将姆潘巴效应扩展到欠阻尼领域
Extending the Mpemba effect to the underdamped realm
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中文总结 AI 辅助
研究将姆潘巴效应扩展到欠阻尼领域，考虑布朗粒子在势场中的欠阻尼动力学，微扰证明过阻尼极限下若存在该效应，大阻尼时仍存在，超弱阻尼下光滑单阱势无此效应，复杂势中可能出现，并用双阱势数值验证。
中文摘要 AI 辅助
姆潘巴效应是一种反直觉现象，即初始较热的系统比初始较冷但其他方面相同的系统冷却得速度速度较快。它已在各种经典过阻尼系统中得到实验证明。在此，我们探索在惯性不可忽略的区域，即欠阻尼区域中相同效应的存在。我们考虑布朗粒子在势场中的欠阻尼动力学。微扰地表明，如果在过阻尼极限下存在该效应，那么对于足够大但有限的阻尼它仍然存在。在超弱阻尼极限下，我们表明对于具有正则初始态的光滑约束单阱势，该效应不会出现，但在更复杂的势中可能出现。我们使用双阱势通过数值方法证明了我们的结果，双阱势是过阻尼极限下姆潘巴效应的典型设置。
英文摘要
The Mpemba effect is the counterintuitive phenomenon in which an initially hotter system cools faster than a colder, otherwise identical system. It has been experimentally demonstrated in various classical overdamped systems. Here, we explore the existence of the same effect in a regime where inertia cannot be neglected, namely, the underdamped regime. We consider the underdamped dynamics of a Brownian particle in a potential. We show perturbatively that, if the effect exists in the overdamped limit, it persists for sufficiently large but finite damping. In the ultra-weak-damping limit, we show that the effect cannot occur for smooth confining single-well potentials with canonical initial states, but can arise in more complex potentials. We demonstrate our results numerically using double-well potentials, the canonical setting for the Mpemba effect in the overdamped limit.
