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Average Spread Complexity and the Higher-Order Level Spacing

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arxiv 2504.14362 v2 pith:7XRGAJQZ submitted 2025-04-19 hep-th cond-mat.stat-mechquant-ph

Amin Faraji Astaneh , Niloofar Vardian This is my paper
classification hep-thcond-mat.stat-mechquant-ph
keywords levelcomplexityspacingsystemschaotichigher-orderintegrablespread
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We investigate the spread complexity of a generic two-level subsystem of a larger system to analyze the influence of energy level statistics, comparing chaotic and integrable systems. Initially focusing on the nearest-neighbor level spacing, we observe the characteristic slope-dip-ramp-plateau structure. Further investigation reveals that certain matrix models exhibit additional iterative peaks, motivating us to generalize the known spacing distributions to higher-order level spacings. While this structure persists in chaotic systems, we find that integrable systems can also display similar features, highlighting limitations in using complexity as a universal diagnostic of quantum chaos.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Krylov-Space Memory Cores

    hep-th 2026-07 conditional novelty 6.0 of 10

    Anomalous initial states in otherwise thermalizing models leave compact, stationary low-depth Krylov-space cores—regions with persistent fluctuations, Gibbs mismatch, and current activity—while generic states do not.

  2. Higher-order spacings in the superposed spectra of random matrices with comparison to spacing ratios and application to complex systems

    physics.data-an 2025-10 conditional novelty 6.0 of 10

    Higher-order spacing distributions of m-superposed COE/CUE/CSE spectra are fitted to Wigner-Dyson forms, yielding tabulated modified Dyson indices β′(k,m,β), with a uniqueness conjecture tested on the quantum kicked t...

  3. Generalized Krylov Complexity

    hep-th 2025-07 conditional novelty 5.0 of 10

    The paper defines generalized Krylov complexity for multi-generator unitary evolutions, computes it for U(1)xU(1), a U(1)xU(1) subgroup of SO(10), and SU(2), and introduces a weighted version.

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