Diffusion on a one-dimensional disordered lattice: A renormalization-group approach

Publisher Website
Google Scholar
Abstract
Diffusion of a particle on a one-dimensional disordered lattice is studied using the renormalization-group (RG) procedure of Goncalves da Silva and Koiller [Solid State Commun. 40, 215 (1981)]. The RG equations are derived and their physical content is discussed. Several examples are studied using the RG equations and a disorder-averaging procedure that permits stepwise averaging of the RG equations. Values of the diffusion constant so calculated, while qualitatively correct, are in poor agreement with the known correct answer. The RG equations are shown to be derivable from a dedecoration carried out on a replica-trick description of the diffusion process. Employing the relationship of the RG equations to dedecoration, a stepwise disorder-averaging procedure is constructed that yields values of the diffusion constant in excellent agreement with expectations. The relationships of the RG equations to the renormalization-group treatment of Machta [Phys. Rev. B 24, 5260 (1981)] and to the logistic equation are discussed.