How quantum is quantum geometry?
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 ℓ that precesses in a momentum-dependent magnetic field B(p). Within Hamiltonian classical mechanics, the component of ℓ 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.
Related
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BibTeX
@misc{stern2026quantum,
title = {{How quantum is quantum geometry?}},
author = {Ady Stern and Felix von Oppen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.26269},
eprint = {2608.26269},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.26269},
}
RIS
TY - UNPB
TI - How quantum is quantum geometry?
AU - Ady Stern
AU - Felix von Oppen
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2608.26269
UR - https://arxiv.org/abs/2608.26269
AB - 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 ℓ that precesses in a momentum-dependent magnetic field B(p). Within Hamiltonian classical mechanics, the component of ℓ 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.
ER -