Levy棘轮中的输运：群速度和分布扩散
Transport in a Levy ratchet: Group velocity and distribution spread
摘要：
我们考虑了在对称Lévy噪声影响下，过阻尼粒子在缺乏空间对称性的周期势场中的运动，这是Lévy棘轮的最小设置。由于Lévy噪声的非热特性，即使在没有任何额外的依赖于时间的力的情况下，粒子也会表现出具有优选方向的运动。Lévy棘轮的检验必须基于方向性的特征，这些特征不同于通常使用的测量方法，如平均电流和粒子位置的分散，因为当噪声的时刻发散时，这些测量方法变得不合适。为了克服这个问题，我们讨论了鲁棒性的措施的方向性的运输，如粒子位移的分布特征的群速度的中位数的位置，和分位数的距离给出的分布的宽度的措施。此外，我们分析了分裂概率的行为，留下一个给定的长度的间隔，揭示了Lévy指数低于和高于统一的噪声之间的定性差异。最后，我们检查的问题，第一次逃离一个给定长度的间隔，揭示独立的出口时间的结构上的潜力。
英文摘要：
We consider the motion of an overdamped particle in a periodic potential lacking spatial symmetry under the influence of symmetric Lévy noise, being a minimal setup for a ``Lévy ratchet.'' Due to the non-thermal character of the Lévy noise, the particle exhibits a motion with a preferred direction even in the absence of whatever additional time-dependent forces. The examination of the Lévy ratchet has to be based on the characteristics of directionality which are different from typically used measures like mean current and the dispersion of particles' positions, since these get inappropriate when the moments of the noise diverge. To overcome this problem, we discuss robust measures of directionality of transport like the position of the median of the particles displacements' distribution characterizing the group velocity, and the interquantile distance giving the measure of the distributions' width. Moreover, we analyze the behavior of splitting probabilities for leaving an interval of a given length unveiling qualitative differences between the noises with Lévy indices below and above unity. Finally, we inspect the problem of the first escape from an interval of given length revealing independence of exit times on the structure of the potential.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
