Diffusion of tagged particle in an exclusion process

Diffusion of tagged particle in an exclusion process.

We study the diffusion of tagged hard-core interacting Brownian point particles under the influence of an external force field in one dimension. Using the Jepsen line we map this many-particle problem onto a single particle one. We obtain general equations for the distribution and the mean-square displacement <(xT)2> of the tagged center particle valid for rather general external force fields a...

Dynamics of a tagged particle in the asymmetric exclusion process with the step initial condition

The one-dimensional totally asymmetric simple exclusion process (TASEP) is considered. We study the time evolution property of a tagged particle in the TASEP with the step initial condition. Calculated is the multi-time joint distribution function of its position. Using the relation of the dynamics of the TASEP to the Schur process, we show that the function is represented as the Fredholm deter...

Dynamics of a Tagged Particle in the Asymmetric Exclusion Process with Particlewise Disorder

We consider the one-dimensional totally asymmetric asymmetric simple exclusion process. We particularly concentrate on the case where each hopping rate depends on each particle. In the step initial condition, where all sites from the left of some site are occupied and all other sites are empty, we discuss a dynamics of a particular particle (tagged particle). We show that the position fluctuati...

Asymptotic Behavior of a Tagged Particle in Simple Exclusion Processes

Quenched Nonequilibrium Central Limit Theorem for a Tagged Particle in the Exclusion Process with Bond Disorder

For a sequence of i.i.d. random variables {ξx : x ∈ Z} bounded above and below by strictly positive finite constants, consider the nearestneighbor one-dimensional simple exclusion process in which a particle at x (resp. x + 1) jumps to x + 1 (resp. x) at rate ξx. We examine a quenched nonequilibrium central limit theorem for the position of a tagged particle in the exclusion process with bond d...