 08137 Nils Berglund, Barbara Gentz
 The EyringKramers law for potentials with nonquadratic saddles
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Jul 10, 08

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Abstract. The EyringKramers law describes the mean transition time of an overdamped Brownian particle between local minima in a potential landscape. In the weaknoise limit, the transition time is to leading order exponential in the potential difference to overcome. This exponential is corrected by a prefactor which depends on the principal curvatures of the potential at the starting minimum and at the highest saddle crossed by an optimal transition path. The EyringKramers law, however, does not hold whenever one of these principal curvatures vanishes, since it would predict a vanishing or infinite transition time. We derive the correct prefactor up to multiplicative errors that tend to one in the zeronoise limit. As an illustration, we discuss the case of a symmetric pitchfork bifurcation, in which the prefactor can be expressed in terms of modified Bessel functions. The results extend work by Bovier, Eckhoff, Gayrard and Klein, who rigorously analysed the case of quadratic saddles, using methods from potential theory.
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