Derivation of new quantum hydrodynamic equations using entropy minimization

Ansgar Jüngel, Daniel Matthes, Josipa Pina Milišić

Research output: Contribution to journalArticlepeer-review

53 Scopus citations

Abstract

New quantum hydrodynamic equations are derived from a Wigner-Boltzmann model, using the quantum entropy minimization method recently developed by Degond and Ringhofer. The model consists of conservation equations for the carrier, momentum, and energy densities. The derivation is based on a careful expansion of the quantum Maxwellian in powers of the Planck constant. In contrast to the standard quantum hydrodynamic equations derived by Gardner, the new model includes vorticity terms and a dispersive term for the velocity. Numerical current-voltage characteristics of a one-dimensional resonant tunneling diode for both the new quantum hydrodynamic equations and Gardner's model are presented. The numerical results indicate that the dispersive velocity term regularizes the solution of the system.

Original languageEnglish
Pages (from-to)46-68
Number of pages23
JournalSIAM Journal on Applied Mathematics
Volume67
Issue number1
DOIs
StatePublished - 2006
Externally publishedYes

Keywords

  • Current-voltage characteristics
  • Entropy minimization
  • Finite-difference discretization
  • Moment method
  • Numerical simulations
  • Quantum Maxwellian
  • Quantum moment hydrodynamics
  • Resonant tunneling diode

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