Exactly solvable models through the empty-interval method - art. no. 056116

The most general one dimensional reaction-diffusion model with nearest-neig hbor 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 ne ighboring sites. In the thermodynamic limit, the large-time behavior of the system has also been investigated. Releasing translationally invariance, t he evolution equation for the probability that n consecutive sites. startin g from the site k, are empty, E-k,E-n, is obtained. In the thermodynamic li mit. the large time behavior of the system is also considered. Finally, the continuum limit of the model is considered and the empty-interval probabil ity function is obtained.