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

Abstract

Based on the mean first passage time (MFPT) theory, we derive the expression of the MFPT in the energy-diffusion controlled regime with a power-law distribution. We discuss the finite barrier effect (i.e. thermal energy is not small with respect to the potential barrier) and compare it with the Kramers infinite barrier result both in the power-law distribution and in a Maxwell-Boltzmann distribution. It is shown that the MFPT with the power-law distribution extends the Kramers' low damping result to the 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 affects the current distribution function in the experiment of Josephson junctions.