Connection between matrix-product states and superposition of Bernoulli shock measures

TL;DR

This paper explores the relationship between matrix-product states and superpositions of Bernoulli shock measures in a one-dimensional coagulation-decoagulation system, providing a method to compute steady states using algebraic representations.

Contribution

It establishes a connection between matrix-product states and shock measure superpositions, offering a new way to calculate steady states in reaction-diffusion systems.

Findings

Steady states can be expressed as superpositions of Bernoulli shock measures.

Coefficients of the superposition are computed via finite-dimensional algebraic representations.

The approach links matrix-product states with shock measure dynamics in reaction systems.

Abstract

We consider a generalized coagulation-decoagulation system on a one-dimensional discrete lattice with reflecting boundaries. It is known that a Bernoulli shock measure with two shock fronts might have a simple random-walk dynamics, provided that some constraints on the microscopic reaction rates of this system are fulfilled. Under these constraints the steady-state of the system can be written as a linear superposition of such shock measures. We show that the coefficients of this expansion can be calculated using the finite-dimensional representation of the quadratic algebra of the system obtained from a matrix-product approach.