Solution to the Kramers barrier crossing problem caused by two noises: Thermal noise and Poisson white noise

We consider the escape of a particle trapped in a metastable potential well and acted upon by two noises. One of the noises is thermal and the other is Poisson white noise, which is non-Gaussian. Using path integral techniques, we find an analytic solution to this generalization of the classic Kramers barrier crossing problem. Using the barrier climbing path, we calculate the activation exponent. We also derive an approximate expression for the prefactor. The calculated results are compared with the simulations, and a good agreement between the two is found. Our results show that, unlike in the case of thermal noise, the rate depends not just on the barrier height but also on the shape of the whole barrier. A comparison between the simulations and the theory also shows that a better approximation for the prefactor is needed for agreement for all values of the parameters.

Automated summary

This study investigates the escape of a particle trapped in a metastable potential well under the influence of thermal noise and Poisson white noise, finding an analytic solution to the classic Kramers barrier crossing problem. Results show that the rate of escape depends not only on the barrier height but also on the shape of the entire barrier, highlighting the importance of a better prefactor approximation for agreement between theory and simulations.