THERMAL-ACTIVATION - KRAMERS THEORY REVISITED

The Brownian motion model of classical noise-induced escape from a metastable potential well is reconsidered, in particular for the friction dependence of the decay rate. Kramers' Fokker-Planck equation is reformulated in terms of the particle's energy and the action variable near the peak of the barrier. The ensuing probability density ρ{variant}(s, ε{lunate}) - and, hence, the decay rate Γ - is uniquely determined (i) by means of a spectral analysis and (ii) upon specifying the energy distribution of incoming particles. If such particles are taken to be absent, the decay rate goes to zero in the low friction limit according to Kramers' original formula, while for increasing friction it approaches the transition state value. The significance of diffusively re-entering particles for obtaining the correct high friction Kramers-Smoluchov-ski result is discussed. A problem with the underlying density is pointed out. The nature of the intermediate friction - the so-called turnover - regime is critically examined and a comparison is made with related recent work by Büttiker, Harris and Landauer, Mel'nikov and Meshkov, and Grabert. © 1990.