  We use the Wigner transformation and asymptotic analysis to systematically
derive the semi-classical model for the Schr\"{o}dinger equation in arbitrary
spatial dimensions, with any periodic structure. Our particular emphasis lies
in addressing the \textit{diabatic} effect, i.e., the impact of Bloch band
crossings. We consider both deterministic and random scenarios. In the former
case, we derive a coupled Liouville system, revealing lower-order interactions
among different Bloch bands. In the latter case, a coupled system of radiative
transport equations emerges, with the scattering cross-section induced by the
random inhomogeneities. As a specific application, we deduce the effective
dynamics of a wave packet in graphene with randomness.
