Chirikov典型映射的扩散与局部化
Diffusion and localization for the Chirikov typical map
摘要：
本文研究了BorisChirikov在1969年提出的“Chirikov典型映射”的经典和量子性质。这个映射是从著名的奇里科夫标准映射通过引入有限个随机相移角$T$得到的。这些角度诱导小时间尺度的随机行为（$t<T$）和与较大时间尺度相关的$T$ -周期性迭代映射（$t>T$）。我们确定了经典的混沌边界$k_c\sim T^{-3/2} \ll 1$的踢参数$k$和两个政权的扩散行为的短期和长期的时间尺度。量子动力学的特征是奇里科夫局域化（或动力学局域化）效应。我们发现，本地化长度依赖于一个微妙的方式上的两个经典的扩散常数在两个时间尺度制度。
英文摘要：
We consider the classical and quantum properties of the "Chirikov typical map", proposed by Boris Chirikov in 1969. This map is obtained from the well known Chirikov standard map by introducing a finite number $T$ of random phase shift angles. These angles induce a random behavior for small time scales ($t<T$) and a $T$-periodic iterated map which is relevant for larger time scales ($t>T$). We identify the classical chaos border $k_c\sim T^{-3/2} \ll 1$ for the kick parameter $k$ and two regimes with diffusive behavior on short and long time scales. The quantum dynamics is characterized by the effect of Chirikov localization (or dynamical localization). We find that the localization length depends in a subtle way on the two classical diffusion constants in the two time-scale regime.
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。
