在无序的古典系统中缓慢消散和扩散:数字和数学界限之间的直接比较
Wojciech De Roeck1, Francois Huveneers2, Oskar A Prośniak3
1KU Leuven University, Leuven 3000, Belgium.
Physical review. E
|May 17, 2024
概括
我们调查了安德森局部分解在一个混乱的非线性系统. 我们的研究结果表明,平衡脱关系时间比逆乘法所预测的要长,这表明当前的数字可能错过了长期行为.
科学领域:
- 物理 物理学 物理
- 凝聚物质物理学 凝聚物质物理学
- 非线性动力学是一种非线性动力学.
背景情况:
- 安德森局部化描述了波函数在无序系统中的限制.
- 一维非线性克莱恩-戈登链是无序的古典多体系统的关键模型.
- 以前的研究表明,波包传播动态的结果是相互矛盾的.
研究的目的:
- 分析非线性克莱恩 - 戈登链的平衡时代.
- 为了协调波包传播的数值和分析预测之间的差异.
- 为了研究经典无序系统的长期行为.
主要方法:
- 数学定理,以建立一个下限的 decorrelation时间.
- 数字模拟观察系统动态和关系时间.
- 对有效无和度参数 (λ) 的分析.
主要成果:
- 一个数学定理证明了脱关系时间超过了 λ 的任何逆乘法.
- 数字模拟显示,在广泛的 λ 范围内,脱关系时间遵循一个功率定律.
- 数字扩展指数与观察到的权力定律行为保持一致.
结论:
- 在平衡状态下,去关系时间在理论上从下面被一个非乘法函数 λ 所限制.
- 数字结果表明,对于 decorrelation 时间的权力定律依赖性,与扩散实验一致.
- 当前的数值方法可能无法准确地捕捉这些经典无序系统的长期动态.
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