Barrier crossing calculations in chemical reaction-rate theory typically assume that the barrier is large compared to the temperature. When the barrier vanishes, however, there is a qualitative change in behavior. Instead of crossing a barrier, particles slide down a sloping potential. We formulate a renormalization group description of this noisy saddle-node transition. We derive the universal scaling behavior and corrections to scaling for the mean escape time in overdamped systems with arbitrary barrier height. We also develop an accurate approximation to the full distribution of barrier escape times by approximating the eigenvalues of the Fokker-Plank operator as equally spaced. This lets us derive a family of distributions that captures the barrier crossing times for arbitrary barrier height. Our critical theory draws links between barrier crossing in chemistry, the renormalization group, and bifurcation theory.

中文翻译：

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反应速率和嘈杂的鞍节点分叉：障碍穿越的重归一化组

化学反应速率理论中的势垒穿越计算通常假设势垒比温度大。但是，当障碍消失时，行为就会发生质的变化。粒子没有越过障碍而滑落到倾斜的电位上。我们为这种嘈杂的鞍节点过渡制定了重新规范化的群描述。我们推导了通用的缩放行为，并对具有任意势垒高度的过阻尼系统的平均逸出时间进行了缩放校正。通过将等距的Fokker-Plank算子的特征值近似为近似值，我们还可以对障碍逃逸时间的全部分布进行精确估计。这使我们可以得出一个分布族，该分布族可以捕获任意障碍物高度的障碍物穿越时间。