Exactly solvable reaction diffusion models on a Cayley tree
Department of Physics, Alzahra University, Tehran, 1993891167, Iran
Revised: 27 March 2007
Published online: 13 April 2007
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.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 02.50.Ga – Markov processes
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2007