论文标题
眼环形式公式的几何表征
Geometric Characterization of the Eyring-Kramers Formula
论文作者
论文摘要
在本文中，我们考虑了具有光滑电势的局部最小值之间过度阻尼的布朗粒子的平均过渡时间。当最小值和马鞍是非分化的时，这是在低噪声状态下完全以所谓的Eyring-Kramers定律为特征的，并根据最小值和鞍座的曲率给出了平均过渡时间作为数量。在本文中，我们发现了眼环法律的延伸，在两个最小/马鞍都退化（平坦）的平均过渡时间上有一个上限，同时覆盖了相同高度的多个鞍座。我们的主要贡献是两个局部最小值的能力作为两个几何量的比率，即最小的分离表面和地球距离的比率。
In this paper we consider the mean transition time of an over-damped Brownian particle between local minima of a smooth potential. When the minima and saddles are non-degenerate this is in the low noise regime exactly characterized by the so called Eyring-Kramers law and gives the mean transition time as a quantity depending on the curvature of the minima and the saddle. In this paper we find an extension of the Eyring-Kramers law giving an upper bound on the mean transition time when both the minima/saddles are degenerate (flat) while at the same time covering multiple saddles at the same height. Our main contribution is a new sharp characterization of the capacity of two local minimas as a ratio of two geometric quantities, i.e., the smallest separating surface and the geodesic distance.
