Finite-dimensional representation of the quadratic algebra of a generalized coagulation-decoagulation model

TL;DR

This paper analyzes a generalized coagulation-decoagulation model on a lattice, showing that its quadratic algebra admits a four-dimensional matrix representation under certain conditions, and studies shock front dynamics as random walkers.

Contribution

It demonstrates a finite-dimensional matrix representation of the quadratic algebra and characterizes shock front behavior in the model.

Findings

Quadratic algebra has a four-dimensional representation under specific rate constraints.

Shock fronts behave as two repelling random walkers.

Steady-state properties are derived using matrix-product approach.

Abstract

The steady-state of a generalized coagulation-decoagulation model on a one-dimensional lattice with reflecting boundaries is studied using a matrix-product approach. It is shown that the quadratic algebra of the model has a four-dimensional representation provided that some constraints on the microscopic reaction rates are fulfilled. The dynamics of a product shock measure with two shock fronts, generated by the Hamiltonian of this model, is also studied. It turns out that the shock fronts move on the lattice as two simple random walkers which repel each other provided that the same constraints on the microscopic reaction rates are satisfied.