How quantum is quantum geometry?

Title: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 $\boldsymbol{\ell}$ 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.

Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Superconductivity (cond-mat.supr-con); Quantum Physics (quant-ph)

arXiv:2608.26269 [cond-mat.mes-hall]

(or arXiv:2608.26269v2 [cond-mat.mes-hall] for this version)

https://doi.org/10.48550/arXiv.2608.26269 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.