A time-splitting spectral scheme for the Maxwell-Dirac system

Zhongyi Huang; Shi Jin; Peter A. Markowich; Christof Sparber; Chunxiong Zheng

doi:10.1016/j.jcp.2005.02.026

A time-splitting spectral scheme for the Maxwell-Dirac system

Zhongyi Huang^*, Shi Jin, Peter A. Markowich, Christof Sparber, Chunxiong Zheng

^*Corresponding author for this work

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

69 Scopus citations

Abstract

We present a time-splitting spectral scheme for the Maxwell-Dirac system and similar time-splitting methods for the corresponding asymptotic problems in the semi-classical and the non-relativistic regimes. The scheme for the Maxwell-Dirac system conserves the Lorentz gauge condition is unconditionally stable and highly efficient as our numerical examples show. In particular, we focus in our examples on the creation of positronic modes in the semi-classical regime and on the electron-positron interaction in the non-relativistic regime. Furthermore, in the non-relativistic regime, our numerical method exhibits uniform convergence in the small parameter δ, which is the ratio of the characteristic speed and the speed of light.

Original language	English (US)
Pages (from-to)	761-789
Number of pages	29
Journal	Journal of Computational Physics
Volume	208
Issue number	2
DOIs	https://doi.org/10.1016/j.jcp.2005.02.026
State	Published - Sep 20 2005
Externally published	Yes

Keywords

Maxwell-Dirac system
Non-relativistic limit
Schrödinger-Poisson system
Semi-classical asymptotics
Time-splitting spectral method
WKB-expansion

ASJC Scopus subject areas

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

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10.1016/j.jcp.2005.02.026

Cite this

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title = "A time-splitting spectral scheme for the Maxwell-Dirac system",

abstract = "We present a time-splitting spectral scheme for the Maxwell-Dirac system and similar time-splitting methods for the corresponding asymptotic problems in the semi-classical and the non-relativistic regimes. The scheme for the Maxwell-Dirac system conserves the Lorentz gauge condition is unconditionally stable and highly efficient as our numerical examples show. In particular, we focus in our examples on the creation of positronic modes in the semi-classical regime and on the electron-positron interaction in the non-relativistic regime. Furthermore, in the non-relativistic regime, our numerical method exhibits uniform convergence in the small parameter δ, which is the ratio of the characteristic speed and the speed of light.",

keywords = "Maxwell-Dirac system, Non-relativistic limit, Schr{\"o}dinger-Poisson system, Semi-classical asymptotics, Time-splitting spectral method, WKB-expansion",

author = "Zhongyi Huang and Shi Jin and Markowich, {Peter A.} and Christof Sparber and Chunxiong Zheng",

year = "2005",

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doi = "10.1016/j.jcp.2005.02.026",

language = "English (US)",

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journal = "Journal of Computational Physics",

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TY - JOUR

T1 - A time-splitting spectral scheme for the Maxwell-Dirac system

AU - Huang, Zhongyi

AU - Jin, Shi

AU - Markowich, Peter A.

AU - Sparber, Christof

AU - Zheng, Chunxiong

PY - 2005/9/20

Y1 - 2005/9/20

N2 - We present a time-splitting spectral scheme for the Maxwell-Dirac system and similar time-splitting methods for the corresponding asymptotic problems in the semi-classical and the non-relativistic regimes. The scheme for the Maxwell-Dirac system conserves the Lorentz gauge condition is unconditionally stable and highly efficient as our numerical examples show. In particular, we focus in our examples on the creation of positronic modes in the semi-classical regime and on the electron-positron interaction in the non-relativistic regime. Furthermore, in the non-relativistic regime, our numerical method exhibits uniform convergence in the small parameter δ, which is the ratio of the characteristic speed and the speed of light.

AB - We present a time-splitting spectral scheme for the Maxwell-Dirac system and similar time-splitting methods for the corresponding asymptotic problems in the semi-classical and the non-relativistic regimes. The scheme for the Maxwell-Dirac system conserves the Lorentz gauge condition is unconditionally stable and highly efficient as our numerical examples show. In particular, we focus in our examples on the creation of positronic modes in the semi-classical regime and on the electron-positron interaction in the non-relativistic regime. Furthermore, in the non-relativistic regime, our numerical method exhibits uniform convergence in the small parameter δ, which is the ratio of the characteristic speed and the speed of light.

KW - Maxwell-Dirac system

KW - Non-relativistic limit

KW - Schrödinger-Poisson system

KW - Semi-classical asymptotics

KW - Time-splitting spectral method

KW - WKB-expansion

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U2 - 10.1016/j.jcp.2005.02.026

DO - 10.1016/j.jcp.2005.02.026

M3 - Article

AN - SCOPUS:19744363102

SN - 0021-9991

VL - 208

SP - 761

EP - 789

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 2

ER -

A time-splitting spectral scheme for the Maxwell-Dirac system

Abstract

Keywords

ASJC Scopus subject areas

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