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.

17 pages, 4 figures

References in corpus (3)

• Power-Law Distributions for a Trapped Ion Interacting with a Classical Buffer Gas
• Gibbsian theory of power law distributions
• Acoustic Kappa-Density Fluctuation Waves in Suprathermal Kappa Function Fluids

Cited by in corpus (7)

• The collision theory reaction rate coefficient for power-law distributions
• Kramers escape rate in overdamped systems with the power-law distribution
• The rate coefficients of unimolecular reactions in the systems with power-law distributions
• Are power-law distributions an equilibrium distribution or a stationary nonequilibrium distribution?
• Escape rate for the power-law distribution in low-to-intermediate damping
• The power-law TST reaction rate coefficient with tunneling correction
• Mean First Passage Time of the Symmetric Noisy Voter Model with Arbitrary Initial and Boundary Conditions