Diffusive limits for a quantum transport model with strong field

We derive semiclassical diffusive equations for the local electron densities in a semiconductor characterized by a two-band k·p Hamiltonian, under the action of a strong external field. By using a spinorial formalism, we consider the quantum kinetic (Wigner) system endowed with a Bhatnagar-Gross-Krook (BGK)-like interaction term. Diffusive equations are derived by the Chapman-Enskog method. The closure of such equations is obtained by using the quantum version of the minimum entropy principle. In practice, it is unfeasible to put in an explicit form the diffusive equations in the general case, even in the semiclassical limit. Then we investigate the case in which band parameters have little influence on the dynamics at the macroscopic scale.