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Spectral Edge Rigidity of Quantum Chaotic States · arXivDesk

2608.16847Aug 17, 20269 pages, 1 figure

Spectral Edge Rigidity of Quantum Chaotic States

Joaquim Telles de Miranda, Tobias Micklitz

Disordered Systems and Neural Networks Statistical Mechanics Quantum Physics

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 $g/D^{1/3}$

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and exhibit a symmetry-dependent cubic suppression of small susceptibilities, while their algebraic large-

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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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