Shock fluctuations in asymmetric simple exclusion
نویسنده
چکیده
The one dimensional nearest neighbors asymmetric simple exclusion process in used as a microscopic approximation to the Burgers equation. We study the process with rates of jumps p > q to the right and left, respectively, and with initial product measure with densities ~ < 2 to the left and right of the origin, respectively (with shock initial conditions). We prove that a second class particle added to the system at the origin at time zero identifies microscopically the shock for all later times. If this particle is added at another site, then it describes the behavior of a characteristic of the Burgers equation. For vanishing left density (~ = 0) we prove, in the scale t 1/2, that the position of the shock at time t depends only on the initial configuration in a region depending on t. The proofs are based on laws of large numbers for the second class particle.
منابع مشابه
Shock fluctuations in the asymmetric simple exclusion process
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 p...
متن کاملThe Asymmetric Exclusion Process revisited: Fluctuations and Dynamics in the Domain Wall Picture
We investigate the total asymmetric exclusion process by analyzing the dynamics of the shock. Within this approach we are able to calculate the fluctuations of the number of particles and density profiles not only in the stationary state but also in the transient regime. We find that the analytical predictions and the simulation results are in excellent agreement. PACS numbers: 05.40.-a, 05.60....
متن کاملAn upper bound on the fluctuations of a second class particle
This note proves an upper bound for the fluctuations of a second-class particle in the totally asymmetric simple exclusion process. The proof needs a lower tail estimate for the last-passage growth model associated with the exclusion process. A stronger estimate has been proved for the corresponding discrete time model, but not for the continuous time model we work with. So we take the needed e...
متن کاملFluctuations of the one-dimensional asymmetric exclusion process using random matrix techniques
The studies of fluctuations of the one-dimensional Kardar-Parisi-Zhang universality class using the techniques from random matrix theory are reviewed from the point of view of the asymmetric simple exclusion process. We explain the basics of random matrix techniques, the connections to the polynuclear growth models and a method using the Green’s function.
متن کامل