A structure of generator of a quantum dynamical semigroup for the dynamics of a test particle interacting through collisions with the environment is considered, which has been obtained from a microphysical model. The related master-equation is shown to go over to a Fokker-Planck equation for the description of Brownian motion at quantum level in the long wavelength limit. The structure of this ...

The dynamics of the open or closed state region of an ion channel may be described by a probability density p(x,t) which satisfies a Fokker-Planck equation. The closed state dwell-time distribution fc(t) derived from the Fokker-Planck equation with a nonlinear diffusion coefficient D(x) proportional to exp(-gamma(x)), gamma>0 and a linear ramp potential Uc(x), is in good agreement with experime...

The Fokker-Planck equation for the probability f(r,t) to find a random walker at position r at time t is derived for the case that the probability to make jumps depends nonlinearly on f(r,t) . The result is a generalized form of the classical Fokker-Planck equation where the effects of drift, due to a violation of detailed balance, and of external fields are also considered. It is shown that in...

By using the backward fractional Fokker-Planck equation we investigate the barrier crossing event in the presence of Lévy noise. After shortly review recent results obtained with different approaches on the time characteristics of the barrier crossing, we derive a general differential equation useful to calculate the nonlinear relaxation time. We obtain analytically the nonlinear relaxation tim...

In a very long Gaussian polymer on time scales shorter than the maximal relaxation time, the mean squared distance traveled by a tagged monomer grows as approximately t(1/2) . We analyze such subdiffusive behavior in the presence of one or two absorbing boundaries and demonstrate the differences between this process and the subdiffusion described by the fractional Fokker-Planck equation. In par...