关于全息扩散复杂性的评论
Comments on holographic spread complexity
AI总结：
重新审视全息提议，通过对AdS探针量子化及使用外推字典给出更一般推导，还研究其在平坦和德西特时空情况，表明仅半经典极限不足以建立动量-复杂性关系。
AI中文摘要：
我们重新审视了将扩散复杂性的增长率与体探针的径向动量联系起来的全息提议，旨在确定其潜在假设，并阐明经典探针动力学如何从量子动力学中产生。通过直接对反德西特（AdS）探针进行量子化并使用外推字典，我们提供了该提议更一般的推导。特别是，我们将其解释为在‘复杂性=任何事物’框架中经典复杂性可观测量及其量子化的具体实现。由于探针动力学并非本质上与AdS/共形场论（CFT）对应相关，我们还在平坦时空和德西特时空中研究了该提议。在平坦时空中，物理哈密顿量不保持相干态结构，扩散复杂性测量波包的色散展宽而非经典动量。在德西特空间中，静态补丁能量表示中的一般半经典波包表现出相同的色散行为。相比之下，适应主系列表示的相干态可以表现出扩散复杂性的指数增长，其增长率与经典径向动量具有相同的时间依赖性。这些例子表明，仅半经典极限不足以建立动量-复杂性关系。
英文摘要：
We revisit the holographic proposal relating the growth rate of spread complexity to the radial momentum of a bulk probe, aiming to identify its underlying assumptions and clarify how classical probe dynamics emerges from quantum dynamics. By quantizing AdS probes directly and using the extrapolation dictionary, we provide a more general derivation of the proposal. In particular, we interpret it as a concrete realization of a classical complexity observable and its quantization in the ``complexity=anything'' framework. Since probe dynamics is not intrinsically tied to the AdS/CFT correspondence, we also examine the proposal in flat and de Sitter spacetimes. In flat spacetime, the physical Hamiltonian does not preserve the coherent-state structure, and spread complexity measures the dispersive broadening of the wave packet rather than classical momentum. In de Sitter space, generic semiclassical wave packets in the static-patch energy representation show the same dispersive behavior. By contrast, coherent states adapted to the principal-series representation can exhibit exponential growth of spread complexity, with a growth rate that has the same time dependence as the classical radial momentum. These examples indicate that a semiclassical limit alone is not sufficient for a momentum--complexity relation.
