Models solvable through the empty-interval method

TL;DR

This paper characterizes the most general one-dimensional reaction-diffusion models solvable via the empty-interval method, highlighting how particle-generation reactions influence the spectral properties and relaxation times of the system.

Contribution

It identifies the broad class of models solvable through the empty-interval method without restrictions on particle-generation from empty sites.

Findings

Reactions generating particles from two adjacent empty sites create a spectral gap.

Presence of a spectral gap leads to finite relaxation times.

The study extends understanding of solvable reaction-diffusion models.

Abstract

The most general one dimensional reaction-diffusion model with nearest-neighbor interactions solvable through the empty interval method, and without any restriction on the particle-generation from two adjacent empty sites is studied. It is shown that turning on the reactions which generate particles from two adjacent empty sites, results in a gap in the spectrum of the evolution operator (or equivalently a finite relaxation time).