Nonuniform autonomous one-dimensional exclusion nearest-neighbor reaction-diffusion models

TL;DR

This paper introduces a class of nonuniform one-dimensional reaction-diffusion models with boundary conditions, providing a transfer matrix method for static solutions and exploring phase transitions, exemplified by a solvable nonuniform voter model.

Contribution

It defines superautonomous models where the transfer matrix can be explicitly obtained, and solves a nonuniform voter model as a key example.

Findings

Transfer matrix can be expressed in closed form under certain reaction rate conditions.

Static phase transitions are possible in these models.

Explicit solution provided for a nonuniform voter model.

Abstract

The most general nonuniform reaction-diffusion models on a one-dimensional lattice with boundaries, for which the time evolution equations of corre- lation functions are closed, are considered. A transfer matrix method is used to find the static solution. It is seen that this transfer matrix can be obtained in a closed form, if the reaction rates satisfy certain conditions. We call such models superautonomous. Possible static phase transitions of such models are investigated. At the end, as an example of superau- tonomous models, a nonuniform voter model is introduced, and solved explicitly.