Quantum hydrodynamics for semiconductors in the high-field case

P. Markowich*, C. Ringhofer

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We derive a quantum hydrodynamic model from a relaxation time approximation of the quantum Boltzmann equation by mean-free path asymptotics. The (formal) asymptotics are carried out in the case of a large electric field. They give a linear model for the position, current and energy densities of the electron gas.

Original languageEnglish (US)
Pages (from-to)37-41
Number of pages5
JournalApplied Mathematics Letters
Issue number5
StatePublished - Sep 1994
Externally publishedYes

Bibliographical note

Funding Information:
The first author acknowledges support from the EC-Network #ERBCHRXCT 930413 and from the project entitled ‘Mathematische Analysis und Numerik von Quantenhydrodynamischen Modellen der Halbleiderphysik’ funded by the Deutsche Forschungsgemeinschaft.


  • Moment hierarchy
  • Quantum Boltzmann equation
  • Small mean free path asymptotics

ASJC Scopus subject areas

  • Applied Mathematics


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