Average Spread Complexity and the Higher-Order Level Spacing

2025/04/19 by Amin Faraji Astaneh, Astaneh, Amin Faraji, Niloofar Vardian +1 · 4 citations
Physics and Astronomy · #Chaos control and synchronization #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #Quantum many-body systems #Statistical Mechanics (cond-mat.stat-mech)

paper · pdf · doi:10.48550/arxiv.2504.14362

openalex publication_date 2025/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

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Cited by

• On Krylov Complexity as a Probe of the Quantum Mpemba Effect
• Generalized Krylov Complexity
• Comparative Study of Indicators of Chaos in the Closed and Open Dicke Model

Related

• Spacing ratios in mixed-type systems
• Spread complexity evolution in quenched interacting quantum systems
• Higher-Order Krylov State Complexity in Random Matrix Quenches
• Variations on a Theme of Krylov
• Universal Growth of Krylov Complexity Across A Quantum Phase Transition