Diffusion-limited reactions of hard-core particles in one dimension

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 [Sov. Phys. JETP 64, 811 (1986)] 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 and Stinchcombe [Phys. Rev. E 50, 957 (1994); Phys. Rev. Lett. 74, 1242 (1995); 76, 851 (1996)], which was developed to treat stochastic adsorption-desorption models, we provide in a second step the exact two-point (one- and two-time) correlation functions of Lushnikov’s model. We then propose a formulation of the problem in terms of path integrals for pseudo- fermions. This formalism can be used to advantage in the multispecies case, especially when applying perturbative renormalization group techniques.