Research Paper#Physics, Statistical Physics, Atomic Physics, Magnetometry🔬 ResearchAnalyzed: Jan 3, 2026 16:43
Sub-Ensemble Correlations as a Covariance Geometry
Published:Dec 30, 2025 20:14
•1 min read
•ArXiv
Analysis
This paper challenges the conventional assumption of independence in spatially resolved detection within diffusion-coupled thermal atomic vapors. It introduces a field-theoretic framework where sub-ensemble correlations are governed by a global spin-fluctuation field's spatiotemporal covariance. This leads to a new understanding of statistical independence and a limit on the number of distinguishable sub-ensembles, with implications for multi-channel atomic magnetometry and other diffusion-coupled stochastic fields.
Key Takeaways
- •Challenges the assumption of independent localized responses in spatially resolved detection.
- •Introduces a field-theoretic framework based on spatiotemporal covariance.
- •Defines sub-ensembles as statistical projections of a single stochastic field.
- •Establishes a geometry where statistical independence is linked to orthogonality.
- •Identifies a field-level limit on the number of distinguishable sub-ensembles.
- •Applies to multi-channel atomic magnetometry and other diffusion-coupled stochastic fields.
Reference
“Sub-ensemble correlations are determined by the covariance operator, inducing a natural geometry in which statistical independence corresponds to orthogonality of the measurement functionals.”