RESEARCH ON ERGODIC PROBLEMS IN HAMILTONIAN DYNAMICS

哈密​​顿动力学中各态历经问题的研究

• 批准号: 02640296
• 负责人: AIZAWA Yoji
• 金额: $ 1.41万
• 依托单位: WASEDA 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: 1990
• 资助国家: 日本
• 起止时间: 1990 至 1992
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-02640296/
• 关键词: Multi-Ergodicity; KAM Torus; Stagnant Layr Theory; Semi-Classical Theory; Quantum Chaos; Orbital Correlation; Irreversibility; Hushimi function; 平衡への接近; 多重エルゴ-ド性; 散乱カオス; 誘導現象; 1; fスペクトル; 法則収束; リャプノフ指数; 最近接間隔分布; 周期軌道; 多重エルゴ-ド運動; リャプノフ数 /

1. The origin of the long time tail was explained from the scaling structures immersed in the stagnant layr. We have propsed the stagnant layr theory to characterize the non-stationrity and the multi-ergodicity of Hamiltonian dynamics. Computer simulations regarding scattering processes and lattice vibrations have justified the theoretical results.2. The irregulatiry of wave functions and energy levels was characterized from the viewpoint of quantum chaos. The Gutzwiller formulae was rederived from the semi-classical approximation of the finite element method.3. The origin of the irreversibility, both in quantal and in classical, was discussed from the weak convergence of the distribution function. The irreversibility in quantal systems was especially surmised to occur in the limit (〕SY.plcnst.〔)->0 for Hushimi functions.

1.从停滞层中的尺度结构解释了长时间尾的起源。我们提出了停滞层理论来表征哈密顿动力学的计算机模拟的非平稳性和多遍历性。 2．从量子混沌的角度重新推导了波函数和能级的不规则性。 3．从分布函数的弱收敛性出发，讨论了量子不可逆性和经典不可逆性的根源。 (]SY.plcnst.〔)->0 对于 Hushimi 函数。