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This research introduces a stationary framework for identifying structured quantum memory within the Krylov space of nonintegrable systems. By analyzing depth-resolved occupation profiles, the study reveals how anomalous initial states maintain residual fluctuations and persistent currents even as they thermalize. Such insights are fundamental to understanding information retention in complex quantum many-body dynamics rather than offering immediate product applications or classical computing breakthroughs.
Krylov-Space Memory Cores
arXiv:2607.26011v1 Announce Type: cross Abstract: We introduce Krylov-space memory cores as stationary, depth-resolved structures that reveal how anomalous initial-state memory is organized inside the Krylov space of otherwise thermalizing nonintegrable systems. The stationary occupation profile identifies where late-time probability is concentrated along the Krylov chain, while complementary diagnostics of residual equilibration fluctuations, deviation from the Gibbs reference, and long-time Krylov-current fluctuations determine the physical character of that region. Across weak thermalization, confinement-induced anomalous dynamics, and many-body scarring, anomalous initial states develop compact low-depth memory cores that carry appreciable residual fluctuations, Gibbs mismatch, and persistent current-fluctuation activity. These cores are often embedded within substantially broader stationary occupation halos. Generic reference states, by contrast, do not exhibit a comparable combination of signal strength and spatial compactness. An auxiliary integrable comparison further shows that compact Krylov memory is state selective rather than a generic consequence of integrability. Krylov-space memory cores therefore provide a stationary framework for identifying where structured quantum memory resides and how it remains dynamically encoded.
Abstract:We introduce Krylov-space memory cores as stationary, depth-resolved structures that reveal how anomalous initial-state memory is organized inside the Krylov space of otherwise thermalizing nonintegrable systems. The stationary occupation profile identifies where late-time probability is concentrated along the Krylov chain, while complementary diagnostics of residual equilibration fluctuations, deviation from the Gibbs reference, and long-time Krylov-current fluctuations determine the physical character of that region. Across weak thermalization, confinement-induced anomalous dynamics, and many-body scarring, anomalous initial states develop compact low-depth memory cores that carry appreciable residual fluctuations, Gibbs mismatch, and persistent current-fluctuation activity. These cores are often embedded within substantially broader stationary occupation halos. Generic reference states, by contrast, do not exhibit a comparable combination of signal strength and spatial compactness. An auxiliary integrable comparison further shows that compact Krylov memory is state selective rather than a generic consequence of integrability. Krylov-space memory cores therefore provide a stationary framework for identifying where structured quantum memory resides and how it remains dynamically encoded.
High Energy Physics - Theory (hep-th); Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)
arXiv:2607.26011 [hep-th]
(or arXiv:2607.26011v1 [hep-th] for this version)
https://doi.org/10.48550/arXiv.2607.26011 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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