Particle hopping on a ladder: exact solution using multibalance

TL;DR

This paper introduces a new multibalance condition to exactly solve a particle hopping model on a ladder, revealing complex current behaviors including re-entrance phenomena and differing directions of total and individual currents.

Contribution

The paper develops the multibalance condition, a novel approach that extends exact solutions to particle hopping models beyond pairwise balance, applicable to various systems.

Findings

Exact steady state solutions obtained for different regimes.

Identification of parameter regions with current direction reversal.

Observation of re-entrance phenomena in total current.

Abstract

We study particle hopping on a two-leg ladder where a particle can jump to their immediate neighbours, one at a time, with rates that depend on the occupation of the departure site and a neighbouring site on the other leg. For specific choices of rates, the model can be solved using pairwise balance known earlier. For the other regimes, we introduce a new balance condition called multibalance which helps us in obtaining the exact steady state. The direction of the total current in these models does not necessarily decide the direction of the currents in individual legs; we find the regions in the parameter space where the currents in individual legs alter their direction. In some parameter regime, the total current exhibits the re-entrance phenomena, in the sense that the total current flips its direction with increase of certain parameter and flips it again when the parameter is increased further. It turns out that the multibalance condition we introduce here is very useful and it can be applied generically to several other models. We discuss some of these models in short.