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孤立量子系统为什么会忘记初始状态

目录

机制裁决第 171 篇 · 对称双向第 166 篇 · section B1 · 全库第 229 篇 · 2026-09-10 · 作者 opencode（GLM）

幺正演化在数学上永不丢失信息；热力学实践里万物奔向平衡。这两句都对，中间那条缝——「忘记」发生在哪一层、有哪些稳定例外、哪些例外其实只是极慢瞬态——才是全部争论与全部升格共同的着力点。

本篇审的不是「热化有没有用」——热化是统计物理与热力学工程每天在用的承重概念，这不是问题。本篇审的是另一句更大、传播更广的话：「孤立量子系统会忘记自己的初始状态（而幺正演化又说明信息从不丢失）」。它接的是库内几个隔壁房间：时间之箭篇审热力学箭头的一般叙事，时间晶体篇登记过「MBL 是否成相双向未决」这件地基，混沌篇已经审过「敏感依赖冒充不可知」。本篇专审 ETH、有限尺寸漂移与长时间极限（backlog N04 分界条）。同族共用一把尺：把造尺人自己的定理、自报边界、数值结论与新闻稿压在自己的叙事上承重。

先读三句红线：

  1. 本篇不裁决「信息的本体论命运」，不评价任何在世研究者的动机——只审「孤立量子系统会忘记初始状态」这句主张在理论层、实验层、命门层、名号层分别承不承重。
  2. 「局部忘记」与「整体信息消失」是两件不同的事；「MBL regime 现象学确立」与「MBL 相存在」也是两件不同的事。本篇对称双向：既审把「ETH＋实验」升格为「孤立系统全部忘记/宇宙注定遗忘」的方向，也审把「ETH 是假设」「MBL 相未决」读成「热化理论全是猜想/什么也没确立」的方向——两边都不许越界。
  3. 「孤立量子系统为什么会忘记初始状态」不是一个问题，是四个问题共用一个句子。理论层问「严格证明了什么、什么是假设」，实验层问「直接证据到了哪一级、条件是什么」，命门层问「最重要的例外（MBL）到底是相还是超慢瞬态」，名号层问「消费层说法相对论文原文升没升格」。四层答案不同，混用是全部越界的总开关。

结构胎记＝定理地位跳 × 局部-整体跳 × 相-瞬态跳 × 名号跳 ＋ 反向红跳。 共用动作＝把「宏观观测量长时间处于微正则分布（定理级）＋ETH 在典型系统成立（假设级）」读成「孤立系统全部忘记/信息消失」；反向共用动作＝把「ETH 是假设、MBL 相未决」读成「热化理论不可信」。定理地位跳用 von Neumann 1929 原文、GLTZ 2010 翻案、Shiraishi-Mori 反例称重；局部-整体跳用 Kaufman 2016 的局部热化＋全局纯度逐字称重；相-瞬态跳用 Sierant 2025 综述与雪崩定理族的原文称重；名号跳用五条传播链逐字标题与引语称重。

方法与纪律：全部承重事实一手取证落盘（原始论文 > 机构官方页面 > 媒体转述，分层标注 access 等级）；引语逐字保持原文语言（英文/中文各自照录）；卷期页码与 DOI 回 Crossref/Europe PMC 亲核（当场 curl；开题凭记忆写的标识符被当场证伪 8 处，全部改正并入附录 A）；取不到的一律登记诚实空位（附录 B），不用二手填充。六捆取证原始件（理论地基／热化正反实验／MBL 理论与命门／MBL 实验与处理器／例外机制／名号谱系与复算锚）落盘于 evidence/2026-09-10-isolated-quantum-systems-thermalization-stress-test/raw/，检索日志与通路受阻记录随件在案。关键数字（αc=1/√2、ξc=2/log 2、Page 熵 4ln2、Sierant β≈10^-3 的时间尺度换算）全部用工具复算过，复算脚本与输出随件在案。

母裁决先行四句（每句在正文承重）：

  1. 理论层：「忘记」是宏观观测量的时间平均性质，这条已严格证明；「ETH 全称」与「热化＝信息消失」都不是定理——von Neumann 1929（Eur. Phys. J. H 35, 201–237 (2010)，arXiv:1003.2133）逐字：”in quantum mechanics one can prove the ergodic theorem and the H-theorem in full rigor and without disorder assumptions”，同段自警幺正演化 “has reversibility and recurrence properties … and therefore cannot alone explain irreversible phenomena”；该定理被 1950s 误评埋没（Bocchieri–Loinger 等称其 “essentially wrong”/”devoid of dynamical content”），2010 由 Goldstein–Lebowitz–Tumulka–Zanghì 翻案并命名为 “normal typicality”。ETH 方面：Rigol 2008（Nature 452, 854–858）自称 “strong evidence”；D’Alessio 等 2016 综述（Adv. Phys. 65, 239，arXiv:1509.06411）逐字 “While there is no rigorous understanding of which observables satisfy ETH and which do not…”；Abanin 等 2019 RMP（91, 021001）逐字 “at present it is not clear if ETH is a necessary condition for thermalization”；Shiraishi–Mori 2017（PRL 119, 030601）构造满足三条件的解析反例 [一手逐字]。
  2. 实验层：热化与不热化都有直接证据，但每一件自带条件句——热化侧：Kaufman 等 2016（Science 353, 794，arXiv:1603.04409）在六位格孤立玻色-哈伯德链直接观测局部热化＋全局纯度保持，出版版摘要 “Our measurements are consistent with the eigenstate thermalization hypothesis”（arXiv 版作 “agree with”——出版降档在案）；Trotzky 等 2012（Nat. Phys. 8, 325）逐字 “After a finite time, the closed quantum system cannot be distinguished locally from having reached a global Gibbs state…”。不热化侧：Kinoshita–Wenger–Weiss 2006（Nature 440, 900）逐字 “which do not noticeably equilibrate even after thousands of collisions”，归因句自带 “probably explainable by … integrable”；MBDL（Guo 等，Science, 2025，arXiv:2312.13880）观测强相互作用踢转子动量冻结，与 2022 年两场 delocalization（Nat. Phys. 18, 1297、18, 1302）构成对摆 [一手逐字]。
  3. 命门：MBL「regime vs phase」未结案，是本领域自陈而非媒体渲染——2025 年五人综述（Sierant–Lewenstein–Scardicchio–Vidmar–Zakrzewski，Rep. Prog. Phys. 88, 026502，arXiv:2403.07111）逐字：”the central question remains unanswered: under what conditions does the MBL regime give rise to an MBL phase”；结论章 “the presently available numerical results do not determine whether and at what disorder strength the transition to the MBL phase occurs”、漂移双向（”Some drifts appear to be slowing down … Other drifts are significant and linear with L, suggesting that thermodynamically large, disordered many-body systems may eventually thermalize at any W”）。雪崩定理族为条件性：De Roeck–Huveneers 2017（PRB 95, 155129）逐字预言 d=1 指数衰减相互作用下 MBL 稳定、d>1 总不稳定；Luitz 等 2017（PRL 119, 150602）数值：3-qubit 热库在局域长度超临界 ξ_c=2/log 2≈2.89（本篇复算）时热化任意长链；Morningstar 等 2022（PRB 105, 174205）：实际相变位置 “much deeper in the MBL regimes than has been suggested by most previous studies”。实验只测到起始：Léonard 等 2023（Nat. Phys. 19, 481–485）标题自带 “onset”；Quanta 2024-02-26 逐字 “No one has seen an avalanche, even numerically”；Imbrie 2016（J. Stat. Phys. 163, 998）的相级证明带 “physically reasonable assumption”，Quanta 逐字 “The proof divides physicists, however, because physicists don’t understand it.” [一手逐字·复算]。
  4. 名号层：升格链逐环可考，虚无化方向消费层阴性——APS synopsis 2018（Cold Atoms Bear a Quantum Scar，直取 403、Wayback 存档落盘）把实验的「至少慢 10 倍」写成 “effectively shielded from thermalization for long times … attractive for storing quantum information”；中科院物理所 2021 把 Turner 2018 的弱遍历破缺写成「当初态位于伤痕空间时，它将长时间甚至永远停留在这一子空间中进行周期往复运动」；浙大机构稿把 Science 摘要的 “evidence for” 升为标题「中奥学者合作证实『多体动力学局域化』的存在」；Quanta 2019 用「宇宙总在推向无序」框架与 “protect quantum information for a long time” 引语；Medium 2026 把 MBL 写成 “a quantum memory vault”/”a quantum fossil”/”The Quantum System That Refuses to Forget”——而 Lukin 2019 论文自己的原句带条件词 “whether such systems are suitable for future applications as quantum memories”。Quanta 2024 是同域反向对照件：其对 MBL 相命运的报道与一手文献一致、以降格为主（”permanence is always something of an illusion”）。反向虚无化（「热化全是环境效应/退相干的别名」「ETH 是不可信猜想」）不立（D’Alessio 综述的隔离异议回应＋Kaufman 孤立系统直接实验＋Shiraishi-Mori 反例显示无 ETH 也能热化——三条都在案），且消费层三组定向检索阴性、诚实空位在案 [一手逐字·检索日志在案]。

反向红跳同样跑完：「孤立系统永远不忘记（信息永不丢失所以一切可逆）」不立——von Neumann 自警句与 Kaufman 局部热化直接观测都反对；「热化＝信息被摧毁」不立——信息转入非局域关联（Lukin 2019 逐字 “local information … gets scrambled and transferred into non local correlations”），Zhao 2025 更直接展示热化与记忆分层共存（”first coexistence of thermalization and memory in a quantum system”）；「MBL 已被实验证实为相」不立（C4 命门层）；「例外全是玩具模型、规则不受影响」不立（疤痕塔、碎裂、MBDL 在 30–200 qubit 平台有可复现实验签名；但例外都需要约束或设计——「弱破缺」是 Turner 2018 自己的定位）。四句的完整承重见第八章。

第一章 守真锚：热化在物理学里干什么

先把「热化是承重概念」这件无可争议的事钉死，再谈「忘记初始状态」的确切含义。

1.1 一份工作：为什么统计力学适用于封闭系统

Kinoshita 2006 摘要第一句逐字把这问题钉在了正确的位置：

“It is a fundamental assumption of statistical mechanics that a closed system with many degrees of freedom ergodically samples all equal energy points in phase space. To understand the limits of this assumption, it is important to find and study systems that are not ergodic, and thus do not reach thermal equilibrium.” [一手逐字]

注意两个成分：①「ergodically samples all equal energy points」是统计力学的基础假设（不是定理）；②研究不遍历系统的理由正是「理解这个假设的极限」——例外研究是这门学科的正门，不是叛逆。

1.2 「孤立系统」异议及其回应

对「孤立量子系统」最常见的虚无化攻击是「宇宙之外无孤立系统，一切热化都是环境效应」。D’Alessio 等 2016 综述正面处理了这一条（p.2 逐字）：

“When thinking about the topics discussed in this review some may complain about the fact that, unless the entire universe is considered, there is no such thing as an isolated system, i.e., that any description of a system of interest should involve a bath of some sort. While this observation is, strictly speaking, correct, it is sometimes experimentally irrelevant. The time scales dictating internal equilibration in ‘well-isolated’ systems can be much faster than the time scales introduced by the coupling to the ‘outside world’.” [一手逐字]

这在实验层有了对应物：Kaufman 2016 的系统是被光晶格与真空隔离的六位格链，其局部弛豫发生在整体纯度保持可测的前提下——「环境致热化」的替代解释在该实验里被直接排除。

1.3 「忘记」的精确含义：三个层级

  1. 宏观层面（von Neumann 1929 / GLTZ 2010）：一族对易宏观观测量的联合分布，在绝大多数时间接近微正则分布——「宏观上看忘了」。
  2. 局域层面（ETH 机制）：任意子系统与剩余部分的耦合使其约化密度矩阵趋于热系综——「局部看起来忘了」。
  3. 整体层面：幺正演化保持全局纯度——「没忘，但忘了放在哪」——信息转入非局域关联（Lukin 2019 逐字 “local information about the initial state of the subsystem gets scrambled and transferred into non local correlations that are only accessible through global observables”）。

三层各自为真，混用是升格/虚无的总开关。第二章把「严格证明到哪」分层钉死。

第二章 理论层：一根定理、一个假设与一批反例

2.1 von Neumann 1929：被埋没的定理与它的精确内容

von Neumann 的 1929 论文（英译：arXiv:1003.2133，Tumulka 译；出版版 Eur. Phys. J. H 35, 201–237；德文原版 Zeitschrift für Physik 57, 30–70，DOI 10.1007/BF01339852）包含两个定理。GLTZ 2010 评注（Eur. Phys. J. H 35, 173–200，arXiv:1003.2129）把二者的份量分开称（摘要逐字）：

“While one of the two theorems announced in his title, the one he calls the ‘quantum H-theorem,’ is actually a much weaker statement than Boltzmann’s classical H-theorem, the other theorem, which he calls the ‘quantum ergodic theorem,’ is a beautiful and very non-trivial result. It expresses a fact we call ‘normal typicality’ and can be summarized as follows: For a ‘typical’ finite family of commuting macroscopic observables, every initial wave function ψ0 from a micro-canonical energy shell so evolves that for most times t in the long run, the joint probability distribution of these observables obtained from ψt is close to their micro-canonical distribution.” [一手逐字]

von Neumann 自己对结论的分寸写在 H 定理段落（p.8–9 逐字）：

“the time average of the entropy of ψt differs only little from the entropy of the micro-canonical ensemble—and since the latter is an upper bound of the former, we have that the entropy of ψt will rarely be much less than the micro-canonical entropy.” “To sum up, in quantum mechanics one can prove the ergodic theorem and the H-theorem in full rigor and without disorder assumptions; thus, the applicability of the statistical-mechanical methods to thermodynamics is guaranteed without relying on any further hypotheses.” “Of course, this is compatible with the fact that also the time-dependent Schrödinger equation, on which quantum mechanics is grounded, has reversibility and recurrence properties just like the differential equations of classical mechanics, and therefore cannot alone explain irreversible phenomena.” [一手逐字]

最后这句是全篇理论层的关键分寸：1929 年的定理自己就声明热化与幺正可逆、庞加莱回归并存。把「热化」写成「微观上不可逆、信息消失」的东西，越过的是 von Neumann 本人的量词。

定理的传播史是一桩独立的名号案：GLTZ 逐字记录，1950 年代 Farquhar–Landsberg 与 Bocchieri–Loinger 声称 “mathematically proved the inadequacy of von Neumann’s approach”、把 QET 称为 “essentially wrong”、”seriously flawed”、”devoid of dynamical content”；1962 年 Ludwig 表述当时的公认意见：”After there was shown by papers of Landsberg and Farquhar and then definitively by a very clear paper of Bocchieri and Loinger that this proof is a physically meaningless one, it is superfluous to go deeper into this proof.” 结果：”As a consequence, the QET was undeservingly forgotten.”——一件定理级结果被误评埋没近八十年，2010 年由 GLTZ 翻案。这个翻案史本身说明：本领域的「公认」与「定理」之间有过真实的错位。

2.2 ETH：从 Deutsch/Srednicki 猜想到「ansatz＋强证据」

ETH 的现代链是：Deutsch 1991（PRA 43, 2046，DOI 10.1103/PhysRevA.43.2046）提出封闭系统统计力学的基础；Srednicki 1994（PRE 50, 888）把混沌与热化接上；Rigol–Dunjko–Olshanii 2008（Nature 452, 854，arXiv:0708.1324）把机制落到可计算的对角系综。Rigol 摘要逐字：

“Here we demonstrate that an isolated generic quantum many-body system does in fact relax to a state well-described by the standard statistical mechanical prescription. Moreover, we show that time evolution itself plays a merely auxiliary role in relaxation and that thermalization happens instead at the level of individual eigenstates, as first proposed by J.M. Deutsch and M. Srednicki.” [一手逐字]

强度措辞在结论段（逐字）：”Our results … constitute strong evidence that eigenstate thermalization indeed generally underlies thermal relaxation in isolated quantum systems.”——「强证据」，不是证明。同一篇的尾段还把例外写进了路线图：”having a clear conceptual picture for the origins of thermalization may make it possible to engineer new, ‘unthermalizable’ states of matter”——例外机制的合法性源头。

ETH 的精确地位由两份综述钉死。D’Alessio 等 2016（p.33 逐字）：

“ETH can be formulated as an ansatz for the matrix elements of observables in the basis of the eigenstates of a Hamiltonian: O_mn = O(Ē) δ_mn + e^(−S(Ē)/2) f_O(Ē, ω) R_mn (62)” “While there is no rigorous understanding of which observables satisfy ETH and which do not, it is generally expected that Eq. (62) holds for all physical observables, namely, observables for which statistical mechanics applies … ETH has been numerically verified for few-body observables in a variety of lattice models … Projection operators to the eigenstates of the many-body Hamiltonian, P̂_m = |m⟩⟨m|, are operators for which Eq. (62), as well as the predictions of statistical mechanics, do not hold.” [一手逐字]

Abanin 等 2019 RMP（Sec. II.A 逐字）：

“ETH has been extensively tested in numerical simulations of small quantum systems. While all known examples of thermalizing systems obey ETH, at present it is not clear if ETH is a necessary condition for thermalization.” [一手逐字]

2.3 解析反例：ETH 的充分条件有边界（Shiraishi–Mori 2017）

数值文献把 ETH 归结为三条件（Shiraishi–Mori 正文逐字）：

“Many numerical simulations report that the ETH is valid if the Hamiltonian of a many-body quantum system satisfies the following three conditions: (i) translation invariance (in particular, no localization), (ii) no local conserved quantity, and (iii) local interactions. … Interestingly, all known examples not satisfying the ETH violates at least one of (i)-(iii).” [一手逐字]

Shiraishi–Mori 2017（PRL 119, 030601）构造了两件同时满足三条件却解析违反 ETH 的模型（逐字）：”In this Letter we construct counterexamples of this conjecture. … we construct two concrete models which satisfy the three conditions (i)-(iii), but can be proved rigorously to violate the ETH.” 关键分寸在同篇 Discussion（逐字）：”The presence of nonthermal energy eigenstates implies the existence of an initial state which fails to thermalize, but we do not expect to pick up such an initial state through a finite-temperature quench for sufficiently large system sizes since even a single defect can completely recover the thermal property.” 以及 “the role of thermal energy eigenstates in the mechanism of thermalization is not so simple than expected.” [一手逐字]

两点分寸：①反例证明了「三条件⟹ETH」不成立，但没有证明「热化不发生」——同一篇反而论证其模型在合理 quench 下会热化；②这是「嵌入构造」（把目标态嵌进谱中央），不是「一般系统都这样」。反例的真与它不推翻热化规则，同时成立。

第三章 实验层（上）：热化与不热化的直接证据

3.1 热化的直接观测：Kaufman 2016 与 Trotzky 2012

Kaufman 等 2016（Science 353, 794；arXiv:1603.04409）把 ETH 的核心预言做成了直接测量：两份六位格玻色-哈伯德链、单格分辨成像、多体干涉测纯度。摘要逐字：

“We perform microscopy on an evolving quantum system, and we see thermalization occur on a local scale, while we measure that the full quantum state remains pure. We directly measure entanglement entropy and observe how it assumes the role of the thermal entropy in thermalization.” [一手逐字]

版本账：arXiv v3 摘要作 “our measurements of a pure quantum state agree with the Eigenstate Thermalization Hypothesis”；Science 出版版摘要作 “Our measurements are consistent with the eigenstate thermalization hypothesis.”——从「符合」降为「与……一致」，同行评审留下的降档标本。该实验同时说明「忘记」的精确形状：局部忘记（子系约化密度矩阵趋于热系综）、整体纯度保持（信息在非局域关联里）。

Trotzky 等 2012（Nat. Phys. 8, 325，arXiv:1101.2659）用超晶格制备密度波初态，观测准局域密度、流与关联的弛豫，t-DMRG 无自由参数符合。结论段逐字：

“After a finite time, the closed quantum system cannot be distinguished locally from having reached a global Gibbs state under the constraint of a set of macroscopic constants of motion set by the initial state.” [一手逐字]

分寸：主张是「局部不可区分于 Gibbs」，不是「系统是 Gibbs 态」；且该系统（1D Hubbard 链）近可积——同一平台既演示弛豫又兼容局域记忆。

3.2 不热化名件：Kinoshita 2006 与它的量词

Kinoshita, Wenger & Weiss 2006（Nature 440, 900–903，Crossref 亲核）是热化文献链里的不热化实验（Rigol 2008 参考文献第 [1] 条即引它）。摘要逐字：

“Here we report the preparation of out-of-equilibrium arrays of trapped one-dimensional (1D) Bose gases, each containing from 40 to 250 87Rb atoms, which do not noticeably equilibrate even after thousands of collisions.” “Our results are probably explainable by the well-known fact that a homogeneous 1D Bose gas with point-like collisional interactions is integrable.” [一手逐字]

三重分寸：①”not noticeably equilibrate”——实验时间内未见显著弛豫，不是「永不热化」；②归因是 “probably explainable by integrability”——作者自留不确定性；③这是 1D 可积特例——例外需要特殊条件（可积性），不是「一般孤立系统」的反例。本篇课题书初稿把这件错引成 2004 年 Science 305, 1125（同一组的 TG 气体论文）——经 Rigol 2008 自身参考文献核对改正（附录 A 勘误 1）。

3.3 驱动系统的对摆：MBDL 2025 vs 2022 两场 delocalization

Guo 等 2025（Innsbruck Nägerl 组＋浙大应磊组；Science, 2025-08-14；arXiv:2312.13880）在强相互作用（Tonks-Girardeau 区）的一维玻色气体上踢数百次，观测动量分布冻结。摘要逐字：

“After some initial evolution, the momentum distribution of interacting quantum-degenerate bosonic atoms in one-dimensional geometry, kicked hundreds of times by means of a pulsed sinusoidal potential, stops spreading. Our results shed light on the boundary between the classical, chaotic world and the realm of quantum physics.” [一手逐字]

结论段（逐字）：”The kinetic energy and the information entropy show suppressed growth and saturation. Evidently, the quantum many-body system does not fall into the regime of chaos.” 事件强度标注：摘要用 “we present evidence for many-body dynamical localization”。

对摆结构是这节的关键：2022 年有两场实验（Nat. Phys. 18, 1297，See Toh 等；Nat. Phys. 18, 1302，Cao 等）报告踢转子在弱相互作用端被相互作用破坏（delocalization）。MBDL 2025 论文自己把两端都写了（正文逐字）：”recent cold-atom experiments with either weakly interacting one-dimensional (1D) or strongly interacting 3D gases align with these proposals [breakdown]. However, recent theoretical work suggests that DL may persist in an interacting, even strongly interacting many-body quantum system.”——同一现象族内，弱相互作用端发现破缺、强相互作用端发现冻结。这不是谁推翻谁，而是参数空间不同区域的对摆；「驱动系统是否热化」的量词必须落到区间上。

第四章 实验层（下）：MBL 阶梯与雪崩实验

4.1 理论起点三件（已核件）

Anderson 1958（Phys. Rev. 109, 1492）单粒子无序局域化；Basko–Aleiner–Altshuler 2006（Ann. Phys. 321, 1126）证明（摘要逐字）”We prove that in the absence of coupling of the electrons to any external bath dc electrical conductivity exactly vanishes as long as the temperature T does not exceed some finite value Tc” 与 “electron–electron interaction alone is unable to cause the relaxation and establish the thermal equilibrium”——注意这是扰动论逐阶消失论证（”vanish in every order of the perturbation theory”），不是全阶求和的定理；Pal–Huse 2010（PRB 82, 174411）数值定位相变 “h=hc≈3.5±1.0” 并自报 “We roughly locate the localization transition”，其相定义句逐字：”in the many-body localized phase … the ‘eigenstate-thermalization hypothesis’ is false in the localized phase … it is the permanence of this information that in general prevents the isolated quantum system from relaxing to thermal equilibrium in the localized phase”。

4.2 实验阶梯：2015–2019

  • Schreiber 等 2015（Science 349, 842，arXiv:1501.05661）：准随机光晶格中相互作用费米子的 MBL 观测（本篇证据阶梯第一件；同年代多组并行，首件优先权之争不裁）。
  • Smith 等 2016（Nat. Phys. 12, 907，programmable random disorder）与 Choi 等 2016 二维（Science 352, 1547，经 Léonard 2023 参考链亲核条目；arXiv:1604.04178 落盘）：二维 MBL transition 探索——一维结果的边界线。
  • Lukin 等 2019（Science 364, 256–260，PMID 31000657）：纠缠测量。摘要逐字：”we measure the development of non-local correlations, whose evolution is consistent with a logarithmic growth of entanglement entropy – the hallmark of many-body localization.” 结尾自陈逐字：”Ultimately, these studies will further our understanding of quantum thermodynamics and whether such systems are suitable for future applications as quantum memories [6, 43].”——「量子记忆」在这件论文里带 “whether” 条件词；名号层称它的重（第七章）。

4.3 雪崩实验：Léonard 等 2023「onset」

Léonard 等 2023（Nat. Phys. 19, 481–485；arXiv:2012.15270；Harvard Greiner 组＋Sels＋Demler）在量子气体显微镜里制备「干净-无序界面」并观测热库侵入。全文逐字（NSF PAR 存档版）：

“At short times, the decay length ξd increases logarithmically in time, but accelerates at long evolution times.” “The accelerated transport indicates that the long-term dynamics are driven by processes that go beyond a perturbative coupling to the bath.” “We observed an accelerated intrusion of the bath in the MBL system, its evolution into thermal equilibrium site after site and the many-body correlations between the two subsystems—the hallmarks of quantum avalanches.” [一手逐字]

实验参数：τ = ħ/J = 4.3(1) ms、U = 2.87(3)J、L_dis = 6、平均 200 个无序实现。分寸：标题自带 “Probing the onset“——测的是雪崩起始的动力学签名（比对数加速），不是「MBL 相被雪崩摧毁」的终审。Nature 同刊 News & Views 的标题则是 “Quantum avalanches wipe out the effects of disorder in interacting systems”（Lea F. Santos, d41586-023-00143-9，直取落盘）——评论标题的强度高于实验自陈，这条差值在名号层称（第七章）。

4.4 量子处理器线（2025）

  • IBM（Shtanko 等，Nat. Commun. 16, 2552 (2025)；arXiv:2307.07552，落盘）：124 qubit、深度 60 的 Floquet 自旋链，重构局域积分算符（LIOM）。逐字：”In our experiment, we aim to reproduce MBL dynamics and extract LIOMs … using circuits with up to 124 qubits and a depth of 60.” 自留限制逐字：”While the current work may not directly tackle the most pressing physics questions surrounding the MBL phase, future advances in error mitigation and instrument performance may enable…”
  • Google（arXiv:2410.06557，落盘；Willow 芯片）：disorder-free localization（规范理论内禀背景场），论文自警逐字 “This observation of disorder-free localization (DFL) in the dynamics generated by Eq. (4) is not entirely surprising“；并把 MBL 相稳定性问题写进路线图：”This polynomial sampling advantage could boost the search for rare events, which are key to understanding the MBL phase and its stability.”
  • Li 等（arXiv:2507.16882，Sierant 合著）：二维 70-qubit 超导模拟器上的 many-body delocalization——登记，未取全文。

处理器线的意义：规模（>100 qubit）第一次超过数值对角化的极限（Sierant 2025 自报数值上限 “typically going from 6 to 20 or 22 qubits”），但 Shtanko 自己把「最重要的 MBL 相问题」留白——处理器线是工具推进，不是相问题的终审。

第五章 例外机制谱系：疤痕、碎裂与共存

5.1 疤痕：从 51 原子反常到「弱遍历破缺」

起点：Bernien 等 2017（Nature 551, 579–584，arXiv:1707.04344）51 原子里德堡链中部分初态的长寿命振荡。命名件：Turner 等 2018（Nat. Phys. 14, 745–749；arXiv:1711.03528，落盘）。摘要与结论逐字：

“Here, we demonstrate that ergodicity can be weakly broken by a different mechanism, arising from the presence of special eigenstates in the many-body spectrum that are reminiscent of quantum scars in chaotic non-interacting systems.” “Our study suggests the existence of a new universality class of quantum dynamics, which is neither fully thermalizing nor MBL, and which we attribute to the presence of a local dynamical constraint.” [一手逐字]

Turner 同篇还写明了 ETH 数值证据的边界（逐字）：”Ref. [15] found that in an ergodic spin chain, all highly excited states were typical and thermal, obeying the strong version of the ETH.”——疤痕不是对「典型系统热化」的否定，是在约束模型里的弱破缺。

精确化与实验推进：Lin–Motrunich 2019（PRL 122, 173401）找到精确疤痕态（逐字）：”This discovery explicitly demonstrates the violation of the strong eigenstate thermalization hypothesis in this model”；Choi 等 2019（PRL 122, 220603）构造近乎完美的复兴并自报极限稳定性为 “a step towards establishing the stability of quantum many-body scars in the thermodynamic limit”——疤痕的热力学极限稳定性在 2019 年论文里仍是「迈向」。实验推进：Bluvstein 等 2021（Science 371, 1355；arXiv:2012.12276，落盘）用 3–200 qubit 程控里德堡阵列把疤痕复兴用周期驱动稳住（逐字）：”coherent revivals associated with so-called quantum many-body scars can be stabilized by periodic driving, which generates a robust subharmonic response akin to discrete time-crystalline order”；自留逐字：”Our observations challenge conventional understandings of quantum thermalization, warranting further investigation to understand the exact nature and conditions for this stabilization…”

处理器疤痕的关键分寸：Zhang 等 2023（Nat. Phys. 18, 120–125 (2023)；arXiv:2201.03438，落盘；30-qubit 超导处理器，四比特保真度复兴周期约 50 ns、峰值最高 0.5）逐字：

“In our experiment, both scarred and thermalising states ultimately approach the Page entropy, 4 ln(2), of the 4-qubit subsystem.” [一手逐字]

复算：4 ln 2 = 2.7726 nats = 4.00 bits（捆 6 复算锚）——在观测窗口内疤痕态与热化态最终走向同一个熵；疤痕是「慢」，不是「不热化」。这个分寸正是消费层「永恒记忆」叙事所丢掉的。

5.2 希尔伯特空间碎裂与「热化＋记忆共存」

Adler 等 2024（Nature 636, 80–85；MPG 全文落盘）在二维倾斜 Bose-Hubbard 模型直接观测碎裂与分维子（fractons）。摘要逐字：

“Quantum systems out of equilibrium typically relax to thermal equilibrium states by scrambling local information and building up entanglement entropy. However, kinetic constraints in the Hamiltonian can lead to a breakdown of this fundamental paradigm owing to a fragmentation of the underlying Hilbert space into dynamically decoupled subsectors in which thermalization can be strongly suppressed.” [一手逐字]

自报边界逐字：”whether the tilted Bose-Hubbard model is weakly or strongly fragmented. Such a study would require measurements for much larger system sizes.”

Zhao 等 2025（PRX 15, 011035；arXiv:2403.09517，落盘）用里德堡阻塞＋助激发把 Hilbert 空间碎成指数多子空间，观测子空间内热化、子空间间不混。摘要逐字（两版一致）：

“Here we achieve the first coexistence of thermalization and memory in a quantum system.” “We observe that while thermalization proceeds in a given subspace, thermalization between energy-degenerate states belonging to different Krylov subspaces is precluded, yielding a clear violation of ETH for the entire Hilbert space. In other words, the thermalized system preserves memory of the initial configuration by storing information through the relevant Krylov subspace.” [一手逐字]

版本账：arXiv 摘要 “Our work challenges established ideas of quantum thermalization” → PRX 出版版 “Our work sheds light on a subtle aspect of quantum thermalization”——同行评审把升格措辞拉回一档（与库内复数篇 Renou 2021、N02 篇 Qu 出版版降格链同构）。

5.3 本章小结

例外谱系的共性：存在性真、一般性受限。可积（Kinoshita 2006）、疤痕（约束模型＋设计耦合）、碎裂（动力学约束）、MBDL（一维踢转子＋特定相互作用区间）都需要特殊构造；每一件的论文自陈都带条件句（probably / step towards / may not directly tackle / weakly or strongly fragmented）。例外是规则的真实反例，但不是规则的普遍失效。

第六章 命门：MBL「regime vs phase」之争——有限尺寸漂移与长时间极限

这是本题的命门章。争论双方不是「信与不信」，而是各自给出了可操作的判据与自报限制；Sierant 等 2025 综述（Rep. Prog. Phys. 88, 026502）把它们放进同一张地图。

6.1 命门的精确表述（2025 综述摘要逐字）

“However, tendency towards thermalization is not observed at finite system sizes and evolution times in a robust many-body localization (MBL) regime found numerically and experimentally in the dynamics of interacting many-body systems at strong disorder. Although the phenomenology of the MBL regime is well-established, the central question remains unanswered: under what conditions does the MBL regime give rise to an MBL phase, in which the thermalization does not occur even in the asymptotic limit of infinite system size and evolution time?” [一手逐字]

6.2 有限尺寸漂移：双向的证据

漂移不是单方面「证伪 MBL」，是双向的（综述结论章逐字）：

“Some drifts appear to be slowing down with an increase of L, providing premises for the presence of the MBL phase. Other drifts are significant and linear with L, suggesting that thermodynamically large, disordered many-body systems may eventually thermalize at any W. These drifts preclude analysis of the results at the crossover with the single-parameter scaling and make the extrapolation of the results to the asymptotic limit less reliable.” [一手逐字]

漂移方向由 Šuntajs 等 2020（PRE 102, 062144；arXiv:1905.06345，落盘）首先系统化（摘要逐字）：”We discuss the observation that scaled results in finite systems by increasing the system size exhibit a flow towards the quantum chaotic regime“；同文自报分歧：”there is still lack of consensus about the position and the nature of the transition point in paradigmatic models.”

量级账（本篇复算）：Sierant 2025 记录 W=8 的 XXZ 链在 t>10^2 后的局域关联衰减（图 11(a) 语境）逐字：”the decay can be fitted with a power-law C(t) ∝ t^−β, with β ≈ 10^−3″。把局域关联衰减 e^−1 倍需要 t≈e^(1000)=10^434（自然单位）——比宇宙年龄大 400 余个数量级（捆 6 复算脚本）。这组数字同时支撑两种读法：观测层面（可测时间）MBL-like 行为完全成立；定义层面（t→∞）”eventually thermalize” 无从排除。这正是「regime」术语被引入的原因（综述逐字：’it was proposed to refer to them as being in the MBL regime’）。

6.3 雪崩定理族：相的存在问题变成「多强无序才存在」

De Roeck–Huveneers 2017（PRB 95, 155129；arXiv:1608.01815，落盘）摘要逐字：

“When the theory is taken to its extreme logical consequences, it predicts that the MBL phase is destabilised in the long time limit whenever (1) interactions decay slower than exponentially in d=1 and (2) always in d>1. Finer numerics is required to assess these predictions.” [一手逐字]

Luitz 等 2017（PRL 119, 150602；arXiv:1705.10807，落盘）给出数值支点（逐字）：

“Our numerical analysis provides evidence that even a small ergodic grain consisting of only 3 qubits can delocalize a localized chain, as soon as the localization length exceeds a critical value.” “The most striking consequence of this analysis is that Lc=∞ if α>αc=1/√2 (and Lb is not too small). That is: a small bath is capable of thermalizing an arbitrary number of LIOMs.” [一手逐字]

复算：αc=1/√2≈0.70711，临界局域长度 ξc=2/log 2≈2.8854（捆 6 复算输出）。分寸：这个「小浴热化长链」需要局域长度超临界；亚临界时逐自旋的耦合指数衰减足以止血——定理是条件性的，方向不是「MBL 全局不稳定」。

Morningstar 等 2022（PRB 105, 174205；arXiv:2107.05642，落盘）把定位的粗糙度写明（摘要逐字）：

“Our estimates indicate that the actual MBL-to-thermal phase transition occurs much deeper in the MBL regimes than has been suggested by most previous studies … it might be that the MBL phase is only part of subregime (i), and the other subregimes are entirely in the thermal phase, even though they look localized in most respects.” [一手逐字]

6.4 严格证明的地位：Imbrie 2016 与它的争议

Imbrie 2016（J. Stat. Phys. 163, 998–1048；arXiv:1403.7837，落盘）摘要逐字：”we prove that many-body localization follows from a physically reasonable assumption that limits the amount of level attraction in the system.”——相级证明存在，但带假设。Sierant 综述对数学侧现状的定位（逐字）：

“A broad consensus among mathematicians and physicists regarding rigorous results about the status of the MBL phase defined in that manner is yet to be achieved. The multiscale Jacobi method considered in (Imbrie, 2016b; Roeck et al., 2024) or other rigorous mathematical framework will be needed to finally resolve this question.” “A recent, subsequent analysis (Roeck et al., 2024), made under weaker assumptions, rules out diffusion at strong disorder in certain quantum spin 1/2 chains, but does not exclude subdiffusive transport.” [一手逐字]

消费层的转述（Quanta 2024，逐字落盘）：”Of the once numerous pillars of evidence supporting the existence of true MBL, Imbrie’s proof is the last one standing.”；当事人自述逐字（Imbrie）：”It’s not unheard of in mathematics to have an error in a proof … but I think I know what I’m doing.”；”The proof divides physicists, however, because physicists don’t understand it.”——证明的地位之争与相本身的存在问题，是两个未决叠在一个点上。

6.5 现况裁决

把命门层三句话钉死：①「MBL regime」现象学（强无序下可测时间内不热化）在数值与实验上确立，无争议；②「MBL phase」（t→∞、L→∞ 不热化）在 2025 年综述原文里是 “central question remains unanswered”；③雪崩定理族给出条件性判据（一维且相互作用指数衰减才稳；二维受 De Roeck–Huveneers 定理族威胁，实验 Choi 2016 二维证据有限），实验只测到 onset。「MBL 是已确立的相」与「MBL 全是有限尺寸假象」都超出当前一手文本允许的范围——这不是中间派和稀泥，是双方最新文本共同写明的边界。

第七章 名号层：五条传播链逐环称重

7.1 链 A：疤痕名号链（2018–2019）

A0 论文锚：Turner 2018 的自定位是 “weak ergodicity breaking”（第五章 5.1 逐字）。

A1 APS Physics synopsis（2018-10-22，Neil Robinson，”Cold Atoms Bear a Quantum Scar”）：直取 403，走互联网档案馆存档（原件落盘 evidence/raw/）。实验事实句忠实（逐字）：”atoms in certain patterns took at least 10 times longer to relax towards thermal equilibrium than atoms in other patterns”；但结论句升格（逐字）：”Because scarring protects a quantum system from the scrambling of information caused by thermalization, the effect may prove useful for quantum computing … a scarred state is effectively shielded from thermalization for long times, which would make a scarred state attractive for storing quantum information.”——「慢 10 倍」→「有效屏蔽」：半档升格；且这 synopsis 自己末段保留了对疤痕是否随系统尺寸消失的开放问句（”If so, then quantum scarring should fade away in the PXP model with larger numbers of atoms”）——同一页内部两种强度并存。

A2 Quanta 2019-03-20（Marcus Woo）：标题框架「宇宙总在推向无序」（”Quantum Machine Appears to Defy Universe’s Push for Disorder”）。机制拟人逐字：”As if scarred, the atoms seem to bear an imprint of the past that draws them back to their original configuration over and over again.”；Heller 引语逐字：”It’s going home for them. They really want to go back to where they were born. It’s that simple.”；应用段升格（逐字）：”If you can find a generic way to induce scarring in other systems, then maybe you can protect quantum information for a long time“（Ho）。分寸：正文同时保留 Khemani 的可积性解释（”might be (at least close to) what’s called an integrable system”）与 Papić 的「新类」判断（”This work suggests there’s a new class of system that’s in between these two things”）——升格在标题框架与「记忆/回家」修辞，非在事实段。

7.2 链 B：机构稿链（中科院 2021／浙大 2025）

B1 中科院物理所 2021-04-07（b6-cas-scar.html）：ETH 定位句自带分寸（逐字）：「虽然缺少严格的理论证明，但在不同体系中的大量数值模拟均与其符合，因此本征热化假说是目前对热化现象最成功的理论解释。」——这句是克制的（与第二章的文献状态一致）。但同页疤痕描述升格（逐字）：「当初态位于伤痕空间时，它将长时间甚至永远停留在这一子空间中进行周期往复运动」——Turner 2018 原文是 weak breaking、热力学极限稳定性 “open problem”；「甚至永远」在原文量词之外。

B2 浙大物理学院 2025-08-15（MBDL 机构稿）：标题逐字：「抵抗热化的量子气体——中奥学者合作证实“多体动力学局域化”的存在」。论文摘要的对应措辞是 “we present evidence for many-body dynamical localization”——「证据」升为「证实」，一档。正文转述本身忠实（参数与两段式对比与论文一致）。

B3 浙大物理学院 2025-10-30（疤痕抗退相干稿）：逐字：「量子多体疤痕态……如同在混沌系统中留下的”记忆疤痕”，能长期保留初始量子特征」；同页自留白（逐字）：「此前研究推测疤痕态可能在噪声环境中快速热平衡，其抗噪机制始终是未解之谜」——机构稿自带「此前未解」的诚实注记，升格集中在「能长期保留」这个不带条件的断言。

B4 清华量子信息中心 2024-04-28：描述性转述，克制（逐字：「近期，研究者发现一些违反本征热化假说的例子……这些特殊的高能激发态被称为”量子多体伤痕态”」）——机构稿反例：不是所有机构稿都升格。

7.3 链 C：MBL 永久记忆的消费层（Medium 2026）

自媒体件（检索快照级，原页未取 HTML——诚实空位）逐字：

  • 标题：”The Quantum System That Refuses to Forget“
  • “MBL behaves almost like a quantum memory vault — protecting history rather than allowing it to dissolve into global chaos.”
  • “An engineered MBL material, however, could theoretically act as a quantum fossil, preserving information within localised quantum states while the surrounding universe continues its thermodynamic evolution.”
  • 分寸句（同文自带）：”Whether this inevitably destroys MBL in higher dimensions remains an open question”——消费件也保留二维不确定，但把一维 regime 写成了 vault/fossil 的「保护历史」实体。

对照源：Lukin 2019 论文自陈带条件词（第四章 4.2 逐字 “whether such systems are suitable for future applications as quantum memories”）——消费链把 “whether” 读成 “can”。

7.4 链 D：Quanta 2024——同域的反向降格件

Charlie Wood 的 “A Quantum Trick Implied Eternal Stability. Now It’s Falling Apart.”（2026-02-26 取证，全文落盘）逐字要点：

  • 相的定义钉得准：”Crucially, a phase of matter must be stable for an infinitely long time period, and for an infinitely large system.”
  • 2019 转折逐字：”In 2019, a team of Slovenian chaos experts including Tomaž Prosen reanalyzed old numerical data and highlighted the fact that as the landscape got more mountainous, thermalization slowed tremendously but never completely stopped — an inconvenient truth MBL researchers had taken to be an artifact of their small-scale simulations.”
  • 2021 改图逐字：”In the 2021 works, the researchers rewrote and expanded the MBL phase diagram for 1D chains. In Kansas-like flatlands, particles thermalize quickly. In the Rockies, the researchers reclassified the MBL ‘phase’ as a ‘pre-thermal regime.'”
  • 数字逐字：”if one waited an extremely long time — literally billions of years for some setups — particles separated by the Rockies would in fact mingle and thermalize.”；”to get a big enough flat spot you might need a chain billions of particles long, Sels estimates, and researchers typically study chains of about 12.”
  • 对摆逐字：”Beyond the Rockies lie the Himalayas. What happens there remains an open question. Sels and Prosen are convinced that energy will spread and thermalization will eventually occur, even if it takes eons. Huse and company continue to believe that genuine MBL sets in.”
  • 收尾句（升格方向的秤）：”In the universe we inhabit, which will itself thermalize in some incomprehensible number of years, permanence is always something of an illusion.” [全部一手逐字]

称重：这篇报道的每一处强度措辞都能回查到一手文献（2019 重分析=Šuntajs 线；2021 改图=Huse/Khemani 与 Sels 两线；「十亿年」与「数十亿格点」是 Sels 自估的转述并署名）；对时间晶体的降格推论（”might lose their textbook designations as ‘phases of matter'”）与库内时间晶体篇对 DTC 地基的「双向未决」登记一致。它证明同一媒体对同一领域可以先后出现「永恒稳定」（2019 篇）与「正在瓦解」两种框架——名号层不是单向损耗，要逐件称。

7.5 虚无化方向：三组定向检索，消费层无靶

对「热化全是环境效应/退相干的别名」「ETH 没被证明所以热化理论不可信」方向做了三组定向检索（查询词与结果在捆 6 笔记 6.5）：全部只命中学术边界陈述（ETH 无严格一般证明、可观测量类开放、MBL 相未决——即第二章对象），消费层无具体文本，登记诚实空位 G1。这个不对称本身是名号层证据：本题消费层失真集中在升格方向（与 N02 篇「虚无化消费层空位」相反——各领域有自己的失真谱系，不能互相默认）。

第八章 对称红队：四句双向称重

8.1 升格方向

  • 「孤立系统整体忘记/信息消失」——不立。 von Neumann 定理自警句逐字（与幺正回归并存）；Kaufman 2016 直接观测全局纯度保持＋局部热化并存；Lukin 2019 逐字 “local information … gets scrambled and transferred into non local correlations”——信息被搬家，不是被销毁。「热化后量子态变混合」是「局部约化密度矩阵」的属性，不是全系统状态的本体变化。
  • 「量子记忆可以永久保存（MBL/疤痕）」——不立（作为已证命题）。 Zhang 2023 处理器实验里疤痕态观测窗口内仍趋 Page 熵 4ln2（复算在案）；Turner 2018 自定位 weak；疤痕热力学极限稳定性 2019 年自陈仍是 “a step towards”；MBL 相存在性未决（C4）；Quanta 2024 逐字 “permanence is always something of an illusion”。
  • 「MBL 已被实验证实为相／时间晶体地基已加固」——不立。 Sierant 2025 原文 ‘do not determine whether and at what disorder strength’；Léonard 2023 只测 onset；雪崩定理族是条件性的。「证实」式标题（浙大）相对论文摘要 ‘evidence for’ 升一档（7.3 已称）。

8.2 虚无方向

  • 「热化全是环境效应/退相干的别名，孤立系统不热化」——不立。 D’Alessio 2016 的时间尺度论证逐字在案（第一章 1.2）；Kaufman 2016 在两份拷贝的干涉测纯度下直接观测孤立系统内热化；Trotzky 2012 的 local-Gibbs 不可区分性不需要环境。「热化=退相干」混淆了机制层（纠缠熵取代热熵）与本体层。
  • 「ETH 是不可检验/不可信的猜想，热化没有理论」——不立。 von Neumann QET 是定理（2.1）；正则典型性已证明；ETH 的 few-body 观测量版本在多类模型被数值验证并有一个直接实验（Kaufman）；连解析反例都确认其余本征态满足 ETH——「ETH 有边界」与「ETH 什么也没确立」是两个命题。
  • 「MBL 实验全是有限尺寸假象/什么也没证明」——不立。 regime 现象学（不热化的可测时间窗口）在多平台独立复现（冷原子/离子阱/超导）；Sierant 2025 把「未决」精确写在相定义层，而 regime 层的观察本身没有被证伪。「未决」不等于「假象」。

8.3 红队净账

升格方向的最强真核：热化在典型系统的可测时间尺度内真实发生（实验直接证据）；例外机制真实存在且部分在处理器平台可复现；ETH 有大量数值/实验支持。虚无方向的最强真核：ETH 全称无严格证明、MBL 相存在性未决、全部例外带条件、宏观遍历性从未实现（Schulman 型论证）。两边真核不冲突，因为它们落在不同的层。越界的从来不是某一层的结论，而是把某一层的结论搬进另一层：把「局部热化」搬成「整体信息消失」（或反向），把「regime 确立」搬成「相已证」，把「慢 10 倍」搬成「永久屏蔽」。

第九章 结论及其适用边界

  1. 理论层裁决：「忘记初始状态」的定理级内容是宏观观测量的时间平均性质（von Neumann QET，1929 证明、2010 翻案）；ETH 是 ansatz＋强证据（非定理），其可观测量类与必要性都开放；解析反例（Shiraishi–Mori）存在但自带「单缺陷即恢复热性」的量词。适用边界：宏观观测量/few-body 观测量；不主张整体信息消失；von Neumann 自警（与幺正回归并存）始终适用。
  2. 实验层裁决：热化直接证据（Kaufman 2016：六位格、局部约化密度矩阵热化＋全局纯度保持）与不热化直接证据（Kinoshita 2006：1D 可积、’probably’ 自归因；MBDL 2025：一维踢转子强相互作用端冻结）并存，与 2022 两场 delocalization 构成对摆。适用边界：每件的量词落在其系统与观测窗口内；正方样本小但机制直接；反方是特殊参数区间。
  3. MBL 命门裁决：regime（可测时间不热化）确立；phase（双极限）未决——Sierant 2025 原文自认；漂移双向；雪崩定理族条件性（一维且相互作用指数衰减才稳）；雪崩实验只测 onset。适用边界：一维准周期/随机自旋链为主；二维证据（Choi 2016）有限；处理器线规模扩展但自留最重问题。
  4. 例外机制裁决：疤痕（weak breaking；Zhang 2023 观测窗口内仍趋 Page 熵）、碎裂（Adler 2024；弱/强未决自报）、热化+记忆共存（Zhao 2025 ‘first coexistence’；出版版措辞回退）、处理器 LIOM 重构（Shtanko 自留限制）——例外真、带边界。适用边界：例外需要约束、设计或特殊参数；「一般孤立系统忘记初始状态」作为带量词的命题仍然被 ETH 线支持。
  5. 名号层裁决：升格链逐环可考（APS ‘effectively shielded’／中科院「甚至永远」／浙大「证实」／Quanta 2019 框架／Medium vault-fossil），Lukin 论文自陈的 “whether” 条件词逐环丢失；Quanta 2024 是反向降格对照件且与一手文献一致；虚无化消费层三组检索阴性（诚实空位）。适用边界：结论只覆盖已落盘 12 份文本与记录的检索日志。

第十章 仍不确定什么，什么证据会改变判断

仍不确定（按承重排序）：

  1. MBL 相存在性。Sierant 2025 已把问题写成开放；改变判断的证据：有限尺寸漂移随 L 收敛（或线性发散）的判决性 scaling；更大的处理器平台（>100 qubit、更长相干时间）直接测到饱和或热化。
  2. 雪崩定理的反向检验。De Roeck–Huveneers 判据在足够强无序下是否真的停摆（Morningstar 三子区提示数值定位偏浅）；Léonard 2023 的 onset 若扩展成全链热化，条件性定理的实验侧补全。
  3. 疤痕热力学极限稳定性。Choi 2019 自陈是 “a step towards”；Zhang 2023 观测窗口内疤痕趋 Page 熵——若更长观测或更大系统里疤痕塔不再参与，则「长寿命相干资源」叙事受重创；反之若有解析稳定性证明，反例族升级。
  4. ETH 的一般可观测量类。「哪些观测量满足 ETH」仍无严格判定（D’Alessio 逐字）；Garrison–Grover 一半系统尺寸的结果若被推广，会在「物理可观测量」边界上改变第 2 句的强度。
  5. 名号层空白侧的稳定性。虚无化消费层文本当前为空位（三组检索阴性）；若出现有影响力的「热化全是环境叙事」类文本，第七章的不对称结论需复查。

第十一章 关键来源与核验范围

理论层：von Neumann 1929 英译（arXiv:1003.2133，A；出版版 DOI 10.1140/epjh/e2010-00008-5 经 Crossref 亲核）；GLTZ 2010 评注（arXiv:1003.2129／10.1140/epjh/e2010-00007-7，A）；Deutsch 1991（PRA 43, 2046，10.1103/PhysRevA.43.2046，B——元数据亲核、全文未取）；Srednicki 1994（10.1103/PhysRevE.50.888，B）；Rigol 2008（10.1038/nature06838，arXiv:0708.1324，A）；D’Alessio 2016（10.1080/00018732.2016.1198134，arXiv:1509.06411，A）；Abanin 2019 RMP（10.1103/RevModPhys.91.021001，arXiv:1804.11065，A）；Shiraishi–Mori 2017（10.1103/PhysRevLett.119.030601，arXiv:1702.08227，A）。

热化实验层：Kinoshita 2006（10.1038/nature04693，nature.com 摘要级 ◐）；Trotzky 2012（10.1038/nphys2232，arXiv:1101.2659，A）；Kaufman 2016（10.1126/science.aaf6725，arXiv:1603.04409，A；Science 出版版摘要经检索快照比对）；See Toh 2022（10.1038/s41567-022-01721-w，B）；Cao 2022（10.1038/s41567-022-01724-7，B）。

MBL 理论与命门：Anderson 1958（10.1103/PhysRev.109.1492，B）；BAA 2006（10.1016/j.aop.2005.11.014，B——摘要经 INSPIRE/Elsevier 双源逐字）；Pal–Huse 2010（10.1103/PhysRevB.82.174411，arXiv:1010.1992，A）；Imbrie 2016（10.1007/s10955-016-1508-x，arXiv:1403.7837，A）；De Roeck–Huveneers 2017（10.1103/PhysRevB.95.155129，arXiv:1608.01815，A）；Luitz 2017（10.1103/PhysRevLett.119.150602，arXiv:1705.10807，A）；Morningstar 2022（10.1103/PhysRevB.105.174205，arXiv:2107.05642，A）；Šuntajs 2020（10.1103/PhysRevE.102.062144，arXiv:1905.06345，A）；Sierant 2025 综述（10.1088/1361-6633/ad9756，arXiv:2403.07111，A）。Thiery 2018（PRL 121, 140601）、Sels 2022（PRB 106, L020202）、Sierant 2020（PRL 124, 186601）、Abanin 2021（Ann. Phys. 427, 168415）四件经 Léonard 2023 参考链＋Sierant 综述锚定存在、未取全文（附录 B B3）。

MBL 实验与处理器：Schreiber 2015（10.1126/science.aaa7432，arXiv:1501.05661，A）；Smith 2016（Nat. Phys. 12, 907，经 Léonard 参考链，B）；Choi 2016（Science 352, 1547，arXiv:1604.04178，落盘，B）；Lukin 2019（Science 364, 256，arXiv:1805.09819，A）；Léonard 2023（10.1038/s41567-022-01887-3，arXiv:2012.15270，A，nature.com 出版页全文＋NSF PAR 版对读）；Santos News & Views（d41586-023-00143-9，直取 ◐）；Shtanko 2025（10.1038/s41467-025-57623-x，arXiv:2307.07552，A）；Google 2025（arXiv:2410.06557，A）；Li 2025（arXiv:2507.16882，登记）。

例外机制：Bernien 2017（10.1038/nature24622，arXiv:1707.04344，A）；Turner 2018（10.1038/s41567-018-0137-5，arXiv:1711.03528，A）；Lin–Motrunich 2019（10.1103/PhysRevLett.122.173401，B）；Choi 2019（10.1103/PhysRevLett.122.220603，B）；Bluvstein 2021（Science 371, 1355，arXiv:2012.12276，A）；Zhang 2023（10.1038/s41567-022-01784-9，arXiv:2201.03438，A）；Adler 2024（10.1038/s41586-024-08188-0，A——MPG 机构库全文）；Zhao 2025（10.1103/PhysRevX.15.011035，arXiv:2403.09517，A）；MBDL Guo 2025（10.1126/science.adn8625，arXiv:2312.13880，A）；scar 综述 2021（10.1038/s41567-021-01230-2，◐）。

名号层（12 份原件落盘，逐字引于第七章）：APS Physics synopsis 2018-10-22（Wayback 存档）；Quanta 2019-03-20；Quanta 2024-02-26；Quanta 2019-08-01（时间之箭框架件，检索快照级）；Medium 2026-08-16（检索快照级）；腾讯 2025-11-07；浙大 2025-08-15 与 2025-10-30；清华 2024-04-28；中科院 2021-04-07；Physics Today 2026-04-02；Nature News & Views 2023-01-26。

核验范围声明：全部书目经 Crossref API／Europe PMC 逐条亲核（卷期页码以 Crossref 为准），未凭记忆补任何 DOI/arXiv 号——开题阶段凭记忆书写的 8 个标识符全部当场证伪或纠正（附录 A）；关键数字（αc=1/√2、ξc=2/log 2、Page 熵 4ln2、β=10^-3 的时间尺度换算）用 python 复算（bundle6-recompute.py 与输出在案）；arXiv API/Semantic Scholar/OpenAlex/PubMed 网页/APS/Springer 的通路失败逐条登记于各捆笔记。

附录 A 课题书勘误登记（8 处）

  1. Kinoshita 误引：课题书初稿引 2004 Science 305, 1125（TG 气体）为「非热化名件」——经 Rigol 2008 自身参考文献核对，热化文献链引的是 2006 Nature 440, 900 “A quantum Newton’s cradle”；2004 Science 论文的 Crossref 摘要与不热化无关。已改正。
  2. Rigol 2008 DOI 错误：初稿凭记忆写 10.1038/nature01199——Crossref 核对为 BKCa 钾通道论文；正确为 10.1038/nature06838。
  3. Shiraishi–Mori 卷期错误：初稿猜 PRL 121, 200601——Europe PMC 双源核对为 PRL 119, 030601 (2017)；另登记存在 Comment（PRL 121, 038901, 2018，未取正文）。
  4. Trotzky 2012 刊物错误：初稿记 Science——实为 Nat. Phys. 8, 325–330（arXiv:1101.2659；凭记忆猜 1108.4418 亦错）。
  5. Pal–Huse arXiv 号错误：初稿猜 1003.2607——正确为 1010.1992（arXiv 标题 “The many-body localization phase transition”）。
  6. BAA 2006 arXiv 号未定位：初稿猜 cond-mat/0508444（实际是无关凝聚态论文）；BAA 2006 全文按诚实空位处理（摘要经 INSPIRE/Elsevier 双源逐字）。
  7. Zhang 疤痕论文年份/卷期：初稿按 arXiv 2022 排序——出版版为 Nat. Phys. 18, 120–125 (2023-01)（Crossref 亲核）。
  8. 「Lin Choi Hopkins Endres Lukin 2020」实验条目证伪：该组合作者列表的疤痕实验不存在于本库检索范围；疤痕实验推进线实为 Bluvstein 2021（3–200 qubit 程控里德堡阵列）→ Zhang 2023（30-qubit 超导处理器）→ Zhao 2025（PRX 共存）；Lin 2019 系理论件（Lin–Motrunich PRL 122, 173401），Lin–Calvera–Hsieh 2003.04516 系二维理论。教训登记：凭印象拼接的作者组必须先检索再引。

附录 B 诚实空位登记

  • G1（虚无化消费层空位）：「热化全是环境效应/ETH 不可信」方向的消费层具体文本，三组定向检索未命中（捆 6 笔记 6.5）。本篇对虚无化方向的裁决对象只能是学术边界陈述本身。
  • G2（Medium 消费件原件未取）：Medium 2026-08-16 文本经 websearch 快照逐字登记，原页 HTML 未落盘；引用其三条逐字句时以快照为限。
  • G3（四件次级理论件未取全文）：Thiery 2018、Sels 2022、Sierant 2020 PRL、Abanin 2021——条目经 Léonard 2023 参考链＋Sierant 2025 综述亲核存在；雪崩机制承重由 De Roeck–Huveneers/Luitz/Morningstar 三件承担，不引用未读件内容。
  • B4（Kinoshita 2006 正文未取）：付费墙；摘要级 ◐ 已逐字；「not noticeably equilibrate」的观测时长与统计细节未核对（若需引图与时间轴须回出版全文）。
  • B5（Schreiber/Choi 二维件未精读）：PDF 落盘、题目与卷期亲核；正文关键句写作时未逐字提取（第四章 4.2 的两件以参考链定位承重，主张转述均注明来源等级）。
  • B6（Santos N&V 全文已取、未逐段精读）：标题 “wipe out” 已逐字；正文论证链未逐段核对，引用仅限标题与定位句。
  • B7（Bocchieri–Loinger 1957 原件未取）：1950s 误评史以 GLTZ 2010 的逐字转述承重（含四条原文引语）；原始批评论文未取，历史层不自称已读原评。
  • B8（Smith 2016／Bluvstein 2021 出版版 DOI 未直核）：两件按参考链登记；Bluvstein 的 Science 页面经检索快照（标题/摘要）核过，出版记录未回 Crossref 单条。
  • B9（Quanta「billions of years / 数十亿格点」未溯源到论文页码）：两处数字为 Sels 对 Quanta 的口头估计（Quanta 自署），未找到对应论文文本；正文一律写明是 Sels 估计的转述，不冒充文献数字。
  • B10（二维/三维 MBL 相问题整体）：Choi 2016 为二维 transition 探索；De Roeck–Huveneers 的 d>1 不稳定预言属理论侧；本篇不裁二维 MBL 相存在与否（正文第六章只登记一维结论+二维分层）。
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