Spectral Edge Rigidity of Quantum Chaotic States

• URL: http://arxiv.org/abs/2608.16847v1
• Date: Mon, 17 Aug 2026 17:33:24 GMT
• Title: Spectral Edge Rigidity of Quantum Chaotic States
• Abstract summary: We determine the distribution of fidelity susceptibility for chaotic eigenstates at the spectral edge of Gaussian random-matrix ensembles.<n>Our results establish universal, symmetry-dependent spectral-edge fidelity-susceptibility statistics in systems whose chaotic dynamics extends down to the ground state.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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