Non-Markovian theory of activated rate processes. III. Bridging between the Kramers limits

Abstract

Kramers' theory of activated processes yields expressions for the steady-state escape rate in the large-and small-friction limits and for Markovian dynamics. The present work extends this theory to non-Markovian dynamics and to the whole friction range. Kramers results are recovered in the appropriate limits.

Fractional Kinetics in Kac–Zwanzig Heat Bath Models

“…13 we show the distribution of exit times, 2 y, 2 The problem of exit times for non-Markovian process was studied extensively in the context of activation rate theory. Kramers' theory and its extension to systems with memory kernels is reviewed by Hänggi et al (28) The original work can be found in Grote and Hynes, (22) Hänggi and Mujtabai, (27) and Carmeli and Nitzan; (9) numerical tests for an exponential memory function were conducted by Straub et al (46,47) .…”

Fluorescence Excitation Spectrum, Lifetimes and Photoisomerization of Jet-Cooled Conformers of 1,1´-bi(benzocyclobutylidene)

“…The bridged stilbene 4 at the same time offers the possibility to investigate the aspect of dimensionality of the barrier crossing process [50][51][52][53][54][55][56][57][58][59]. As it was suggested that the anomalous viscosity effect in the case of trans-1 could be caused by the effective multidimensionality of motion involving the phenyl torsion coordinate [60] and quantum chemical calculations revealed a significant variation of the effective barrier to photoisomerization in the S 1 -state [61], stilbene derivatives in which the phenyl rings are fixed by linking them covalently to the ethylenic carbon atoms are of particular interest.…”

Improved rate theories of chemical reactions

“…Equations (6) and (8) are not identical, because introduction of sin Eq. (7) corresponds to the principal transformation of X and v to cancel the cross terms, which should require that of another variable, say,…”