Diffusion in a potential field: Path-integral approach

Within the framework of the path-integral formalism we develop a simple method to solve the Fokker-Planck diffusion problems in a potential field, including the decay of an unstable state. Unlike previous approaches, it yields a unified treatment of all time regimes, and is legitimate for any value of the diffusion coefficient. An attractive feature of our method is that it provides numerical results in regions where there are no analytical solutions. In particular, being valid for an arbitrary shape of the potential, it is very useful for studying a diffusion problem near and in the critical point where the standard treatments break down. Moreover, our method, after a simple transformation, permits to obtain also the first passage times of the process.