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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弛豫，并提出了一致的解释，解释了为什么液态水动力学表现出幂律弛豫行为并可以形成相空间的瓶颈，即使它是一个多维和强混沌系统。历史上，人们长期以来一直认为液态水动力学是典型的指数快速弛豫。这确实是通过实验观察到的，并据此提出了理论论证。然而，Sasai等人对液态水进行了长时间的微正则MD模拟，发现总势能涨落在室温下呈现出1/f型光谱，而诸如氩之类的更简单的液体呈现出接近白色的光谱。我们的想法受到哈密顿系统微扰理论最新发展的启发，并让人想起所谓的玻尔兹曼-詹斯猜想。在这种情况下，很自然地期望表现出的松弛不限于液态水动力学。我们发现我们的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的关系。 2．研究了矩形盒子中的两个硬球作为最小模型，以观察玻璃态或过冷态的缓慢动力学。严格地证明了盒子中的两个硬球具有混合性和遍历性，并通过数值证明了在适当的条件下观察到了两步相关剖面。这里，特别关注模型中的两种类型的周期轨道：（1）弹跳球模式，这是一种单参数周期轨道族，在单粒子台球模型中引起缓慢松弛；（2）存在于两个硬球之间瓶颈中的周期轨道。后者可以看作是在高维空间中起过渡态作用的所谓常双曲不变流形。大量的数值模拟表明，相关函数显示出两步分布，但两者都是指数的，因此在如此小的系统中不会发生拉伸型相关。此外，发现随着自由度的增加，弹跳球模式的影响减弱。较少的