Exact domain wall theory for deterministic TASEP with parallel update
Mon, Nov. 04th 2013, 14:00-15:00
Salle Claude Itzykson, Bât. 774, Orme des Merisiers
Domain wall theory (DWT) has proved to be a powerful tool for the analysis of many statistical systems among which one-dimensional transport processes. In this talk I will review how it was implemented for the Totally Asymmetric Simple Exclusion Process (TASEP) with random sequential update, which presents relatively large fluctuations. This formulation was found to give accurate predictions for this TASEP and several of its variants. However, a general implementation of DWT is still missing in the case of updates with less fluctuations, which are often more relevant for applications. I shall adress this issue by showing how an exact DWT can be developed for TASEP with parallel update and deterministic bulk motion (hopping probability equal to one). Remarkably, the dynamics of this system can be described by the motion of a 'flag' similar to the domain wall not only on the coarse-grained level but also exactly on the microscopic scale for arbitrary system size. All properties of this latter TASEP shall be shown to follow from the solution of a closed bivariate master equation whose variables are not only the position but also the velocity of the flag. In the continuum limit this exactly soluble model then allows one to perform a first principle derivation of a Fokker-Planck equation for the position of the wall with a diffusion constant different from the one obtained with the traditional DWT.