Multiphase semiclassical approximation of an electron in a one-dimensional crystalline lattice I. Homogeneous problems

Laurent Gosse*, Peter Markowich

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

Abstract

We present a computational approach for the WKB approximation of the wave function of an electron moving in a periodic one-dimensional crystal lattice. We derive a nonstrictly hyperbolic system for the phase and the intensity where the flux functions originate from the Bloch spectrum of the Schrödinger operator. Relying on the framework of the multibranch entropy solutions introduced by Brenier and Corrias, we compute efficiently multiphase solutions using well adapted and simple numerical schemes. In this first part we present computational results for vanishing exterior potentials which demonstrate the effectiveness of the proposed method.

Original languageEnglish (US)
Pages (from-to)387-417
Number of pages31
JournalJournal of Computational Physics
Volume197
Issue number2
DOIs
StatePublished - Jul 1 2004

Keywords

  • Homogenization
  • Moment method
  • Non-strictly hyperbolic systems
  • Periodic potential
  • Semiclassical limit
  • Vlasov equation

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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