Distribution of currents in a system of active particles with biased hops and Ising interactions

Abstract

We consider an ensemble of particles performing a biased random walk on a two-dimensional lattice. Due to the adhesion between particles (nearest-neighbor Ising interactions), the probability of hopping depends on the number of neighbors and the strength of adhesive interaction. The asymmetry in the hopping directions leads to a macroscopic current of particles through the system. We theoretically compute the distribution of currents and verify the results in stochastic particle simulations. To make theoretical progress, one has to determine the probabilities of various particle configurations such as single particles, pairs, and different configurations of three-particle clusters. These probabilities are theoretically derived by formulating rate equations for the concentrations of various structures resembling Becker-Döring cluster equations. One intriguing finding is that the concentration of left-handed triplets is not equal to the concentration of right-handed triplets for non-zero asymmetry of hops and non-zero interaction between particles.