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.

43 pages, 18 figures

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Cited by in corpus (3)

• Cross-over between diffusion-limited and reaction-limited regimes in the coagulation-diffusion process
• Exact correlation functions in particle-reaction models with immobile particles
• Binary lattice-gases of particles with soft exclusion: Exact phase diagrams for tree-like lattices