English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The Eyring-Kramers law describes the mean transition time of an overdampedBrownian particle between local minima in a potential landscape. In theweak-noise limit, the transition time is to leading order exponential in thepotential difference to overcome. This exponential is corrected by a prefactorwhich depends on the principal curvatures of the potential at the startingminimum and at the highest saddle crossed by an optimal transition path. TheEyring-Kramers law, however, does not hold whenever one of these principalcurvatures vanishes, since it would predict a vanishing or infinite transitiontime. We derive the correct prefactor up to multiplicative errors that tend toone in the zero-noise limit. As an illustration, we discuss the case of asymmetric pitchfork bifurcation, in which the prefactor can be expressed interms of modified Bessel functions, as well as bifurcations with two vanishingeigenvalues. The corresponding transition times are studied in a fullneighbourhood of the bifurcation point. These results extend work by Bovier,Eckhoff, Gayrard and Klein, who rigorously analysed the case of quadraticsaddles, using methods from potential theory.

The Eyring-Kramers law for potentials with nonquadratic saddles