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Thermal Energy Microscopically, thermal energy is the kinetic energy associated with the random motion of atoms and molecules. Temperature is a quantitative measure of “hot” or “cold”, which depends on the amount of thermal energy. When the atoms and molecules in an object are moving or vibrating quickly, they have a higher average kinetic energy (KE) (or higher thermal energy), and the object is perceived as “hot”, or it is described as being at a higher temperature. When the...
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Heat and temperature are essential concepts for everyone every day. The study of heat and temperature is part of an area of physics known as thermodynamics. It is not always easy to distinguish heat and temperature.
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使用 Toda 积分来测量 FPUT 热化.

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  • 1School of Mathematics and Physics, University of Lincoln, Brayford Pool Campus, Lincoln, United Kingdom.

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概括
此摘要是机器生成的。

这项研究揭示了费米-帕斯塔-乌拉姆-辛古-α模型是如何达到平衡的. 托达积分表明系统大小影响了ergodization时间,特别是在与科尔摩戈罗夫-阿诺德-莫瑟制度相关的临界能量密度附近.

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科学领域:

  • 非线性动力学是一种非线性动力学.
  • 统计力学就是统计力学.
  • 计算物理学的计算物理.

背景情况:

  • 费米-帕斯塔-乌拉姆-辛古-α (FPUT-α) 模型是研究非线性动态和向混乱过渡的基本系统.
  • 了解这些系统的 ergodic 特性对于验证统计力学预测至关重要.

研究的目的:

  • 为了研究FPUT-α模型在通用初始条件下的ergodic特性.
  • 确定与系统平衡方法相关的特征时间尺度.
  • 探索系统大小和能量密度对ergodization的影响.

主要方法:

  • 使用Toda积分作为一个adiabatic不变量和可观测的平衡时间.
  • 将Toda积分的ergodization时间与最大Lyapunov指数的逆值及其和时间进行比较.
  • 数字测量能量密度对临界系统大小的依赖.

主要成果:

  • 对于大型链,Toda积分ergodization时间是独立于系统大小的,但对于一个临界值以下的较小大小,它会急剧增长.
  • 这个临界尺寸取决于能量密度,这表明与科尔摩戈罗夫-阿诺德-莫泽 (KAM) 制度的联系.
  • 对于KAM模式,临界能量密度大致遵循1 / N2衰变,其粒子数为N.

结论:

  • 动作扩散导致FPUT-α模型在其平衡时间尺度上的ergodic时间波动.
  • 系统的大小和能量密度在ergodicity的出现和KAM制度的潜在崩中发挥着关键作用.
  • 观察到的1/N2缩放为多体系统的混乱过渡提供了洞察力.