Exactly solvable models through the generalized empty interval method: multi-species and more-than-two-site interactions

TL;DR

This paper develops exactly solvable models for multi-species reaction-diffusion systems with complex interactions on a one-dimensional lattice, identifying conditions for closed-form solutions of certain expectation values.

Contribution

It derives necessary and sufficient constraints on interaction rates to ensure the closedness of the evolution equations for multi-species systems with more-than-two-site interactions.

Findings

Derived constraints for interaction rates ensuring solvability.

Extended the empty interval method to multi-species, multi-site interactions.

Provided a framework for exactly solvable reaction-diffusion models.

Abstract

Multi-species reaction-diffusion systems, with more-than-two-site interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution equation for $E^{\mathbf a}_n(t)$'s, the expectation value of the product of certain linear combination of the number operators on $n$ consecutive sites at time $t$.