Frahm Klaus M, Shepelyansky Dima L
Université de Toulouse-UPS, F-31062 Toulouse, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Jul;80(1 Pt 2):016210. doi: 10.1103/PhysRevE.80.016210. Epub 2009 Jul 21.
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) approximately T (-3/2)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.
我们考虑1969年鲍里斯·奇里科夫提出的“奇里科夫典型映射”的经典和量子特性。该映射是通过引入有限数量T的随机相移角从著名的奇里科夫标准映射得到的。这些角度在小时间尺度（t<T）上诱导出随机行为，以及在大时间尺度（t>T）上相关的T周期迭代映射。我们确定了踢参数k的经典混沌边界k(c)约为T^(-3/2)，以及在短时间和长时间尺度上具有扩散行为的两种状态。量子动力学的特征是奇里科夫局域化（或动态局域化）效应。我们发现局域化长度以一种微妙的方式依赖于两个时间尺度状态下的两个经典扩散常数。
