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This study establishes a precise scaling law for late-time quantum chaos in many-body systems, demonstrating that unresolved Krylov complexity depends strictly on the dimensions of individual symmetry sectors rather than global averages. By resolving exact symmetries, researchers can more accurately diagnose operator growth and information spreading dynamics after initial transients subside. This refined analytical framework offers a superior method for characterizing chaotic behavior in complex quantum environments compared to previous averaging techniques.

Source coveringQuantum Zeitgeist

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Researchers Link Symmetry to Quantum Chaos Equipartition

Quantum ZeitgeistAugust 25, 20264 min read

Late-time quantum chaos exhibits an unexpected order: unresolved Krylov complexity scales not with average behaviour, but precisely with d_(q)(d_(q) -1), where d_(q) represents each symmetry sector’s Hilbert space dimension. This reveals how accessible operator space, not simply overall averages, dictates chaotic dynamics after initial transients subside. Resolving these conserved symmetries proves vital when using Krylov complexity to diagnose operator growth in complex systems.

Resolving exact symmetries advances understanding of chaotic operator growth within quantum many-body systems. After reaching saturation, unresolved Krylov complexity accumulates across different symmetry sectors; this enables improved interpretation of dynamics in complex scenarios. The approach differs from previous analyses focused on early-time weighted averages, instead focusing on dimensions defining accessible operator spaces to better characterise chaos. Understanding of chaos in quantum systems is refined through analysis within individual symmetries, distinct sub-systems which proves more accurate than averaging methods previously used.…

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