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

研究了多维隧道现象，以特别强调混乱现象。在复杂域的半经典理论方面，对动态隧道和屏障隧道进行了广泛的研究。它揭示了一种特征性的综合经典歧管，我们称之为“ Laputa链”在该相位空间的混沌和整体域中动态隧道的经典描述中起着至关重要的作用。进入拉普塔链，我们发现半经典理论再现了隧道波函数的每个细节。我们还表明，拉普塔链与朱莉娅集合密切相关，朱莉娅集合是复杂的动力系统的核心概念。在屏障隧道问题中，我们发现隧道屏障的不稳定歧管与输入梁表面的不稳定歧管起着至关重要的作用。这种效果彻底改变了多维隧道，通过能量屏障，这在传统的多维隧道理论中被完全忽略了

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)。

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)。

T.Takahashi and K.S.Ikeda: "Complex semiclassical description of scattering problem in systems with 1.5-degrees of freedom"Ann.Phys,. (印刷中). (2000)

T. Takahashi 和 K. S. Ikeda：“1.5 自由度系统中的散射问题的复杂半经典描述”Ann Phys（2000 年出版）。