The mean first passage time in an energy-diffusion controlled regime with power-law distributions

Based on the mean first passage time (MFPT) theory, we derive an expression of the MFPT in an energy-diffusion controlled regime with a power-law distribution. We discuss the finite barrier effect (i.e. the thermal energy k(B)T is not small with respect to the potential barrier E-b) and compare it with Kramers' infinite barrier result both in a power-law distribution and in a Maxwell-Boltzmann distribution. It is shown that the MEPT with a power-law distribution extends Kramers' low-damping result to a relatively low barrier. We pay attention to the energy-diffusion controlled regime, which is of great interest in the context of Josephson junctions, and study how the power-law parameter kappa affects the current distribution function in experiments with Josephson junctions.