Iomin A, Fishman S, Zaslavsky G M
Department of Physics, Technion, Haifa, 32000, Israel.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Mar;65(3 Pt 2A):036215. doi: 10.1103/PhysRevE.65.036215. Epub 2002 Feb 21.
Dynamical localization of classical superdiffusion for the quantum kicked rotor is studied in the semiclassical limit. Both classical and quantum dynamics of the system become more complicated under the conditions of mixed phase space with accelerator mode islands. Recently, long time quantum flights due to the accelerator mode islands have been found. By exploration of their dynamics, it is shown here that the classical-quantum duality of the flights leads to their localization. The classical mechanism of superdiffusion is due to accelerator mode dynamics, while quantum tunneling suppresses the superdiffusion and leads to localization of the wave function. Coupling of the regular type dynamics inside the accelerator mode island structures to dynamics in the chaotic sea proves increasing the localization length. A numerical procedure and an analytical method are developed to obtain an estimate of the localization length which, as it is shown, has exponentially large scaling with the dimensionless Planck's constant (tilde)h<<1 in the semiclassical limit. Conditions for the validity of the developed method are specified.
在半经典极限下研究了量子受踢转子的经典超扩散的动力学局域化。在具有加速器模式岛的混合相空间条件下，系统的经典和量子动力学都变得更加复杂。最近，发现了由于加速器模式岛导致的长时间量子飞行。通过对其动力学的探索，这里表明飞行的经典 - 量子对偶性导致了它们的局域化。超扩散的经典机制归因于加速器模式动力学，而量子隧穿抑制了超扩散并导致波函数的局域化。加速器模式岛结构内部的规则型动力学与混沌海中的动力学耦合证明增加了局域化长度。开发了一种数值程序和一种解析方法来获得局域化长度的估计值，结果表明，在半经典极限下，该估计值与无量纲普朗克常数(\hbar\ll1)呈指数大尺度关系。指定了所开发方法的有效性条件。
