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The semiclassical description of the dynamics of wave packets in periodicpotentials and subject to an applied force relies on the concepts of effectivemass and anomalous transport. This picture is valid if the force changes slowlyin time and space, so that the particle described by the wave packet has timeto respond according to the properties of the lattice. We analyze the dynamicalcorrections to this picture when a uniform force is suddenly applied,identifying separate corrections to the usual group and anomalous velocities.We find approximate semianalytical expressions for generalized "dynamical"group and anomalous velocities, and the associated accelerations. We use atwo-dimensional optical lattice with finite Berry curvature to illustrate thesemianalytical approximation in a regime where the dynamical corrections aresignificant, suggesting the possibility of experiments to detect them; wecompare the results with a full numerical solution, showing excellent agreementfor weak forces.

Dynamics of the effective mass and the anomalous velocity in two-dimensional lattices