Autonomous models solvable through the full interval method

TL;DR

This paper introduces the most general class of one-dimensional exclusion reaction-diffusion models that are autonomous and exactly solvable via the full interval method, providing explicit solutions for key correlation functions.

Contribution

It defines a broad class of models solvable by the full interval method and derives explicit solutions for the probability of full intervals and other correlations.

Findings

Explicit solutions for $F_n$ using generating functions

Certain correlation functions remain uncorrelated under specific initial conditions

The models encompass the most general autonomous exclusion processes solvable by this method

Abstract

The most general exclusion single species one dimensional reaction-diffusion models with nearest-neighbor interactions which are both autonomous and can be solved exactly through full interval method are introduced. Using a generating function method, the general solution for, $F_n$, the probability that $n$ consecutive sites be full, is obtained. Some other correlation functions of number operators at nonadjacent sites are also explicitly obtained. It is shown that for a special choice of initial conditions some correlation functions of number operators called full intervals remain uncorrelated.