通过康托集的量子输运。

Quantum transport through cantori.

作者信息

Maitra NT, Heller EJ

机构信息

Department of Physics, Harvard University, Cambridge, Massachusetts 02138 and Harvard-Smithsonian Center for Astrophysics, Harvard University, Cambridge, Massachusetts 02138, USA.

出版信息

Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Apr;61(4 Pt A):3620-31. doi: 10.1103/physreve.61.3620.

DOI:10.1103/physreve.61.3620

PMID:11088140

Abstract

We study the effect of classical cantori in quantum mechanics, extending previous results by several groups. We find that cantori form exponential barriers to quantum transport not only when Planck's constant exceeds the flux through the cantorus but also when it is smaller than the flux. The mechanism of localization in the two cases is different, and we describe the switch from dynamical localization to a mechanism we call "retunneling" as Planck's constant increases. We investigate the Planck's over 2pi dependence of the exponential decay for retunneling and find that the Planck's over 2pi(-0.66) coefficient found previously at criticality appears to hold also away from criticality provided piPlanck's over 2pi is large enough compared to the flux. Numerical evidence as well as an analytic argument are given. Our final contribution to this subject is a phase space view of cantori in quantum mechanics. We illustrate our results using the whisker map.

摘要

我们研究了经典康托集在量子力学中的效应，扩展了此前多个团队的研究成果。我们发现，康托集不仅在普朗克常数超过通过康托环面的通量时，而且在其小于通量时，都会对量子输运形成指数势垒。两种情况下的局域化机制不同，并且我们描述了随着普朗克常数增加，从动力学局域化到一种我们称为“再隧穿”机制的转变。我们研究了再隧穿过程中指数衰减对普朗克常数与(2\pi)比值的依赖性，发现先前在临界状态下得到的普朗克常数与(2\pi)比值为(-0.66)的系数，在远离临界状态时似乎也成立，前提是与通量相比，(\pi)乘以普朗克常数与(2\pi)的比值足够大。文中给出了数值证据以及一个解析论证。我们对该主题的最后一项贡献是量子力学中康托集的相空间视图。我们使用晶须映射来说明我们的结果。