AI 中文总结
该研究针对多粒子纯态，提出马德隆流体动力学中局域可分性与依赖的诊断方法，通过波函数对数的混合导数分析，揭示交叉块与可分性的关联，可用于相关量子态性质的判定。
AI 中文摘要
对于固定位置表象下的多粒子纯态，我们考虑波函数对数的粒子间混合导数：其实部是组态密度的Holland-Wang局域依赖函数的一半，虚部是马德隆速度场的交叉雅可比。在无节点乘积区域内，该区域所有交叉块消失等价于局域乘性可分性。在实标势下的薛定谔演化中，可分态初始时交叉块的增长由势对应的混合海森矩阵引起，且时间一阶项为纯虚数。该构造是局域可分性与依赖诊断工具，而非与基无关的纠缠度量。
英文摘要
For a many-particle pure state in a fixed position representation, we consider the mixed cross-particle derivatives of the logarithm of the wave function. Their real part is one half of the Holland-Wang local dependence function of the configuration density, while their imaginary part is the cross-Jacobian of the Madelung velocity field. On a node-free product region, vanishing of all cross blocks throughout the region is equivalent to local multiplicative separability. Under Schrodinger evolution with a real scalar potential, the initial growth of a cross block from a separable state is sourced by the corresponding mixed Hessian of the potential and is purely imaginary to first order in time. The construction is a local separability and dependence diagnostic, rather than a basis-independent entanglement measure.
Comments7 pages, 1 embedded figure (TikZ)
