量子混沌相互作用哈密尔顿人的中频谱固有状态的平均纠
M Kliczkowski1,2, R Świętek3,4, L Vidmar3,4
1Institute of Theoretical Physics, Faculty of Fundamental Problems of Technology, Wrocław University of Science and Technology, 50-370 Wrocław, Poland.
Physical review. E
|July 19, 2023
概括
量子混沌系统的平均纠密切匹配随机纯态,附带校正只显示微小的偏差. 这项研究量化了这些差异,使用精确的对角化对自旋链.
科学领域:
- 量子信息理论 量子信息理论
- 凝聚物质物理学 凝聚物质物理学
- 统计力学 统计力学
背景情况:
- 量子混沌系统中的纠和随机纯态之间的协议是理解量子混沌的一个关键问题.
- 虽然众所周知,领先阶段的术语 (体积定律) 可以匹配,但下级校正的行为仍然不太了解.
研究的目的:
- 为了研究量子混沌相互作用的哈密尔顿和随机纯态中的中频谱特态的平均纠和随机纯态之间的一致程度.
- 分析子负载项及其与随机纯态预测的偏差,特别是关于O(1) 校正.
主要方法:
- 在旋转-1/2 XYZ 和 XXZ 链上进行了最先进的完全精确的对角化计算,并包含了可整合性断点.
- 引入并利用了由平面间距比率,固态系数分布和纠和随机矩阵理论预测相匹配的"最大混乱状态"概念.
- 进行了有限大小的缩放分析,对频谱的不同分数 (ν) 的纠的子项进行了缩放分析.
主要成果:
- 在最大混乱状态下,对于 ν→0 的纠 Entropy 的负 O(1) 校正的大小仅略大于对随机纯态的预测.
- 一种现象学方法产生了一种简单的表达式,描述了观察到的O(1) 偏差对有限的 ν 的 ν 依赖.
结论:
- 这项研究提供了强有力的数值证据,证明量子混沌自旋链中中谱特态的平均纠非常类似于随机纯态的平均纠,即使是在子负载方面.
- 观察到的偏差被量化,并被证明系统地取决于光谱中包含在平均值中的部分.
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