非厄米随机矩阵的普适特征向量统计
Universal Eigenvector Statistics of Non-Hermitian Random Matrices
- Princeton University（普林斯顿大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究将非厄米随机矩阵的普适性扩展至特征向量重叠统计，通过费米子复制非线性σ模型建立与厄米能级统计的对偶，并在多种物理模型中验证了归一化重叠的普适性。
AI中文摘要：
特征向量重叠量化了非正交性，并控制着非厄米系统的响应和动力学。我们将非厄米随机矩阵的普适性扩展到这些重叠的统计。我们获得了谱体及原点附近特征向量重叠的解析表达式，覆盖了大矩阵尺寸极限下的十种对称类。利用费米子复制非线性σ模型，我们将这些重叠与厄米能级统计联系起来，逐对称类、逐拓扑扇区地建立对应关系。在各种物理模型中的数值计算支持了所研究区域内归一化重叠的普适性。我们的工作建立了厄米能级统计与非厄米特征向量重叠之间的对偶性。
英文摘要：
Eigenvector overlaps quantify nonorthogonality and govern the response and dynamics of non-Hermitian systems. We extend the universality of non-Hermitian random matrices to the statistics of these overlaps. We obtain analytical expressions for eigenvector overlaps in the spectral bulk and near the origin, covering ten symmetry classes in the limit of large matrix size. Using fermionic replica nonlinear $σ$ models, we relate these overlaps to Hermitian level statistics, symmetry class by symmetry class and topological sector by topological sector. Numerical calculations in various physical models support the universality of the normalized overlaps in the regimes studied. Our work establishes a duality between Hermitian level statistics and non-Hermitian eigenvector overlaps.
