Eur. Phys. J. B 56, 243-246 (2007)
https://doi.org/10.1140/epjb/e2007-00103-x

Exactly solvable reaction diffusion models on a Cayley tree

Department of Physics, Alzahra University, Tehran, 1993891167, Iran

Corresponding authors: ^a laleh.matin@alzahra.ac.ir - ^b mohamadi@alzahra.ac.ir - ^c mamwad@mailaps.org

Received: 27 January 2007
Revised: 27 March 2007
Published online: 13 April 2007

Abstract

The most general reaction-diffusion model on a Cayley tree with nearest-neighbor interactions is introduced, which can be solved exactly through the empty-interval method. The stationary solutions of such models, as well as their dynamics, are discussed. Concerning the dynamics, the spectrum of the evolution Hamiltonian is found and shown to be discrete, hence there is a finite relaxation time in the evolution of the system towards its stationary state.