Studies on Chaotic Tunneling

混沌隧道研究

• 批准号: 10640395
• 负责人: IKEDA Kensuke
• 金额: $ 1.98万
• 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: 1998
• 资助国家: 日本
• 起止时间: 1998 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640395/
• 关键词: turnding effect; chaos; serniclassiate thesrty; complex dynamical system; Julia Aef; 複素力学系; 複素半古典論; カオス的トンネル効果; 半右典論; ストークス現象

Multi-dimensional tunneling phenomena is studied putting particular emphasis on chaotic phenomena. Dynamical tunneling and barrier tunneling are investigated extensively in terms of complex-domain semiclassical theory.It reveals that a characteristic complexified classical manifold which we call "Laputa chain" plays a crucial role in the classical description of dynamical tunneling among chaotic and inte-grable domains of the phase space. Taking into Laputa chains, we found that the semiclassical theory reproduces every detail of tunneling wave function. We also showed that the Laputa chain is closely related with the Julia sets, which is a central concept of complex dynamical systems.In the barrier tunneling problem, we discovered that the heteroclinic entanglement between the unstable manifold of the tunneling barrier and the input beam surface plays a crucial role. Such an effect drastically changes the multi-dimensional tunneling through the energy barrier which has completely been overlooked in the traditional theory of multi-dimensional tunneling

研究多维隧道现象，特别强调混沌现象。动态隧道效应和势垒隧道效应在复杂域半经典理论方面得到了广泛的研究。它揭示了一种特征复杂的经典流形，我们称之为“拉普塔链”，在相空间混沌可积域之间动态隧道效应的经典描述中起着至关重要的作用。考虑到拉普达链，我们发现半经典理论再现了隧道波函数的每一个细节。我们还表明，拉普达链与朱莉娅集密切相关，朱莉娅集是复杂动力系统的中心概念。在势垒隧道问题中，我们发现隧道势垒的不稳定流形与输入光束表面之间的异宿纠缠起着至关重要的作用。这种效应极大地改变了传统多维隧道理论中完全忽略的穿过能量势垒的多维隧道效应

项目成果

H.Yamada and K.S.Ikeda: "Dynamical delocalization in one-dimensional disordered system with oscillatory perturbation" Phys.Rev.E. (印刷中). (1999)

H. Yamada 和 K. S. Ikeda：“具有振荡扰动的一维无序系统中的动态离域”Phys.Rev.E（出版中）。

首藤啓,池田研介: "カオス的トンネル効果"日本物理学会誌. 54. 716-725 (1999)

Kei Shuto、Kensuke Ikeda：“混沌隧道效应”日本物理学会杂志 54. 716-725 (1999)。

K.Takahashi and K.S. Ikeda: "Complex-domain semiclassical theory : application to time-dependent barrier tunneling problems."Foundations of Physics. 31. 177-201 (2001)

高桥 K.S.

首藤啓、池田研介: "カオス的トンネル効果"日本物理学会誌. 54. 716-725 (1999)

Kei Shuto、Kensuke Ikeda：“混沌隧道效应”日本物理学会杂志 54. 716-725 (1999)。

高橋公也: "複素力学系と多次元トンネル効果"数理科学. 434. 11-21 (1999)

Kimiya Takahashi：“复杂动力系统和多维隧道效应”《数学科学》434. 11-21 (1999)。