Hannover 2010 – wissenschaftliches Programm
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A: Fachverband Atomphysik
A 8: Poster I
A 8.43: Poster
Dienstag, 9. März 2010, 16:30–19:00, Lichthof
An efficient numerical propagation scheme for the Klein-Gordon equation — •Matthias Ruf, Heiko Bauke, and Christoph H. Keitel — Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg
The Klein-Gordon equation [1] is a Lorentz invariant equation of motion for spinless particles. We present a real space split operator method [2] for the solution of the time-dependent Klein-Gordon equation with arbitrary electromagnetic fields. Split operator methods for the Schrödinger equation and the Dirac equation typically operate alternately in real space and momentum space and, therefore, require the computation of a Fourier transform in each time step. However, the fact that the kinetic energy operator K in the two-component representation of the Klein-Gordon equation is a nilpotent operator, that is K2=0, allows us to implement the split operator method for the Klein-Gordon equation entirely in real space.
Consequently, the proposed split operator method does not require the computation of a Fourier transform. We implemented a highly parallel computer program for the propagation of the Klein-Gordon equation. Parallelization is based on domain decomposition. Our poster will outline the real space split operator method and will present applications as well as performance measurements.
[1] H. Feshbach and F. Villars, Rev. Mod. Phys. 30, 24–45 (1958)
[2] Matthias Ruf, Heiko Bauke and Christoph H. Keitel, J. Comp. Phys. 228, 9092–9106 (2009)