Single-cone real-space finite difference scheme for the time-dependent Dirac equation

JOURNAL OF COMPUTATIONAL PHYSICS

卷:265

Article

Hammer, Rene¹  Poetz, Walter¹  Arnold, Anton² 

[1] Karl Franzens Univ Graz, Inst Phys, A-8010 Graz, Austria

[2] TU Wien, Inst Anal & Sci Comp, A-1040 Vienna, Austria

关键词: Dirac equation;    Leap-frog;    Staggered grid;    Fermion doubling;    FDTD;    Klein step;   

DOI  :  10.1016/j.jcp.2014.01.028

来源: Elsevier

【 摘 要 】

A finite difference scheme for the numerical treatment of the (3 + 1)D Dirac equation is presented. Its staggered-grid intertwined discretization treats space and time coordinates on equal footing, thereby avoiding the notorious fermion doubling problem. This explicit scheme operates entirely in real space and leads to optimal linear scaling behavior for the computational effort per space-time grid-point. It allows for an easy and efficient parallelization. A functional for a norm on the grid is identified. It can be interpreted as probability density and is proved to be conserved by the scheme. The single-cone dispersion relation is shown and exact stability conditions are derived. Finally, a single-cone scheme for the two-component (2 + 1)D Dirac equation, its properties, and a simulation of scattering at a Klein step are presented. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free