Exact solution of a one-parameter family of asymmetric exclusion processes

Abstract

We define a family of asymmetric processes for particles on a one-dimensional lattice, depending on a continuous parameter $\ensuremath{\lambda}\ensuremath{\in}[0,1]$, interpolating between the completely asymmetric processes (for $\ensuremath{\lambda}=1)$ and the $n=1$ drop-push models (for $\ensuremath{\lambda}=0)$. For arbitrary $\ensuremath{\lambda}$, the model describes an exclusion process, in which a particle pushes its right neighboring particles to the right, with rates depending on the number of these particles. Using the Bethe ansatz, we obtain the exact solution of the master equation.