Solvable multi-species reaction-diffusion processes, with particle-dependent hopping rates

TL;DR

This paper introduces two new exactly solvable multi-species reaction-diffusion models with particle-dependent hopping rates, derived from the asymmetric exclusion process, and analyzes their two-particle probabilities and long-term behavior.

Contribution

The paper develops two novel multi-species reaction-diffusion models with particle-dependent hopping rates that are exactly solvable via Bethe ansatz, expanding the class of solvable stochastic processes.

Findings

Models are exactly solvable using Bethe ansatz.

Two-particle conditional probabilities are explicitly calculated.

Large-time behavior of the systems is characterized.

Abstract

By considering the master equation of the totally asymmetric exclusion process on a one-dimensional lattice and using two types of boundary conditions (i.e. interactions), two new families of the multi-species reaction-diffusion processes, with particle-dependent hopping rates, are investigated. In these models (i.e. reaction-diffusion and drop-push systems), we have the case of distinct particles where each particle $A_\alpha$ has its own intrinsic hopping rate $v_{\alpha}$. They also contain the parameters that control the annihilation-diffusion rates (including pair-annihilation and coagulation to the right and left). We obtain two distinct new models. It is shown that these models are exactly solvable in the sense of the Bethe anstaz. The two-particle conditional probabilities and the large-time behavior of such systems are also calculated.