Generalized empty-interval method applied to a class of one-dimensional stochastic models

Abstract

In this work we study, on a finite and periodic lattice, a class of one-dimensional (bimolecular and single-species) reaction-diffusion models which cannot be mapped onto free-fermion models. We extend the conventional empty-interval method, also called {\it interparticle distribution function} (IPDF) method, by introducing a string function, which is simply related to relevant physical quantities. As an illustration, we specifically consider a model which cannot be solved directly by the conventional IPDF method and which can be viewed as a generalization of the {\it voter} model and/or as an {\it epidemic} model. We also consider the {\it reversible} diffusion-coagulation model with input of particles and determine other reaction-diffusion models which can be mapped onto the latter via suitable {\it similarity transformations}. Finally we study the problem of the propagation of a wave-front from an inhomogeneous initial configuration and note that the mean-field scenario predicted by Fisher's equation is not valid for the one-dimensional (microscopic) models under consideration.

19 pages, no figure. To appear in Physical Review E (November 2001)

References in corpus (3)

• Exact solution of a class of one-dimensional nonequilibrium stochastic models
• Solution of a class of one-dimensional reaction-diffusion models in disordered media
• Solution of a one-dimensional stochastic model with branching and coagulation reactions

Cited by in corpus (10)

• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• Models solvable through the empty-interval method
• Exact correlations in the one-dimensional coagulation-diffusion process by the empty-interval method
• Exactly solvable reaction diffusion models on a Cayley tree
• Static- and dynamical-phase transition in multidimensional voting models on continua
• Particle Statistics and Population Dynamics
• Autonomous models solvable through the full interval method
• Perturbative calculation of one-point functions of one-dimensional single-species reaction-diffusion systems
• The spectrum and the phase transition of models solvable through the full interval method
• Cluster approximation solution of a two species annihilation model