The noise-driven motion in a bistable potential acts as the archetypal model of various physical phenomena. Here, we contrast properties of the overdamped escape dynamics with the full (underdamped) dynamics. In the weak noise limit, for the overdamped particle driven by nonequilibrium, $\alpha$-stable noise the ratio of forward to backward transition rates depends only on the width of a potential barrier separating both minima. Using analytical and numerical methods, we show that in the regime of full dynamics, contrary to the overdamped case, the ratio of transition rates depends on both the widths and the heights of the potential barrier separating minima of the double-well potential. The derived analytical formula for the ratio of transition rates is corroborated by extensive numerical simulations. Results of numerical simulations follow especially well the analytical predictions in the weak noise limit when the most probable escape scenario is via a single, strong, noise kick, which is sufficient to induce a quasideterministic transition over the potential barrier. Such an escape trajectory can be analyzed in terms of the instantaneous velocity, which is fully characterized by its density function, which is of the same type as the probability density underlying the noise distribution.

中文翻译：

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双阱势能的阻尼不足，异常动力学

双稳态电势中的噪声驱动运动充当各种物理现象的原型模型。在这里，我们将过度阻尼逃逸动力学的特性与完整（欠阻尼）动力学的特性进行对比。在弱噪声极限中，对于由非平衡驱动的过阻尼粒子，$\alpha$稳定噪声前向与后向过渡速率之比仅取决于将两个极小值分隔开的势垒的宽度。使用分析和数值方法，我们表明，在全动力学状态下，与过阻尼情况相反，过渡速率之比取决于势垒的宽度和高度，该势垒将双阱电势的最小值分开。广泛的数值模拟证实了所得出的过渡速率比的解析公式。当最可能的逃生场景是通过单个强噪声踢时，数值模拟的结果特别符合弱噪声极限的分析预测，这足以在势垒上引发准确定性过渡。