Solution of a one-dimensional stochastic model with branching and coagulation reactions

Details Solution of a one-dimensional stochastic model with branching and coagulation reactions Solution of a one-dimensional stochastic model with branching and coagulation reactions

2001-07-13

arxiv.org/abs/cond-mat/0107286v4

Phys. Rev. E 64, 045101(R) (2001)

Physics

Condensed Matter

Statistical Mechanics

5 pages, no figure. To appear as a Rapid Communication in Physical Review E (September 2001)

Scientific paper

10.1103/PhysRevE.64.045101

We solve an one-dimensional stochastic model of interacting particles on a chain. Particles can have branching and coagulation reactions, they can also appear on an empty site and disappear spontaneously. This model which can be viewed as an epidemic model and/or as a generalization of the {\it voter} model, is treated analytically beyond the {\it conventional} solvable situations. With help of a suitably chosen {\it string function}, which is simply related to the density and the non-instantaneous two-point correlation functions of the particles, exact expressions of the density and of the non-instantaneous two-point correlation functions, as well as the relaxation spectrum are obtained on a finite and periodic lattice.

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