Multi-species extension of the solvable partially asymmetric reaction- diffusion processes

TL;DR

This paper extends solvable reaction-diffusion models to multiple species on a one-dimensional lattice, deriving conditions for exact solvability and calculating two-particle probabilities.

Contribution

It introduces three new multi-species models with complex interactions and provides exact solutions for their two-particle conditional probabilities.

Findings

Derived conditions for reaction rates ensuring solvability

Developed three new multi-species reaction-diffusion models

Calculated exact two-particle conditional probabilities

Abstract

By considering the master equation of the partially asymmetric diffusion process on a one-dimensional lattice, the most general boundary condition (i.e. interactions) for the multi-species reaction-diffusion processes is considered. Resulting system has various interactions including diffusion to left and right, two-particle interactions $A_a A_b --> A_c A_d $ and the extended n-particle drop-push interactions to left and right. We obtain three distinct new models. The conditions on reaction rates to ensure the solvability of the resulting models are obtained. The two-particle conditional probabilities are calculated exactly.