A new family of exactly solvable disordered reaction-diffusion systems

TL;DR

This paper introduces a new family of disordered reaction-diffusion systems solvable via a matrix product approach, providing detailed analysis of their steady-states and a novel algebraic framework.

Contribution

It presents a new generalized quadratic algebra and its matrix representations, expanding the class of exactly solvable disordered reaction-diffusion models.

Findings

Steady-states of two specific models are explicitly derived.

A new algebraic structure enables solving these systems exactly.

The approach can be extended to other disordered reaction-diffusion systems.

Abstract

Using a matrix product method the steady-state of a family of disordered reaction-diffusion systems consisting of different species of interacting classical particles moving on a lattice with periodic boundary conditions is studied. A new generalized quadratic algebra and its matrix representations is introduced. The steady-states of two members of this exactly solvable family of systems are studied in detail.