Sub-Ensemble Correlations as a Covariance Geometry

• URL: http://arxiv.org/abs/2512.24451v1
• Date: Tue, 30 Dec 2025 20:14:47 GMT
• Title: Sub-Ensemble Correlations as a Covariance Geometry
• Authors: Zuoxian Wang, Yuhao Zhang, Gaopu Hou, Zihua Liang, Gen Hu, Lu Liu, Yuan Sun, Feilong Xu, Mao Ye,
• Abstract summary: It is shown that observable correlations are governed by the practice of inducing a global spin-fluctuation field.<n>For collective spin fluctuations described by a diffusion-relaxation Ornstein-Uhlenbeck field, the covariance spectrum admits only a finite set of modes in a bounded domain.<n>The loss of sub-ensemble independence is formalized through the notion of spatial overlap.
• Score: 10.879505450964418
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Conventional practice of spatially resolved detection in diffusion-coupled thermal atomic vapors implicitly treat localized responses as mutually independent. However, in this study, it is shown that observable correlations are governed by the intrinsic spatiotemporal covariance of a global spin-fluctuation field, such that spatial separation specifies only overlapping statistical projections rather than independent physical components. A unified field-theoretic description is established in which sub-ensembles are defined as measurement-induced statistical projections of a single stochastic field. Within this formulation, sub-ensemble correlations are determined by the covariance operator, inducing a natural geometry in which statistical independence corresponds to orthogonality of the measurement functionals. For collective spin fluctuations described by a diffusion-relaxation Ornstein-Uhlenbeck stochastic field, the covariance spectrum admits only a finite set of fluctuation modes in a bounded domain, imposing an intrinsic, field-level limit on the number of statistically distinguishable sub-ensembles. The loss of sub-ensemble independence is formalized through the notion of spatial sampling overlap, which quantifies the unavoidable statistical coupling arising from shared access to common low-order fluctuation modes. While multi-channel atomic magnetometry provides a concrete physical setting in which these constraints become explicit, the framework applies generically to diffusion-coupled stochastic fields.

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