权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Multidimensional Tunnelling Effect and Complexified Classical Dynamics

多维隧道效应和复杂的经典动力学

基本信息

批准号：
13640410
负责人：
IKEDA Kensuke
金额：
$ 2.56万
依托单位：
Ritsumeikan University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2004
项目状态：
已结题

项目摘要

Multi-dimensionality of the systems radically influences tunnelling phenomena. In particular, if the system is classically non-integrable, complicated tunneling phenomenona, which are due to the presence of chaotic set and are called chaotic tunnelling, are observed. The fundamental mechanism of chaotic tunnelling is investigated by using classical dynamics extended to the fully complex domain, i.e. the complex semiclassical method.(1) Tunnelling in the presence of chaos is investigated for a class of quantum map system. Extensive numerical studies reveal that the tunnelling trajectories dominantly contributing the dynamical tunnelling process form a very limited class of sets in the initial manifold, which is called "Laputa chains" from their characteristic shape. Mathematical significance of such a set is investigated applying the results of hormorphic dynamical theory to numerically clarified natures. The main results is that the closure of Laputa chain is bounded by two sets, namel … More y, the Jula set J^+, and the filled-in Julia set K^+, from below and above, respectively. It is further conjectured that K^+=J^+. If this is the case, the closure of Laputa chain is nothing more than Julia set. The wavefunction tunnelling through the dynamical barrier is constructed along the real component of J^-. These facts means that the major trajectories tunnells being guided by the complexified stable manifolds of saddles dense in the chaotic sea, and are scatterd along their unstable manifold.(2) Confining ourselves to a class of barrier tunnelling process, we elucidate how multi-dimensionality of the system results in a new universal mechanism causing complicated tunnelling phenomena peculiar to multi-dimensional barrier systems. First we showed that the complex semiclassical theory surely reproduces the purely quantum wave matrix even in the strong coupling regime, where the tunnelling component is accompanied by complicated fringes. Next, it is shown that the complexified trajectories guided by complexified stable and unstable manifolds are responsible for the fringed tunneling effect. Such a mechanism provides a new picture of tunnelling quite different from the classical instanton mechanism. Seen from a mathematical side, the mechanism is explained in terms of a divergent shift of movable singularities, which are the origins of the multivaluedness of complexified trajectories in one-dimensional tunnelling problem. Less

系统的多维性从根本上影响隧穿现象。特别地，当系统是经典不可积的时，由于混沌集的存在，会出现复杂的隧穿现象，称为混沌隧穿。本文用经典动力学方法推广到全复域，即复半经典方法研究了混沌隧穿的基本机制。(1)研究了一类量子映射系统在混沌状态下的隧穿现象。大量的数值研究表明，隧道轨道占主导地位的动力学隧道过程中形成一个非常有限的一类集的初始流形，这是所谓的“Laputa链”，从他们的特征形状。数学意义的这样一个集的研究应用的结果，数值澄清的性质的准态动力学理论。主要结果是Laputa链的闭包是由两个集合有界的，即 ...更多信息 y、Julia集J^+和填充Julia集K^+。进一步证明K^+=J^+。如果是这样，Laputa链的闭包只不过是Julia集。穿过动力学势垒的波函数是沿着J^-的真实的分量构造的。这些事实意味着主轨迹由混沌海中稠密的鞍形的复杂稳定流形引导，并沿着其不稳定流形散布。(2)限制自己的一类势垒隧穿过程中，我们阐明如何多维的系统结果在一个新的普遍机制，造成复杂的隧穿现象特有的多维势垒系统。首先，我们表明，复杂的半经典理论肯定再现纯粹的量子波矩阵，即使在强耦合制度，其中隧道分量伴随着复杂的条纹。其次，证明了由复化稳定流形和不稳定流形引导的复化轨迹是产生边缘隧穿效应的原因。这种机制提供了一种不同于经典瞬子机制的新的隧穿图景。从数学的角度来看，该机制被解释为一个发散移动的可移动的奇点，这是起源的复杂的轨迹在一维隧道问题的多值性。少