AI 中文总结
本文研究量子动力学中非阿贝尔序信息的态依赖可见性，通过定义操作可见性揭示其在不同量子态及量子相变中的可见性变化，表明动力学阿贝尔化是态依赖过程的属性。
AI 中文摘要
非零对易子可证明两个序作为算子存在差异，但无法确保物理态能揭示该差异。本文探究非阿贝尔序信息何时会在动力学中变得不可见。对于厄米算子$B$和$C$，我们对比由相反序乘积$M=(B+iC)(B-iC)$与$\tilde{M}=(B-iC)(B+iC)$产生的演化，并在归一化时间窗口内，通过输出态的最小重叠定义其操作可见性。该可见性在所选态的所有可观测量上界定了两种序产生的差异。精确的单量子比特解表明，同一固定算子对可在一个态中完全不可见，而在另一个态中可见。随后，我们保持有序生成元固定，仅在量子相变中改变多体基态，发现同一序差异在一个相区几乎不可见，而在另一相区清晰可见。此外，具有相同主导二次衰减的态会因一阶区分出现在更高阶，而呈现出截然不同的有限时间可见性。该效应在不同算子对和系数扰动下均存在。因此，动力学阿贝尔化是态依赖过程的属性，即即便基础算子仍保持非对易性，非阿贝尔序信息也可能在操作上无法获取。
英文摘要
A nonzero commutator proves that two orderings differ as operators, but it does not ensure that a physical state can reveal the difference. We ask when non-Abelian ordering information becomes dynamically invisible. For Hermitian operators $B$ and $C$, we compare the evolutions generated by the opposite-order products $M=(B+iC)(B-iC)$ and $\widetilde M=(B-iC)(B+iC)$, and define their operational visibility from the minimum overlap of the output states over a normalized time window. This visibility bounds the difference produced by the two orderings in every observable on the chosen state. An exact one-qubit solution shows that the same fixed pair can be perfectly invisible in one state and visible in another. We then keep the ordered generators fixed and vary only the many-body ground state across a quantum phase transition. The same ordering difference is nearly invisible in one regime and clearly visible in the other. Moreover, states with identical leading quadratic decay can develop sharply different finite-time visibility because their first distinction appears at higher order. The effect persists across distinct operator pairs and coefficient perturbations. Thus dynamical Abelianization is a property of the state-dependent process, i.e., non-Abelian ordering information can become operationally inaccessible even though the underlying operators remain non-commuting.
Comments24 pages. 8 figures
