Average Spread Complexity and the Higher-Order Level Spacing

Amin Faraji Astaneh; Niloofar Vardian

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arXiv · 2504.14362

Average Spread Complexity and the Higher-Order Level Spacing

Amin Faraji Astaneh·Niloofar Vardian

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Abstract

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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Amin Faraji Astaneh, Niloofar Vardian. 2025-04-19. Average Spread Complexity and the Higher-Order Level Spacing. https://arxiv.org/abs/2504.14362

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