Kinetic and Hydrodynamic Models for Multi-Band Quantum Transport in Crystals

This chapter of the book describes the multiband models that have recently been formulated in both classes (statistical and non-statistical). Attention is given to the definitions of the relevant quantities which characterize each model and to the advantages and disadvantages of each model compared to others. The technical details of the derivations of the various models, as well as the rigorous proofs of consistency and existence of the solutions, are diverted directly to the papers where the models have been described and that are cited in the chapter.