Collective fluctuations generate dynamical Berry curvature via non-commutative transverse quantum fluctuations and non-local-time interactions, distinguishable from bare band geometry in antisymmetric inelastic scattering channels.
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A first-frequency-moment constraint on antisymmetric optical conductivity vanishes exactly in zero-field moiré continuum models and equals a magnetic-flux-determined constant in Hofstadter models, implying spectral compensation for anomalous Hall absorption.
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Geometric curvature driven by many-body collective fluctuations
Collective fluctuations generate dynamical Berry curvature via non-commutative transverse quantum fluctuations and non-local-time interactions, distinguishable from bare band geometry in antisymmetric inelastic scattering channels.
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Optical Hall absorption sum rule and spectral compensation in time-reversal-breaking moir\'e and Hofstadter systems
A first-frequency-moment constraint on antisymmetric optical conductivity vanishes exactly in zero-field moiré continuum models and equals a magnetic-flux-determined constant in Hofstadter models, implying spectral compensation for anomalous Hall absorption.