Kramers问题的短时间尺度：过去，现在，未来（回顾和路线图，献给Emmanuel Rashba的95岁生日）
Short-time scales in the Kramers problem: past, present, future (review and roadmap dedicated to the 95th birthday of Emmanuel Rashba)
摘要：
噪声诱导跃迁的问题通常与亨德里克·克拉默斯（Hendrik Kramers）有关，这是由于他在1940年的开创性论文，其中考虑了一个典型的例子-线性阻尼和弱白噪声的一维势系统-并估计了极小和中等到大阻尼范围内的准稳态势垒逃逸率。80年代，拉什巴最喜欢的弟子之一弗拉基米尔·伊万诺维奇·梅尔尼科夫填补了这些山脉之间的空白。很自然地会提出一个问题：逃逸率如何达到准稳态？至少在单个势垒的情况下，答案似乎是显而易见的：逃逸率应该从初始时刻的零平稳单调地增长到准稳态值，其时间尺度为在势阱内形成准稳态分布所需的时间量级。这样的答案似乎得到了维塔利·施奈德曼（Vitaly Shneidman）1997年的分析工作的证实。然而，我们在90年代末和2000年代初与拉什巴最喜欢的弟子瓦伦丁·伊万诺维奇·谢卡（Valentin Ivanovich Sheka）和里卡多·曼内拉（Riccardo Mannella）合作的工作表明，在较短的时间尺度上，即在势阱中自然振荡周期的量级上，逃逸率的增长一般是逐步甚至以振荡的方式发生的。分析结果得到了计算机模拟的证实。在本文中，我们回顾了这些结果，并提供了一个路线图的主题的发展，特别是表明，各种最近开发的实验系统是观察上述非平凡的理论预测的优秀候选人，而且，他们承诺有用的应用。
英文摘要：
The problem of noise-induced transitions is often associated with Hendrik Kramers due to his seminal paper of 1940, where an archetypal example - one-dimensional potential system subject to linear damping and weak white noise - was considered and the quasi-stationary rate of escape over a potential barrier was estimated for the ranges of extremely small and moderate-to-large damping. The gap between these ranges was covered in the 80th by one of Rashba's favourite disciples Vladimir Ivanovich Mel'nikov. It is natural to pose a question: how does the escape rate achieve the quasi-stationary stage? At least in case of a single potential barrier, the answer seems to be obvious: the escape rate should smoothly and monotonously grow from zero at the initial instant to the quasi-stationary value at time-scales of the order of the time required for the formation of the quasi-stationary distribution within the potential well. Such answer appeared to be confirmed with the analytic work of Vitaly Shneidman in 1997. However our works in the end of the 90th and in the beginning of the 2000th in collaboration with one more Rashba's favorite disciple Valentin Ivanovich Sheka and with Riccardo Mannella showed that, at a shorter time-scale, namely that of the order of the period of natural oscillations in the potential well, the escape rate growth generically occured stepwise or even in an oscillatory manner. Analytic results were confirmed with computer simulations. In the present paper, we review those results and provide a roadmap for the development of the subject, in particular demonstrating that various recently exploited experimental systems are excellent candidates for the observation of the above non-trivial theoretical predictions and, moreover, they promise useful applications.
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。
