The combined viscous semi-classical limit for a quantum hydrodynamic system with barrier potential

Michael Dreher, Johannes Schnur

Research output: Contribution to journalArticle

1 Citation (Scopus)
22 Downloads (Pure)

Abstract

We investigate the viscous model of quantum hydrodynamics, which describes the charge transport in a certain semiconductor. Quantum mechanical effects lead to third order derivatives, turning the stationary system into an elliptic system of mixed order in the sense of Douglis-Nirenberg. In the case most relevant to applications, the semiconductor device features a piecewise constant barrier potential. In the case of thermodynamic equilibrium, we obtain asymptotic expansions of interfacial layers of the particle density in neighbourhoods of the jump points of this barrier potential, and we present rigorous proofs of uniform estimates of the remainder terms in these asymptotic expansions.

Original languageEnglish
Pages (from-to)1113-1133
Number of pages21
JournalJournal of Mathematical Analysis and Applications
Volume425
Issue number2
Early online date14 Jan 2015
DOIs
Publication statusPublished - 15 May 2015

Keywords

  • Boundary layers
  • Quantum hydrodynamics
  • Remainder estimates

Fingerprint Dive into the research topics of 'The combined viscous semi-classical limit for a quantum hydrodynamic system with barrier potential'. Together they form a unique fingerprint.

  • Cite this