Exact propagator for a Fokker-Planck equation, first passage time distribution, and anomalous diffusion

We obtain an exact form for the propagator of the Fokker-Planck equation partial derivative(t)rho = partial derivative(x) (D(x)partial derivative(x)rho) -partial derivative x (F(x, t)rho), with D(x) = (D) over tilde |x|(-eta). in presence of the external force F(x, t) = -k(t) x + (K/x) |x|(-eta). Using the results found here, we also investigate the mean square displacement, survival probability, and first passage time distribution. In addition, we discuss the connection of these results with anomalous diffusion phenomena. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3621823]