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arXiv · 1207.2247

Exact correlation functions in particle-reaction models with immobile particles

Christophe Chatelain·Malte Henkel·Mário J. De Oliveira·Tânia Tomé
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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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Christophe Chatelain, Malte Henkel, Mário J. De Oliveira, Tânia Tomé. 2012-09-21. Exact correlation functions in particle-reaction models with immobile particles. https://doi.org/10.1088/1742-5468%2F2012%2F11%2Fp11006

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