEN SYSTEMS

Systems of particles sitting on the integers and interacting only by simple exclusion are considered. An electric field is imposed on the motion. Each particle after a time that may be random or deterministic jumps to its right nearest neighbor site provided that it is empty. The time can be either continuous or discrete. Assume that at time zero we start from a configuration chosen according to an appropriate distribution that has density p to the left of the origin and lambda to its right, p < lambda. Then it is possible to define a position X(t) that we call microscopic shock such that the distribution of the configuration at time t has roughly densities p and lambda to the left and right of X(t), respectively, uniformly in t. The connection between the systems and the Burgers equation is reviewed. The microscopic shock is related to the characteristics of the Burgers equation. Laws of large numbers and lower bounds for the diffusion coefficient of the shock are given.