Exactly solvable models through the empty interval method

Details Exactly solvable models through the empty interval method Exactly solvable models through the empty interval method

2001-05-06

arxiv.org/abs/cond-mat/0105124v1

Phys. Rev. E64 (2001) 056116

Physics

Condensed Matter

12 pages, LaTeX2e

Scientific paper

10.1103/PhysRevE.64.056116

The most general one dimensional reaction-diffusion model with nearest-neighbor interactions, which is exactly-solvable through the empty interval method, has been introduced. Assuming translationally-invariant initial conditions, the probability that $n$ consecutive sites are empty ($E_n$), has been exactly obtained. In the thermodynamic limit, the large-time behavior of the system has also been investigated. Releasing the translational invariance of the initial conditions, the evolution equation for the probability that $n$ consecutive sites, starting from the site $k$, are empty ($E_{k,n}$) is obtained. In the thermodynamic limit, the large time behavior of the system is also considered. Finally, the continuum limit of the model is considered, and the empty-interval probability function is obtained.

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