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| Auteurs principaux: | , , , , , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2512.24451 |
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| _version_ | 1866908740918181888 |
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| author | Wang, Zuoxian Zhang, Yuhao Hou, Gaopu Liang, Zihua Hu, Gen Liu, Lu Sun, Yuan Xu, Feilong Ye, Mao |
| author_facet | Wang, Zuoxian Zhang, Yuhao Hou, Gaopu Liang, Zihua Hu, Gen Liu, Lu Sun, Yuan Xu, Feilong Ye, Mao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24451 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sub-Ensemble Correlations as a Covariance Geometry Wang, Zuoxian Zhang, Yuhao Hou, Gaopu Liang, Zihua Hu, Gen Liu, Lu Sun, Yuan Xu, Feilong Ye, Mao Atomic Physics Quantum Physics 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. |
| title | Sub-Ensemble Correlations as a Covariance Geometry |
| topic | Atomic Physics Quantum Physics |
| url | https://arxiv.org/abs/2512.24451 |