Dynamical origin of hierachial time scale in many degrees of freedom systems Hamitonian systems with internal degreees of freedom

多自由度系统中分级时间尺度的动力学起源具有内部自由度的哈密顿系统

基本信息

批准号：
15540375
负责人：
SHUDO Akira
金额：
$ 1.54万
依托单位：
Tokyo Metropolitan University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2005
项目状态：
已结题

项目摘要

1. Slow relaxation in dynamics of liquid water at room temperatures is studied and a consistent interpretation explaining why liquid water dynamics exhibits power-law relaxation behavior and can form the bottleneck in phase space is proposed even though it is a many dimensional and strongly chaotic system. Historically, it had long been believed that the liquid water dynamics is a typical expotentially fast relaxation. This was indeed observed experimentally, and theoretical arguments were made based on it. However, Sasai et al performed a long-time microcanonical MD simulations of liquid water and discovered that the total potential energy flunctuation shows 1/f-type spectrum in room temperatures, whereas simpler liquids such as argon exhibit nearly white spectra.Our idea is inspired by recent developments of perturbation theories of Hamiltonian systems, and is reminiscent of the so-called Boltzmann-Jeans conjecture. Within this scenario, it is natrual to expect that show relaxation i … More s not limited to liquid water dynamics. We found the our hypothesis works well in predicting the relaxation properties of other molecules. Relation to the potential landscape picture is also discussed.2. Two hard spheres in a rectangular box was investigated as a minimal model to see the slow dynamics in glassy or supercooled states. It was rigorously shown that two hard spheres in a box has mixing property and so ergodicity, and also numerically shown that two-step correlation profile is observed in a suitable condition. Here, a particular attention is paid on two types of periodic orbits in the model: (1) bouncing ball mode, which is a one parameter family of periodic orbits that cause slow relaxation in a single particle billiard model, and (2) periodic orbits that exist in the bottleneck between two hard balls. The latter can be regarded as the so-called normally hyperbolic invariant manifold that play the role of transition state in higher dimensional space. Extensive numerical simulations reveal that correlation functions show two-step profile, but both are exponential and thus no stretched type correlation does not occur in such a small system. Furthermore, it was found that the influence of bouncing ball mode is weaken as the degrees of freedom increases. Less

1。研究了室温下液态水动力学的缓慢放松，并始终如一地解释了液体水动力学为何表现出强大的放松行为，并且可以在相空间中形成瓶颈，即使它是许多维度且强烈的混乱系统。从历史上看，长期以来一直认为液态水动力学是一种典型的非常快速的放松。确实是通过实验观察到的，并基于它进行了理论论点。然而，Sasai等进行了长期的液态水的微型典型MD模拟，发现总势能波动显示在室温下的1/F型光谱，而诸如氩气暴露于几乎白色光谱之类的简单液体。我们的想法是受汉密尔顿系统扰动理论的最新发展的启发，并想起了所谓的Boltzmann-Jeans猜想。在这种情况下，期望这种放松I…不仅限于液体水动力学。我们发现该假设可以很好地预测其他分子的弛豫特性。还讨论了与潜在景观图片的关系。2。研究了一个矩形盒中的两个硬球作为最小模型，以查看玻璃状或过冷状态的缓慢动力学。严格地表明，一个盒子中的两个硬球具有混合特性和如此奇妙的性能，并且在数值上表明，在合适的条件下观察到了两步相关曲线。在这里，在模型中的两种定期轨道上特别注意：（1）弹跳球模式，这是一个周期性轨道的一个参数家族，在单个粒子台球模型中引起缓慢的放松，以及（2）在两个硬球之间瓶颈中存在的周期性轨道。后者可以被认为是所谓的正常双曲线不变的流形，该流形在更高维空间中起过渡状态的作用。广泛的数值模拟表明，相关函数显示两个步骤曲线，但两者均指数呈指数，因此在如此小的系统中不会出现拉伸类型的相关性。此外，发现随着自由度的增加，弹跳球模式的影响很弱。较少的