An operator splitting method for the Wigner-Poisson problem

Anton Arnold; Christian Ringhofer

doi:10.1137/S003614299223882X

An operator splitting method for the Wigner-Poisson problem

Anton Arnold, Christian Ringhofer

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

47 Scopus citations

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 language	English (US)
Pages (from-to)	1622-1643
Number of pages	22
Journal	SIAM Journal on Numerical Analysis
Volume	33
Issue number	4
DOIs	https://doi.org/10.1137/S003614299223882X
State	Published - Aug 1996

Keywords

Operator splitting methods
Wigner functions

ASJC Scopus subject areas

Numerical Analysis
Computational Mathematics
Applied Mathematics

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10.1137/S003614299223882X

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N2 - 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.

AB - 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.

KW - Operator splitting methods

KW - Wigner functions

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An operator splitting method for the Wigner-Poisson problem

Abstract

Keywords

ASJC Scopus subject areas

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