Stationary diffusion over a multidimensional potential barrier: A generalization of Kramers' formula

Abstract

We consider diffusion over a potential barrier for n degrees of freedom. Generalizing the procedure of Kramers, we find a quasistationary solution to the associated Fokker-Planck equation. This yields an expression for the diffusion current over the barrier and, finally, a simple and elegant generalization of Kramers' formula for the diffusion rate.

Dinuclear systems in complete fusion reactions

“…Quasi stationary values of flow rates over the two dimensional potential barrier are defined by the following Kramers formula [121,138,139]: (50) Here B i (i = R, η, η sym ) determines a height of the bar rier of fusion (B η = ) or quasifission (B R = B qf or ( = B qf ). In (50), and ω i (i = R, η) are the fre quencies of inverted and normal harmonic oscillators, by which the potential is approximated in variables i = R, η on the barrier tops and at the minimum for the initial DNS.…”

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.…”

The realistic calculation and analyses of the multidimensional fission width in the quasi-stationary approximation

“…In [2J and [3], some numerical calculations were performed, however, with opposite results. In [4] and [5], the authors though considered various situations, but did not perform more realistic calculations. In addition.…”

“…He solved the Fokker-Planck equation (FPE) in the quasi-stationary approximation and obtained an analytical expression for the fission width. In recent years, several authors [2][3][4][5] have generalized Karmers's early work to the n-dimensional case. In [2J and [3], some numerical calculations were performed, however, with opposite results.…”