An interesting result is found that the Kramers-Arrhenius law is not valid and the escape rate is a nonmonotonous function of the anomalous exponent for the Lévy statistics,because the system outside the barrier comes back to the inside and cancels with itself.

It shows that stationary escape rate is non-monotonic as anomalous index α increases.

Mechanism of parameter-adjusted stochastic resonance based on Kramers rate

The escape rate of the bistable sawtooth system driven by correlated white noises in the different cases of multiplicative noise coefficient is calculated accurately.

We also calculate the escape rate as a function of energy above threshold in the Hénon-Heiles system.

By directly resolving Langevin equation with the computer numerical simulation,the escape rate of a particle driven by Gaussian white noise in a one-dimensional potential well is obtained and the calculated results are compared to the theoretical one.

Experimenting with Maxwellian speed distribution and escape speed, this paper gives the escape coefficient and escape probability of gases on the earth and then conducts the qualitative and the quantitative analyses and discusses the results.