Krylov-Space Memory Cores
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. The reference states considered, 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.
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BibTeX
@misc{alishahiha2026krylovspace,
title = {{Krylov-Space Memory Cores}},
author = {Mohsen Alishahiha and Mohammad Javad Vasli},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2607.26011},
eprint = {2607.26011},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.26011},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Krylov-Space Memory Cores
AU - Mohsen Alishahiha
AU - Mohammad Javad Vasli
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2607.26011
UR - https://arxiv.org/abs/2607.26011
AB - 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. The reference states considered, 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.
ER -