Diffusion-limited Reactions of hard-core Particles in one-dimension

Details Diffusion-limited Reactions of hard-core Particles in one-dimension Diffusion-limited Reactions of hard-core Particles in one-dimension

1998-12-07

arxiv.org/abs/cond-mat/9812100v1

Physics

Condensed Matter

Statistical Mechanics

15 pages, no figure, to appear in PRE

Scientific paper

10.1103/PhysRevE.59.1996

We investigate three different methods to tackle the problem of diffusion-limited reactions (annihilation) of hard-core classical particles in one dimension. We first extend an approach devised by Lushnikov and calculate for a single species the asymptotic long-time and/or large distance behavior of the two-point correlation function. Based on a work by Grynberg et al., which was developed to treat stochastic adsorption-desorption models, we provide in a second step the exact two-point correlation function (both for one and two-time) of Lushnikov's model. We then propose a new formulation of the problem in terms of path integrals for pseudo-fermions. This formalism can be used to advantage in the multi-species case, specially when applying perturbative renormalization group techniques.

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