The origin of 1/f spectrum fluctuation in the hamiltonian dynamics for lattice systems.

晶格系统哈密顿动力学中 1/f 谱涨落的起源。

• 批准号: 06640515
• 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 Scientific Research (C)
• 财政年份: 1994
• 资助国家: 日本
• 起止时间: 1994 至 1996
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-06640515/
• 关键词: hamiltonian chaos; 1; f spectrum; critical torus; Arnold diffusion; stagnant layr theory; quantum chaos; level statistics; ハミルトン力学系; KAMトーラス; 淀み運動; 間欠性; 散乱カオス; 格子振動; fゆらぎ; カオス; ハミルトン系; 非線形; 散乱系; 非線形格子振動率; 誘導現象; リーマン曲率; ガウス曲率; FPU-βモ

The classical and quantum mechanical aspects of hamiltonian chaos have been studied in relation to the 1/f spectral fluctuations in the long time behaviors. The recent results are the followings :1.The spectral structure of the most stable KAM torus was determined under the nontwist condition.2.The universality of the 1/f^<mu> spectrum (1<less than or equal>mu<less than or equal>2) was obtained by the computer simulations for the symplectic map in 4 dimensional3.The relaxation mechanisms of resonace states were theoretically elucidated by the geodesics representation and the subdynamics method.4.The level statistics for the l/f quantum billiard was obtained by computer simulations, but the mechanism of level repulsions has not yet been elucidated completely.The preliminary results have been already reported in severeal journals.

研究了哈密顿混沌的经典和量子力学性质与1/f谱涨落的关系。最近的研究结果如下：1.在无扭条件下确定了最稳定的KAM环面的谱结构。2.通过计算机模拟得到了四维辛映射1/f^<mu>谱（1 <less than or equal>μ <less than or equal>2）的普适性。3.用测地线表示和子动力学方法从理论上阐明了共振态的弛豫机制。4.通过计算机模拟得到了1/f量子台球的能级统计。但能级排斥的机制尚未完全阐明，初步结果已在学术期刊上发表。

项目成果

Edited by Y.Awzawa et al.: "Quantum Physics,Chaos Theory and Cosmology" AIP Press, 311 (1996)

Y.Awzawa 等人编辑：《量子物理学、混沌理论和宇宙学》AIP Press，311 (1996)

S.Kurosaki: "Detailed Bifurcations of Periodic Orbits with Threefold Symmetry of the H'enon-Heiles Hamiltonian" J.Phys.Soc.Jpn.64. 3589-3592 (1995)

S.Kurosaki：“具有 Henon-Heiles 哈密顿量三重对称性的周期轨道的详细分叉”J.Phys.Soc.Jpn.64。

M.Tatsuno and Y.Aizawa: "Theory of Characterization of Hippocampal Long-Term Potentiation" To appear in Journal of Physical Society of Japan. (1997)

M.Tatsuno 和 Y.Aizawa：“海马长时程增强特性理论”发表在《日本物理学会杂志》上。

永井 喜則,相澤 洋二: "階層構造とルール・ダイナミクス" 電気学会 IP-95-19. 51-59 (1995)

Yoshinori Nagai、Yoji Aizawa：“等级结构和规则动态”IEEJ IP-95-19 (1995)。

相澤 洋二: "偶然性の物理学" 科学(岩波書店). 4. 266-272 (1995)

相泽洋司：“机会物理学”科学（岩波书店）4. 266-272 (1995)。