Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Stern, Ady, von Oppen, Felix
Institutions: Weizmann Institute of Science, Freie Universität Berlin
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204545281
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