Turnover theory, multidimensional

Hershkovitz E and Poliak E 1997 Multidimensional generalization of the PGH turnover theory for activated rate processes J. Chem. Phys. 106 7678... 

Kramers model is simplistic. It is one-dimensional and assumes that the friction is Markovian—uncorrelated in time. A multidimensional generalization of Kramers problem in the spatial diffusion limit was proposed and solved by Langer (18). The multidimensional energy diffusion limit was solved by Matkowsky, Schuss, and coworkers (19,20). A multidimensional turnover theory has been recently formulated (21). 

One of the main differences between the one-dimensional and the multidimensional turnover theory comes from the change between the one-dimensional and multidimensional energy loss mechanism. 

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