The calculation of rate coefficients is a discipline of nonlinear science of importance to much of physics; chemistry; engineering; and biology. Fifty years after Kramers' seminal paper on thermally activated barrier crossing; the authors report; extend; and interpret much of our current understanding relating to theories of noise-activated escape; for which many of the notable contributions are originating from the communities both of physics and of physical chemistry. Theoretical as well as numerical approaches are discussed for single- and many-dimensional metastable systems (including fields) in gases and condensed phases. The role of many-dimensional transition-state theory is contrasted with Kramers' reaction-rate theory for moderate-to-strong friction; the authors emphasize the physical situation and the close connection between unimolecular rate theory and Kramers' work for weakly damped systems. The rate theory accounting for memory friction is presented; together with a unifying theoretical approach which covers the whole regime of weak-to-moderate-to-strong friction on the same basis (turnover theory). The peculiarities of noise-activated escape in a variety of physically different metastable potential configurations is elucidated in terms of the mean-first-passage-time technique. Moreover; the role and the complexity of escape in driven systems exhibiting possibly multiple; metastable stationary nonequilibrium states is identified. At lower temperatures; quantum tunneling effects start to dominate the rate mechanism. The early quantum approaches as well as the latest quantum versions of Kramers' theory are discussed; thereby providing a description of dissipative escape events at all temperatures. In addition; an attempt is made to discuss prominent experimental work as it relates to Kramers' reaction-rate theory and to indicate the most important areas for future research in theory and experiment.
Search
Reviews
[Write a review of this article]
Find related articles from these CiteULike users
