嵌入的高斯单元组合与k体相互作用的两点相关函数的双变量时刻
1Physical Research Laboratory, Ahmedabad 380 009, India.
Physical review. E
|June 17, 2023
概括
这项研究在随机矩阵组合中推导出两点相关函数的公式,具有k-body相互作用. 这些发现概括了先前的结果,适用于含费米子的量子系统.
科学领域:
- 量子力学就是量子力学.
- 统计物理学的统计物理.
- 随机矩阵理论是随机矩阵理论.
背景情况:
- 嵌入式随机矩阵组合与k体相互作用模型量子系统.
- 这些集合的两点相关函数还没有得到.
- 最近的工作表明,一点函数遵循q-正常分布.
研究的目的:
- 在嵌入式高斯单元集与k体相互作用 (EGUE(k)) 中推导两点相关函数的公式.
- 将现有知识扩展到这些量子系统的所有k值.
- 为分析自身价值波动提供一个通用的框架.
主要方法:
- 使用SU(N) 维格纳-拉卡代数来推导两点相关函数的双变矩 (ΣPQ) 的公式.
- 使用q-正常分布和q-Hermite多项式扩展了自值密度.
- 在具有有限 N 校正的非对称极限中的协差 (SζSζ') 的衍生式.
主要成果:
- 对于EGUE (k) 的两变矩 ΣPQ 与 P+Q≤8 的公式得到了推导.
- 协方差 SζSζ' 在非对称极限中得到.
- 结果概括和统一以前的发现,以极限的k/m.
结论:
- 衍生的公式提供了对EGUE的两点相关函数的全面描述.
- 这项工作将随机矩阵理论的适用性扩展到更广泛的量子系统中.
- 这些发现为分析复杂量子系统中的光谱统计提供了新的工具.
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