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

Journal Article · Tue Sep 20 04:00:00 EDT 2005 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2005.02.026· OSTI ID:20687255

Zhongyi, Huang ^[1]; Shi, Jin ^[2]; Markowich, Peter A ^[3]; Sparber, Christof ^[3]; Chunxiong, Zheng ^[1]

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1. ICMOR, Department of Mathematical Sciences, Tsinghua University, 100084 Beijing (China)
2. ICMOR, Department of Mathematical Sciences, Tsinghua University, 100084 Beijing (China) and Department of Mathematics, University of Wisconsin, Madison, WI 53706 (United States)
3. Fakultaet fuer Mathematik der Universitaet Wein, Nordbergstrasse 15, A-1090 Vienna (Austria)

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 {delta}, which is the ratio of the characteristic speed and the speed of light.

• OSTI ID: 20687255
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 2 Vol. 208; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CONVERGENCE
DIRAC EQUATION
ELECTRON-POSITRON INTERACTIONS
MAXWELL EQUATIONS
RELATIVISTIC RANGE
SEMICLASSICAL APPROXIMATION
WKB APPROXIMATION