Dynamics and chaos of molecules

分子动力学和混沌

• 批准号: 11166214
• 负责人: TAKATSUKA Kazuo
• 金额: $ 24.58万
• 依托单位: The Univensity of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research on Priority Areas (A)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11166214/
• 关键词: Quantum chaos; semclassical; cluster; mesoscopic science; molecular vibration; プロトン移動; 表面化学反応; セルオートマトン; パターン形成; カオス; 複雑性動力学; 分子動力学; 非線形力学

Recently, Takatsuka [1] has proposed a modified semiclassical correlation function that is free of the annoying amplitude factor. We refer this function to the amplitude-free correlation function (AFC), which is written in terms of the Action Decomposed Function [2], AFC is composed of only what we call turn-back orbits. Calculation of the turn-back orbits is by far easier than the periodic orbits. The role of the turn-back orbits in describing a standing wave is physically understandable. As an analogy, one may think of the motion of a string, one of the ends of which is spatially fixed on a wall and the other end is shaken. If the phases of ingoing and outcoming waves reflecting at t = 0 match with each other, they should form a stationary state. Here in this talk, we numerically verify that this theory gives really accurate spectrum in a unified manner both to integrable and nonintegrable systems by showing numerically how the AFC actually reproduces the correct eigenvalues of strongly chaotic systems [3]. This epoch-making method can be readily applied to large systems that could not be quantized otherwise.

最近，Takatsuka [1]提出了一种修正的半经典相关函数，它不含恼人的振幅因子。我们将此函数称为无振幅相关函数（AFC），它是根据作用分解函数[2]编写的，AFC仅由我们称之为折返轨道的轨道组成。折返轨道的计算远比周期轨道容易。折返轨道在描述驻波中的作用在物理上是可以理解的。作为一个类比，人们可以想到一根弦的运动，它的一端在空间上固定在墙上，另一端被摇动。如果在t = 0反射的入射波和出射波的相位彼此匹配，则它们应形成稳态。在这次演讲中，我们数值验证了该理论以统一的方式给出了真正准确的谱，通过数值显示AFC实际上如何再现强混沌系统的正确特征值[3]。这种划时代的方法可以很容易地应用于大型系统，否则无法量化。

项目成果

H. Fujisaki, and K. Takatsuka: "Highly Excited Vibronic Eigenfunctions in a Multimode Nonadiabatic System with Duschinsky Rotation"J. Chem. Phys.. 114. 3497-3507 (2001)

H. Fujisaki 和 K. Takatsuka：“具有 Duschinsky 旋转的多模非绝热系统中的高激发电子振动本征函数”J。

H. Ushiyama, and K. Takatsuka: "Successive Mechanism of Double Proton Transfer in Formic Acid Dimer. A Classical Study"J. Chem. Phys.. 115.

H. Ushiyama 和 K. Takatsuka：“甲酸二聚体中双质子转移的连续机制。经典研究”J。

高塚 和夫: "非平衡系の科学IV 分子の複雑性とカオス"講談社サイエンティフィク. 182 (2001)

高冢一夫：“非平衡系统的科学 IV：分子复杂性和混沌”讲谈社科学 182 (2001)。

A.Inoue-Ushiyama, and K. Takatsuka: "Semiclassical Quantization of Strongly Chaotic Vibrations in M7-like cluster"Phys. Rev. E.. 64. 056223-056237 (2001)

A.Inoue-Ushiyama 和 K. Takatsuka：“M7 类星团中强混沌振动的半经典量子化”Phys。

A.Inoue-Ushiyama, K.Takatsuka: "Semiclassical Quantization of Strongly Chaotic Vibrations in M7-like Cluster"Phys. Rev. E.. 64. 056223-15 (2001)

A.Inoue-Ushiyama、K.Takatsuka：“M7 类星团中强混沌振动的半经典量子化”Phys。