整体平均平均场多体水平密度:一个可整合与混乱单粒子动态的指标
Georg Maier1, Carolyn Echter1, Juan Diego Urbina1
1Universität Regensburg, Institut für Theoretische Physik, D-93040 Regensburg, Germany.
Physical review. E
|June 19, 2025
概括
在多体系统中区分量子混乱是可能的,通过分析平均多体水平密度及其方差,而不仅仅是光谱波动. 这揭示了量子系统中潜在的单粒子动力学.
科学领域:
- 量子力学就是量子力学.
- 统计物理学的统计物理.
- 这是量子混沌.
背景情况:
- 量子混沌范式假定古典动力学 (可整合与混乱) 反映在量子光谱波动中.
- 在平均场极限中的多体光谱表现出波伊森波动,掩盖了底层的单粒子动态.
- 传统分析侧重于普遍的光谱特征,经常删除平均水平密度信息.
研究的目的:
- 为了证明平均多体水平密度及其方差可以区分可整合的与混乱的单粒子动态.
- 调查单个粒子水平相关性在整体平均状态密度及其方差中的作用.
- 为了对比这些效应在玻色子和费米子多体系统.
主要方法:
- 对整体平均状态密度和方差的分析研究.
- 包含Poisson和随机矩阵统计 (各种对称类) 的单个粒子水平相关性.
- 对于具有N≥5颗粒的系统进行了广泛的数值模拟.
主要成果:
- 在平均多体水平密度上发现了显著的差异 (高达数量级),这取决于单粒子动态.
- 对于费米子,Poisson型波动取消了不可区分效应,导致平均多体光谱密度等于托马斯-费米项.
- 该研究突出了平均水平密度及其变异作为总能 (E) 和激发能 (Q) 的函数之间的差异.
结论:
- 平均多体水平密度及其方差作为基本单粒子动态的强有力的指标,克服了光谱波动的局限性.
- 这种方法提供了一种新的方法来探测复杂的多体系统中的量子混乱.
- 这些发现在各种粒子数和统计数据的分析处理和数值模拟中是一致的.
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