AI 中文总结
该研究推导了高斯随机矩阵系综正交与酉系谱边混沌本征态的普适保真度 susceptibility 分布，揭示边态对扰动的敏感性低于体态，确立了相关普适统计规律。
AI 中文摘要
我们确定了高斯随机矩阵系综谱边处混沌本征态的保真度 susceptibility 分布。此前研究表明，在酉系中，边态的特征 susceptibility 尺度随$D^{1/3}$增长，而非谱体中的与$D$成正比，这反映了艾里边能级刚性。我们将针对体态引入的基于行列式的框架扩展，推导了正交和酉系综的普适边分布。两个对称类共享标度变量$g/D^{1/3}$，且表现出依赖于对称性的小 susceptibility 的三次方抑制，而它们的大$g$代数尾部则反映了对应的依赖于对称性的能级排斥。尽管本征矢量统计在整个谱范围内保持随机矩阵形式，但边刚性使得低位混沌态对一般扰动的参数敏感性低于体态。我们的结果确立了混沌动力学延伸至基态的系统中依赖于对称性的普适谱边保真度 susceptibility 统计。
英文摘要
We determine the distribution of fidelity susceptibility for chaotic eigenstates at the spectral edge of Gaussian random-matrix ensembles. Previous work showed that, in the unitary class, the characteristic susceptibility scale of edge states grows as $D^{1/3}$, rather than proportionally to $D$ as in the spectral bulk, reflecting Airy-edge level rigidity. Extending a determinant-based framework introduced for bulk states, we derive the universal edge distributions for both the orthogonal and unitary ensembles. The two symmetry classes share the scaling variable $g/D^{1/3}$ and exhibit a symmetry-dependent cubic suppression of small susceptibilities, while their algebraic large-$g$ tails reflect the corresponding symmetry-dependent level repulsion. Although eigenvector statistics retain their random-matrix form throughout the spectrum, edge rigidity makes low-lying chaotic states parametrically less sensitive to generic perturbations than bulk states. Our results establish universal, symmetry-dependent spectral-edge fidelity-susceptibility statistics in systems whose chaotic dynamics extends down to the ground state.
Comments9 pages, 1 figure
