An exact solution for a quasi-two-dimensional exclusion process

We consider a disordered asymmetric exclusion process with two kinds of particles (labelled 1 and 2, say) on a finite two-dimensional toroidal lattice. The dynamics is controlled by particles of type 1, which only move horizontally, with individual hopping rates. The motion of particles of type 2 depends on the relative position of these with respect to the 1's, and can be both horizontal and vertical. For this process, we compute the partition function, densities and currents exactly. We observe a novel microscopic Scott Russell linkage phenomenon: the current of 2's in the vertical direction is the same as that of 1's in the horizontal direction.

This is joint work with P. Nadeau.