Year: 2001
Type: article
Abstract: The most general one dimensional reaction-diffusion model with nearest-neighbor interactions that can be solved exactly through 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. Here, however, we do not consider reactions changing two empty neighboring sites. In the thermodynamic limit, the large-time behavior of the system has also been investigated. Releasing translationally invariance, 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.
Authors: M. Alimohammadi, M. Khorrami, A. Aghamohammadi
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2021809707