  Surface hopping has seen great success in describing molecular phenomena
where electronic excitations tend to be localized, but its application to
materials with band-like electronic properties has remained limited. Here, we
derive a formulation of fewest-switches surface hopping where both the quantum
and classical equations of motion are solved entirely in terms of
reciprocal-space coordinates. The resulting method is directly compatible with
band structure calculations, and allows for the efficient description of
band-like phenomena by means of a truncation of the Brillouin zone. Using the
Holstein and Peierls models as examples, we demonstrate the formal equivalence
between real-space and reciprocal-space surface hopping, and assess their
accuracy against mean-field mixed quantum--classical dynamics and
numerically-exact results.
