Research for Many-Dimensional Quantum and Classical Chaos

多维量子和经典混沌研究

• 批准号: 62540263
• 负责人: IKEDA Kensuke
• 金额: $ 1.54万
• 依托单位: Kyoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1987
• 资助国家: 日本
• 起止时间: 1987 至 1989
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-62540263/
• 关键词: Chaos; Quantum chaos; Quantum-classical correspondence; Turbulence; Information theory; 量子ー古典対応; 大自由度系; 量子古典対応; 半古典近似; 情報理論的方法; 動的摂動活性; エルゴード性; 混合性; 高次元量子カオス; 一次元乱流系; リアプノフ解析; 情報流率法

1 : Study of many-dimensional quantum chaos--The aim of the present research is to elucidate whether quantum-classical correspondence violated in low-dimensional quantum chaos (Q.C) system is restored with an increase in the number of degrees of freedom. Strong numerical evidences that Q.C. system with more than 3 degrees of freedom can exhibit, though conditionally, the orbital instability that is the essential origin chaotic dynamics. General criterion for the restoration of classical chaotic behavior is established. Through a study of light absorption by Q.C. systeras, we presented numerically "rigorous" evidences showing that Q.C. can be an origin of dissipation.2 : Study of many-dimensional dissipative chaos--An information theoretical method is developed and is shown to be very powerful in characterizing the dynamical structure of complex turbulent behavior in systems of infinite degrees of freedom. We applied this method to the study of various systems modeling optical turbulence, chemical turbulence and so on, and we discovered that a characteristic phenomenon we call (chaotic itinerancy) plays an important role in the process through which a weak turbulence grows into a strong one. Application of the information theoretical method to the study of the fluid turbulence is now being developed.

1：多维量子混沌的研究——本研究的目的是阐明低维量子混沌（Q.C）系统中违反的量子-经典对应是否随着自由度的增加而恢复。强有力的数值证据表明，具有3个以上自由度的qqc系统可以有条件地表现出轨道不稳定性，而轨道不稳定性是混沌动力学的本质根源。建立了恢复经典混沌行为的一般判据。通过对量子阱系统光吸收的研究，我们提供了数值上“严格”的证据，证明量子阱可以是耗散的一个来源。2：多维耗散混沌的研究——发展了一种信息理论方法，并被证明在描述无限自由度系统中复杂湍流行为的动力结构方面非常有效。我们将这种方法应用到光学湍流、化学湍流等各种系统的建模研究中，发现一种我们称之为混沌流动的特征现象在弱湍流发展为强湍流的过程中起着重要作用。信息论方法在流体湍流研究中的应用正处于发展阶段。

项目成果

戸田幹人: "Dynamical aspect of quantum-classical correspondence in quantum chaos" Supplment of Progress of Theoretical Physics. 98. 323-375 (1989)

Mikito Toda：“量子混沌中量子经典对应的动力学方面”理论物理学进展的补充，98. 323-375 (1989)。

水野正彦,池田研介: Physica D.

水野正彦、池田健介：Physica D.

池田研介: "Supplment of Progress of Theoretical Physics" Maxwell-Bloch Turbulence, 1990 (99)

池田健介：《理论物理进展补充》麦克斯韦-布洛赫湍流，1990（99）

池田研介: "Phys.Letter.誌" Can quantum chaos be an origin of dissipotion? Absorption of light by quantum chaos system,

池田健介：“物理快报。”量子混沌系统对光的吸收是否是一个起源？

足立聡, 戸田幹人, 池田研介: Journal of Physics A.

Satoshi Adachi、Mikito Toda、Kensuke Ikeda：物理学杂志 A.