Solvable reaction-diffusion processes without exclusion

TL;DR

This paper classifies and solves all integrable reaction-diffusion models without exclusion on a 1D lattice, including annihilation, using Bethe ansatz to find exact solutions and probabilities.

Contribution

It introduces a comprehensive classification of integrable reaction-diffusion models without exclusion and provides their exact solutions via Bethe ansatz.

Findings

All integrable models identified by boundary conditions.

Exact N-particle conditional probabilities derived.

Includes models with annihilation processes.

Abstract

For reaction-diffusion processes without exclusion, in which the particles can exist in the same site of a one-dimensional lattice, we study all the integrable models which can be obtained by imposing a boundary condition on the master equation of the asymmetric diffusion process. The annihilation process is also added. The Bethe ansatz solution and the exact N-particle conditional probabilities are obtained.