Chiara Manzini

DERIVATION OF A QUANTUM HYDRODYNAMIC MODEL IN THE HIGH-FIELD CASE

1. Introduction and formulation of the scaled problemWe derive a hydrodynamical model for a quantum system evolving in high-field regime, namely when advection and dissipative terms are dominantand have the same order of magnitude. To this aim we consider a rescaledversion of the Wigner equation with unknown the quasi-distribution func-tion

Quantum High-Field Corrections to a Drift-Collision Balance Model of Semiconductor Transport

We derive a fluid-dynamical model describing electron transport in quantum, high-field regime. In the high-field regime, quantum advection and collisions are comparable and dominant. In this article, high-field regime is modeled starting from Wigner-BGK (Bhatnager-Gross-Krook) equation scaled with an asymptotic parameter ϵ. By applying Chapman-Enskog procedure and then moment methods, we obtain a system of equations with unknown electron position density, fluid velocity, and energy density. Diffusive and quantum terms appear as first-order corrections in ϵ.

HYDRODYNAMIC MODELS FOR A TWO-BAND NONZERO-TEMPERATURE QUANTUM FLUID

are preferable, since theyinvolve directly macroscopic quantities and they admit natural boundaryconditions. The Madelung equations constitute the fluiddynamical equiv-alent of the Schr¨odinger equation and they are formally identical to theEuler equations for a perfect fluid at zero temperature, apart for the Bohmpotential