Analytical and computational advances for hydrodynamic models of classicaland quantum charge transport

In recent years, substantial advances have been made in understanding hydro dynamic models, both from the standpoint of analytical infrastructure, as w ell as the parameters which play a decisive effect in the behavior of such models. Both classical and quantum hydrodynamic models have been studied in depth. In this survey paper, we describe several results of this type. We include, for example, well-posedness for both classical and quantum reduced models, and the relaxation drift-diffusion limit as examples of analytical results. As examples of computational results, we include some discussion of effective algorithms, but most importantly, some information gleaned fro m extensive simulation. In particular, we present our findings of the promi nent role played by the mobilities in the classical models, and the role of hysteresis in the quantum models. All models are self-consistent. Included is discussion of recent analytical results on the use of Maxwell's equatio ns. Benchmark devices are utilized: the MESFET transistor and the n(+)/n/n( +) diode for classical transport, and the resonant tunneling diode for quan tum transport. Some comparison with the linear Boltzmann transport equation is included.