Critical dynamics the expansion of the master equation including a critical point: I. Diffusion processes

Abstract

The master equation for a diffusion process that takes place in an external potential will be evaluated systematically in terms of a small parameter, namely the diffusion coefficient. Contrary to the known expansion the present solution is not only uniformly valid in the normal monostable and bistable cases, but also applies at the critical point. This has been achieved by using in zeroth order approximation the complete set of eigenfunctions belonging to the appropriate irreducible description of the process. Successive higher order corrections are evaluated explicitly.