在有限的温度下,光谱形状因子和克里洛夫复杂性的缩放关系
Chengming Tan1, Zhiyang Wei2, Ren Zhang2,3
1University of Science and Technology of China, Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, Hefei 230026, China.
Physical review. E
|February 20, 2025
概括
这项研究探讨了在有限温度下的量子混沌诊断,发现兰佐斯系数与普遍假设一致. 操作者的增长率 (α) 是由温度所限制的,将ergodicity和混乱联系在一起.
科学领域:
- 量子混沌的诊断方法
- 统计力学就是统计力学.
- 凝聚物质物理学 凝聚物质物理学
背景情况:
- 克里洛夫复杂性和光谱形状因子 (SFF) 是研究在无限温度下量子混乱的关键.
- 之前的研究在这些条件下确定了量子混乱系统的普遍性质.
研究的目的:
- 调查有限温度对克里洛夫复杂度和SFF的影响.
- 分析兰佐斯系数的行为及其与普遍假设的关系.
- 在有限的温度下,建立 ergodicity 和操作员生长之间的定量联系.
主要方法:
- 扩展了克里洛夫复杂性和SFF的分析,包括有限温度效应.
- 使用怀特曼内乘积计算了兰佐斯系数.
- 研究了光谱形状因子 (SFF) 和其ergodicity指标 (g).
- 利用高斯正交集和随机旋转模型进行验证.
主要成果:
- 兰佐斯系数 (b_n) 与怀特曼内乘是与普遍假设一致的.
- b_n 的斜率 (α) 被 πk_B*T 所限,其中 k_B 是博尔兹曼常数,T 是温度.
- 温度下降会导致SFF的ergodicity指标 (g) 的下降.
- 埃尔戈迪性指标与兰佐斯系数的斜率 (α) 之间建立了定量关系.
结论:
- 有限温度对克里洛夫复杂度和SFF的影响是显著的,并遵循可预测的模式.
- 这项研究证实了即使在非零温度下,某些量子混乱性质的普遍性.
- 建立了运营商增长率和系统ergodicity程度之间的直接联系.
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