We develop a unified theory of nonadiabatic wave-packet dynamics for Bloch electrons subject to slowly varying spatial and temporal perturbations. Extending the conventional wave-packet ansatz to include interband contributions, we derive the equation governing the interband coefficients from the time-dependent variational principle and refer to it as the wave-packet coefficient equation. Near the adiabatic regime, we can integrate out the small interband amplitudes to obtain the leading nonadiabatic corrections to the effective wave-packet Lagrangian. These corrections take three forms: (i) a nonadiabatic metric in real and momentum space, which in two-band models reduces to an energy-gap-renormalized quantum metric; (ii) gauge-invariant corrections to the Berry connections governing the motion of the wave-packet center; and (iii) an energy correction induced by spatial and temporal variations of the Hamiltonian. When the nonadiabatic metric is invertible, the dynamics can be recast as forced geodesic motion in phase space, providing a restricted gravitational analogy for Bloch-electron dynamics. As an illustration, we apply the formalism to one-dimensional Dirac electrons coupled to a slowly varying exchange field.

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• Electrical properties
• Geometric & topological phases
• Topological materials
• Transport phenomena