Multidimensional activated rate processes with slowly relaxing mode

The multidimensional Kramers problem is considered in the case of highly anisotropic friction. As a development of our previous results involving the study of several new regimes of activated rate process, we construct a theory which incorporates all these regimes and treats the process in every case in a uniform manner. To do this we take advantage of the friction anisotropy and reduce the initial multidimensional Fokker-Planck equation to a set of two effective one-dimensional equations. These equations describe diffusive motion along the slow coordinate in two effective potential wells and inter-well transitions due to the fast coordinate motion. To calculate the rate constant on the basis of the set we use an original method which is a generalization of the Kramers method. As a result we obtain a new formula for the rate constant which depending on the friction anisotropy level is smoothly changed from the well-known Kramers-Langer formula to new ones obtained in our previous papers.