Exact correlation functions in particle-reaction models with immobile particles

TL;DR

This paper derives exact correlation functions for particle-reaction models with immobile particles, revealing detailed stationary states and their entropy, applicable to various lattice structures and initial conditions.

Contribution

It provides exact analytical results for correlation functions in immobile particle models, including their stationary states and entropy, using a generating-function approach.

Findings

Exact correlation functions derived for models with single and multiple species.

Stationary states exhibit non-zero configurational entropy.

Models applicable to chains, Bethe lattice, and related to adsorption and granular materials.

Abstract

Exact results on particle-densities as well as correlators in two models of immobile particles, containing either a single species or else two distinct species, are derived. The models evolve following a descent dynamics through pair-annihilation where each particle interacts at most once throughout its entire history. The resulting large number of stationary states leads to a non-vanishing configurational entropy. Our results are established for arbitrary initial conditions and are derived via a generating-function method. The single-species model is the dual of the 1D zero-temperature kinetic Ising model with Kimball-Deker-Haake dynamics. In this way, both infinite and semi-infinite chains and also the Bethe lattice can be analysed. The relationship with the random sequential adsorption of dimers and weakly tapped granular materials is discussed.