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This research establishes exact mathematical relationships for fluctuation statistics in random free fermions, moving beyond approximations to define the geometric organization of complex quantum systems. By deriving closed-form expressions for covariance factors, the study provides a rigorous framework for understanding how quantum ensembles reach equilibrium without relying on previous simplifications.

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Hubei University Team Maps Eigenstate Overlap Statistics

Quantum Zeitgeist16 septembrie 20261 min de cititArticolul și perspectiva sunt în engleză.

Previously, describing how complex quantum systems reach equilibrium relied on approximations of fluctuating behaviour within eigenstates. Now, exact mathematical relationships define these fluctuations in random free fermions, revealing their geometric organisation via shared one-body modes. Finite-size calculations validate this new understanding beyond simple energy dependence, delivering closed forms for previously intractable covariance factors.

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