Exact correlation functions in particle-reaction models with immobile particles

Christophe Chatelain (1) , Malte Henkel (2) , Mário J. de Oliveira (3) , Tânia Tomé (3)

1 IJL - Institut Jean Lamour
2 Equipe 106, IJL - Groupe de Physique statistique = Statistical Physics Group [Institut Jean Lamour]
3 IFUSP - Instituto de Fisica da Universidade de São Paulo

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.

Domains: Statistical Mechanics [cond-mat.stat-mech]

Christophe Chatelain, Malte Henkel, Mário J. de Oliveira, Tânia Tomé. Exact correlation functions in particle-reaction models with immobile particles. 2012. ⟨hal-00716162v1⟩