Analytical and Computational Advances for Hydrodynamic Models of Classical and Quantum Charge Transport

In recent years, substantial advances have been made in understanding hydrodynamicmodels, both from the standpoint of analytical infrastructure, as well as the parameterswhich play a decisive effect in the behavior of such models. Both classical and quantumhydrodynamic models have been studied in depth. In this survey paper, we describeseveral results of this type. We include, for example, well-posedness for both classicaland quantum reduced models, and the relaxation drift–diffusion limit as examples ofanalytical results. As examples of computational results, we include some discussion ofeffective algorithms, but most importantly, some information gleaned from extensivesimulation. In particular, we present our findings of the prominent role played by themobilities in the classical models, and the role of hysteresis in the quantum models. Allmodels are self-consistent. Included is discussion of recent analytical results on the useof Maxwell’s equations. Benchmark devices are utilized: the MESFET transistor andthe n+/n/n+ diode for classical transport, and the resonant tunneling diode for quantumtransport. Some comparison with the linear Boltzmann transport equation is included