在具有内存的随机系统中对利亚普诺夫指数的附属性方法
1Solid State Institute, Technion, Haifa 32000, Israel.
Chaos (Woodbury, N.Y.)
|November 3, 2025
概括
我们开发了一种对非马科夫的随机过程的下属性方法,具有权力定律相关的噪声. 这种方法揭示了与安德森定位相关的自函数的指数增长,并确定波函数定位长度.
科学领域:
- 统计物理 统计物理
- 量子力学就是量子力学.
背景情况:
- 朗格温方程对于建模随机过程至关重要.
- 非马科夫和非高斯过程带来了重大的分析挑战.
- 安德森局部化描述了波函数衰变在无序的潜力.
研究的目的:
- 为兰格温方程开发一个附属方法,用彩色的,权力定律相关的噪声.
- 在这样的系统中分析自身函数及其衍生函数的行为.
- 为了将这些发现与安德森定位现象联系起来.
主要方法:
- 研究了一种具有特定噪声特征的朗格温方程.
- 开发和应用一个标准的下属性方法.
- 分析了秒秒的指数增长和莱普诺夫指数.
主要成果:
- 导出了自函数及其导数的秒速时刻的指数增长.
- 建立了噪声特性与安德森定位之间的联系.
- 获得的值描述了局部波函数的非对称行为.
结论:
- 开发的下属性方法有效地处理非马科夫和非高斯的过程.
- 这项研究提供了对具有内存的系统中安德森本地化的见解.
- 结果确定了随机电位中的波函数的局部长度.
相关概念视频
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