Reaction-Diffusion Processes as Physical Realizations of Hecke Algebras

TL;DR

This paper demonstrates that the dynamics of certain one-dimensional diffusion and reaction processes can be modeled using Hecke algebras, revealing algebraic structures underlying physical systems.

Contribution

It establishes a novel connection between reaction-diffusion processes and Hecke algebra representations, including hermitian and non-hermitian cases.

Findings

Diffusion processes correspond to reducible hermitian Hecke algebra representations.

Reaction processes relate to non-hermitian supersymmetric quotients of Hecke algebras.

The algebraic framework provides new insights into the structure of reaction-diffusion systems.

Abstract

We show that the master equation governing the dynamics of simple diffusion and certain chemical reaction processes in one dimension give time evolution operators (Hamiltonians) which are realizations of Hecke algebras. In the case of simple diffusion one obtains, after similarity transformations, reducible hermitian representations while in the other cases they are non-hermitian and correspond to supersymmetric quotients of Hecke algebras.