Solvable multi-species reaction-diffusion processes, including the extended drop-push model

TL;DR

This paper derives the most general boundary conditions for multi-species exclusion processes, introducing new particle interactions, and solves a two-species model with explicit conditional probabilities.

Contribution

It presents a comprehensive boundary condition framework for multi-species exclusion processes, including new interactions and an exactly solvable two-species model.

Findings

Derived the most general boundary conditions for multi-species exclusion processes.

Introduced new particle interactions, including extended drop-push.

Solved the two-species model and calculated conditional probabilities.

Abstract

By considering the master equation of asymmetric exclusion process on a one-dimensional lattice, we obtain the most general boundary condition of the multi-species exclusion processes in which the number of particles is constant in time. This boundary condition introduces the various interactions to the particles, including ones which have been studied yet and the new ones. In these new models, the particles have simultaneously diffusion, the two-particle interactions $A_\alpha A_\beta\to A_\gamma A_\delta$, and the $n$-particle extended drop-push interaction. The constraints on reaction rates are obtained and in two-species case, they are solved to obtain a solvable model. The conditional probabilities of this model are calculated.