Exact correlation functions in particle-reaction models with immobile particles

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.
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Submitted on : Friday, September 21, 2012 - 10:43:59 AM
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Christophe Chatelain, Malte Henkel, Mário de Oliveira, Tânia Tomé. Exact correlation functions in particle-reaction models with immobile particles. Journal of Statistical Mechanics: Theory and Experiment, IOP Publishing, 2012, pp.P11006. ⟨10.1088/1742-5468/2012/11/P11006⟩. ⟨hal-00716162v2⟩

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