An anti-symmetric exclusion process for two particles on an infinite 1D lattice
نویسندگان
چکیده
A system of two biased, mutually exclusive random walkers on an infinite 1D lattice is studied whereby the intrinsic bias of one particle is equal and opposite to that of the other. The propogator for this system is solved exactly and expressions for the mean displacement and mean square displacement (MSD) are found. Depending on the nature of the intrinsic bias, the system's behaviour displays two regimes, characterised by (i) the particles moving towards each other and (ii) away from each other, both qualitatively different from the case of no bias. The continuous-space limit of the propogator is found and is shown to solve a Fokker-Planck equation for two biased, mutually exclusive Brownian particles with equal and opposite drift velocity.
منابع مشابه
Diffusion of noninteracting particles into a semi-infinite lattice.
Consider a gas of noninteracting particles diffusing into a semi-infinite lattice, Z+×ZD−1, subject to exclusion of double occupancy. An exact closed set of equations can be obtained and solved (in closed form) for the single-site occupancies or densities. Equations for the n-site occupancies couple only to such functions for n and n-1 sites, as for an infinite lattice. Their analysis reveals t...
متن کاملCombinatorics of the Asymmetric Exclusion Process on a Semi-infinite Lattice
We study two versions of the asymmetric exclusion process (ASEP) – an ASEP on a semi-infinite lattice Z with an open left boundary, and an ASEP on a finite lattice with open left and right boundaries – and we demonstrate a surprising relationship between their stationary measures. The semiinfinite ASEP was first studied by Liggett [6] and then Grosskinsky [5], while the finite ASEP had been int...
متن کاملExact time-dependent correlation functions for the symmetric exclusion process with open boundary.
As a simple model for single-file diffusion of hard core particles we investigate the one-dimensional symmetric exclusion process. We consider an open semi-infinite system where one end is coupled to an external reservoir of constant density rho(*) and which initially is in a nonequilibrium state with bulk density rho(0). We calculate the exact time-dependent two-point density correlation funct...
متن کاملExact Solution of the Master Equation for the Asymmetric Exclusion Process
Using the Bethe ansatz, we obtain the exact solution of the master equation for the totally asymmetric exclusion process on an infinite one-dimensional lattice. We derive explicit expressions for the conditional probabilities P (x1, . . . , xN ; t|y1, . . . , yN ; 0) of finding N particles on lattice sites x1, . . . , xN at time t with initial occupation y1, . . . , yN at time t = 0.
متن کاملLattice gases with a point source
We study diffusive lattice gases with local injection of particles, namely we assume that whenever the origin becomes empty, a new particle is immediately injected into the origin. We consider two lattice gases: a symmetric simple exclusion process and random walkers. The interplay between the injection events and the positions of the particles already present implies an effective collective in...
متن کامل