Extending the wave-packet ansatz for Bloch electrons to include interband contributions and applying the time-dependent variational principle yields leading-order nonadiabatic corrections to the Lagrangian, including an energy-gap-renormalized quantum metric that recasts dynamics as geodesic motion.
Nagaosa, Emergent inductor by spiral magnets, Japanese Journal of Applied Physics58, 120909 (2019)
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Nonadiabatic Wave-Packet Dynamics: Nonadiabatic Metric, Quantum Geometry, and Gravitational Analogy
Extending the wave-packet ansatz for Bloch electrons to include interband contributions and applying the time-dependent variational principle yields leading-order nonadiabatic corrections to the Lagrangian, including an energy-gap-renormalized quantum metric that recasts dynamics as geodesic motion.