2018-12-19
10:15 at HCP F 43.4

Metastability and transition rate estimation methods

Mohsen Talebi

Polymer Physics, Department of Materials, ETH Zurich

In this talk, I will first introduce the general framework of Markov jump processes briefly. Secondly, I will introduce the Kramers problem and his famous formula to derive transition rates. In the third part, I will introduce the concept of metastability using the powerful Quasi-Stationary Distribution method. This method explicitly gives conditions which are needed to be satisfied so that we can coarse-grain the system as a Markov jump process. Moreover, this method gives us another theoretical method to derive transition rates. In the fourth part, I will show three methods that we can use to infer transition rates from the direct simulation of the microscopic dynamics in the situation that the metastability condition is satisfied. In the first method, the transition rate is derived by observing the average escape time of a particle from a potential well. In the second method, an enhanced maximum-likelihood estimator is used to infer the generator of the Markov jump process. In the third method, the transition rate is derived using the form of the backward Kolmogorov equation of Markov jump processes for the evolution of a simple linear function. Application of these methods will be shown for the Kramers problem.