论文标题
克莱默斯问题中的短期尺度：过去，现在，未来（审查和路线图专门为伊曼纽尔·拉什巴（Emmanuel Rashba）诞辰95周年）
Short-time scales in the Kramers problem: past, present, future (review and roadmap dedicated to the 95th birthday of Emmanuel Rashba)
论文作者
论文摘要
噪声引起的过渡问题通常与Hendrik Kramers有关，这是由于他的1940年开创性论文，在该论文中，考虑到一个型号的示例 - 一维电位系统受到线性阻尼和弱白噪声的影响，并且在潜在的范围内估计了准平台的逃逸速率，即逃脱的距离，估计了极度小和中度的高度范围。这些范围之间的差距在第80位，由Rashba最喜欢的门徒Vladimir Ivanovich Mel'nikov覆盖。 提出一个问题是很自然的：逃生率如何达到准平台？至少在单一潜在的障碍的情况下，答案似乎很明显：逃逸率应平稳，单调地从初始瞬间零生长到准平台的时间尺度上的时间尺度，即在电位孔内形成准地理所需的时间的时间。这种答案似乎可以通过1997年的维塔利·谢德曼（Vitaly Shneidman）的分析工作得到证实。但是，我们的工作在90年代末，在2000年代初与另外一位拉什巴（Rashba）最喜欢的门徒伊瓦诺维奇·谢卡（Ivanovich Sheka）合作，并与里卡多·曼内拉（Riccardo Mannella）以及里卡多·曼内拉逐步发生，甚至以振荡方式发生。通过计算机模拟证实了分析结果。 在本文中，我们回顾了这些结果并为受试者的发展提供了路线图，特别是表明各种最近被剥削的实验系统是观察上述非平凡理论预测的出色候选者，而且它们承诺有用的应用。
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.
