分区协议中的连通关联：案例研究及其拓展
Connected correlations in partitioning protocols: a case study and beyond
AI总结：
本文利用分区协议和非相互作用演化，研究可观测量何时足够局域以被广义流体力学描述，通过解耦动力学场推导出仅用根密度描述可观测量的局域性条件，并揭示高斯化的适用边界。
摘要：
非均匀量子淬火中的局域弛豫假设允许通过被称为广义流体力学（GHD）的流体力学论证来渐近计算局域可观测量的期望值。在这项工作中，我们利用分区协议和非相互作用时间演化的平台，正式探讨了一个可观测量何时“足够局域”以至于能够被GHD描述的问题。我们证明，任何在二次哈密顿量下演化的态都可以通过一组解耦的动力学场来描述，使得其中一个场可以被识别为根密度的时空依赖推广。通过独立研究这些场中每一个场对连通自旋关联的贡献，我们推导出了可观测量可以仅用根密度来描述时所满足的局域性条件。这既展示了那些旨在仅用根密度来描述可观测量渐近值的流体力学方法（例如GHD）的适用范围，也展示了高斯化发生所必需的局域性条件。
英文摘要：
The assumption of local relaxation in inhomogeneous quantum quenches allows to compute asymptotically the expectation value of local observables via hydrodynamic arguments known as generalized hydrodynamics (GHD). In this work we address formally the question of when an observable is ``local enough'' to be described by GHD using the playground of partitioning protocols and non-interacting time evolution. We show that any state evolving under a quadratic Hamiltonian can be described via a set of decoupled dynamical fields such that one of those fields can be identified with a space-time-dependent generalisation of the root density. By studying the contribution to a connected spin correlation of each of those fields independently, we derive the locality conditions under which an observable can be described using the root density only. That shows both the regime of validity for hydrodynamic approaches that aim at describing the asymptotic value of observables in term of the root density only, such as GHD, and the locality conditions necessary for Gaussianification to occur.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
