How quantum is quantum geometry?

• URL: http://arxiv.org/abs/2608.26269v1
• Date: Wed, 26 Aug 2026 18:00:23 GMT
• Title: How quantum is quantum geometry?
• Abstract summary: We study a purely classical system in which a magnetic moment precesses in a momentum-dependent magnetic field.<n>Within Hamiltonian classical mechanics, the component of $boldsymbolell$ along the field reproduces the Berry-curvature phenomena.<n>The particle acquires a position spread whose second moment is the metric, an orbital magnetic moment, and - most strikingly - an inertial mass generated by a position-dependent force.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The quantum geometric tensor - the Berry curvature together with the quantum metric - now underlies a long list of observables, from the anomalous Hall effect to the superfluid weight of a flat band. We ask which of these observables actually require quantum mechanics. To answer this question, we study a purely classical system: a point particle carrying a classical magnetic moment $\boldsymbol{\ell}$ that precesses in a momentum-dependent magnetic field $\mathbf{B}(\mathbf{p})$. Within Hamiltonian classical mechanics, the component of $\boldsymbol{\ell}$ along the field reproduces the Berry-curvature phenomena, while its precessing transverse component reproduces the quantum-metric phenomena. The particle acquires a position spread whose second moment is the metric, an orbital magnetic moment, and - most strikingly - an inertial mass generated by a position-dependent force, and with it a nonzero Drude weight in a system that is nominally dispersionless.

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