发表机构
School of Quantum Physics and Matter, Institute for Research in Fundamental Sciences (IPM)（基础科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究引入克雷洛夫空间记忆核，它能揭示非可积系统中异常初始态记忆的组织方式。通过多种诊断确定其物理特性，发现异常初始态形成紧凑记忆核，嵌入更宽晕中，且该记忆是态选择性的，为识别量子记忆位置及编码提供稳态框架。
AI 中文摘要
我们引入了克雷洛夫空间记忆核，它作为一种稳态、深度分辨的结构，揭示了在其他情况下热化的非可积系统的克雷洛夫空间中，异常的初始态记忆是如何组织的。稳态占据分布确定了晚期概率沿克雷洛夫链的集中位置，而对残余平衡涨落、与吉布斯参考的偏差以及长时间克雷洛夫电流涨落的补充诊断则确定了该区域的物理特性。在弱热化、禁闭诱导的异常动力学和多体疤痕等情况中，异常初始态会形成紧凑的低深度记忆核，它们带有可观的残余涨落、吉布斯失配和持续的电流涨落活动。这些核通常嵌入在实质上更宽的稳态占据晕中。相比之下，一般参考态不表现出类似的信号强度和空间紧凑性组合。辅助的可积比较进一步表明，紧凑的克雷洛夫记忆是态选择性的，而非可积性的一般结果。因此，克雷洛夫空间记忆核为识别结构化量子记忆所在位置以及它如何动态编码提供了一个稳态框架。
英文摘要
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.
Comments24 pages, 23 figures, 6 tables, V2; A ref added, V3: 30 pages, 23 figures, 7 tables; equal-gap and chiral-symmetry treatments expanded; numerical analysis expanded; numerical tables and conclusions updated; Ref added;
