An operator splitting method for the Wigner-Poisson problem

Anton Arnold, Christian Ringhofer

Research output: Contribution to journalArticle

38 Citations (Scopus)

Abstract

The Wigner-Poisson equation describes the quantum-mechanical motion of electrons in a self-consistent electrostatic field. The equation consists of a transport term and a non-linear pseudodifferential operator. In this paper we analyze an operator splitting method for the linear Wigner equation and the coupled Wigner-Poisson problem. For this semidiscretization in time, consistency and nonlinear stability are established in an L2-framework. We present a numerical example to illustrate the method.

Original languageEnglish (US)
Pages (from-to)1622-1643
Number of pages22
JournalSIAM Journal on Numerical Analysis
Volume33
Issue number4
StatePublished - Aug 1996

Fingerprint

Wigner Equation
Operator Splitting Method
Poisson Problem
Poisson equation
Time Consistency
Electric fields
Electrostatic Field
Semidiscretization
Electrons
Nonlinear Stability
Nonlinear Operator
Pseudodifferential Operators
Poisson's equation
Linear equation
Electron
Numerical Examples
Motion
Term

Keywords

  • Operator splitting methods
  • Wigner functions

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Computational Mathematics

Cite this

An operator splitting method for the Wigner-Poisson problem. / Arnold, Anton; Ringhofer, Christian.

In: SIAM Journal on Numerical Analysis, Vol. 33, No. 4, 08.1996, p. 1622-1643.

Research output: Contribution to journalArticle

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