发表机构
Chalmers University of Technology（查尔姆斯理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出平稳性要求量子关联的终端标量响应满足一模约束，通过正则化哈特里-福克方法在氦原子上验证，区分了微观谱复杂度与一模能量充分性。
AI 中文摘要
平稳量子态具有一个动力学相位因子和一个标量能量，即使其内部响应跨越一个大的希尔伯特空间。我们的论证关注的不是绝对相位的值或可观测性，而是平稳时间演化的“一”性。在正则化哈特里-福克（reg-HF）中，与平稳平均场的联系在任何一模约化之前就已建立：由高斯HF表示诱导的原初乘积相对坐标高斯测度固定了一个协方差，并且在该协方差下，它同时是最小费舍尔信息和最大香农微分熵分布，也是Stam界取等号的情形。库仑算符允许一个兼容的高斯尺度分解，维里完备化将所得的正则化对位移转化为与平稳性兼容的响应。平稳性激发了对终端标量关联响应的一模约束。决定性的reg-HF假设是一个一模排除公理：由与保留对模正交的响应分量携带的协方差被排除在终端标量能量性质之外，而不断言无约束响应是一维的。氦原子提供了最小非平凡测试。无参数保留库仑载体$-\u03b4/e$和有限$Z$插入$8\u03b4/9$紧密复现了独立的类氦系数和能量，而显式的Bethe-Goldstone计算展示了宽泛的非单分母返回谱，尽管其标量能量恰好是矩可压缩的。该结果将微观谱复杂度与一模能量充分性区分开来。
英文摘要
A stationary quantum state has one dynamical phase factor and one scalar energy even when its internal response spans a large Hilbert space. Our argument concerns not the value or observability of an absolute phase, but the one-ness of stationary time evolution. In regularized Hartree--Fock (reg-HF), the connection to the stationary mean field is established before any one-mode reduction: the primitive-product relative-coordinate Gaussian measure induced by the Gaussian HF representation fixes a covariance and, at that covariance, is simultaneously the minimum-Fisher-information and maximum-Shannon-differential-entropy distribution and the equality case of the Stam bound. The Coulomb operator admits a compatible Gaussian scale resolution, and virial completion converts the resulting regularized pair displacement into a stationary-compatible response. Stationarity motivates a one-mode constraint on the terminal scalar correlation response. The decisive reg-HF hypothesis is a one-mode exclusion axiom: covariance carried by response components orthogonal to the retained pair mode is excluded from the terminal scalar energy property, without asserting that the unrestricted response is one dimensional. Helium provides the minimal nontrivial test. The parameter-free retained Coulomb carrier $-δ/e$ and finite-$Z$ insertion $8δ/9$ closely reproduce independent He-like coefficients and energies, while an explicit Bethe--Goldstone calculation displays a broad non-single-denominator return spectrum even though its scalar energy is exactly moment-compressible. The result separates microscopic spectral complexity from one-mode energetic sufficiency.
Comments5 pages, 2 figures
