AI 中文总结
质疑平均场理论不能描述特定长程开放量子系统的观点，提出将演化分解为独立平均场动力学的方法，通过两个应用展示该方法能重现精确多体动力学，恢复平均场理论精确性，为开放量子系统提供框架。
AI 中文摘要
我们对一种普遍共识提出质疑，即平均场理论无法描述存在对称性破缺和/或从强关联态（如宏观叠加态）出发的长程开放量子系统。虽然近期文献依赖累积量展开来描述此类系统，但这种方法基于无明确依据的截断。我们表明，在强长程 regime 中，它至多在概念上是多余的。我们证明演化可分解为独立的平均场动力学并完全重构。这种分解产生了整个累积量层次结构，还首次识别出累积量展开能精确预测低阶累积量的 regime。我们通过两个应用展示了研究结果的威力：计算非平衡\(\mathcal{Z}_2\)对称性破缺的矩生成函数，以及在时间晶体中构建恢复时间平移对称性的态。在这两种情况下，我们的方法完全重现了精确的多体动力学，这是累积量展开无法企及的。我们的结果恢复了平均场理论的精确性，为大规模开放量子系统提供了一个透明框架。
英文摘要
We challenge the widespread consensus that mean-field theory fails to describe long-range open quantum systems in the presence of symmetry breaking and/or when starting from strongly correlated states (e.g., macroscopic superpositions). While recent literature relies on cumulant expansions to capture such systems, this approach rests on truncations with no clear justification. Here, we show that it is, at best, conceptually redundant in the strong long-range regime. We show that the evolution can be decomposed into, and fully reconstructed from, independent mean-field dynamics. This decomposition generates the entire hierarchy of cumulants and, as a byproduct, identifies---to our knowledge, for the first time---a regime in which cumulant expansions exactly predict low-order cumulants. We illustrate the power of our findings with two applications: we compute the moment generating function for nonequilibrium $\mathcal{Z}_2$ symmetry breaking, and construct states restoring time-translation symmetry in time crystals. In both cases, our method fully reproduces the exact many-body dynamics, which is out of reach of cumulant expansions. Our results reclaim the exactness of mean-field theory, offering a transparent framework for large-scale open quantum systems.
Comments6+7 pages. 2+1 figures
