×

zbMATH — the first resource for mathematics

Convergence of a three-dimensional quantum lattice Boltzmann scheme towards solutions of the Dirac equation. (English) Zbl 1223.82002
Summary: We investigate the convergence properties of a three-dimensional quantum lattice Boltzmann scheme for the Dirac equation. These schemes were constructed as discretizations of the Dirac equation based on operator splitting to separate the streaming along the three coordinate axes, but their output has previously only been compared against solutions of the Schrödinger equation. The Schrödinger equation arises as the non-relativistic limit of the Dirac equation, describing solutions that vary slowly compared with the Compton frequency. We demonstrate first-order convergence towards solutions of the Dirac equation obtained by an independent numerical method based on fast Fourier transforms and matrix exponentiation.

MSC:
82-08 Computational methods (statistical mechanics) (MSC2010)
82B80 Numerical methods in equilibrium statistical mechanics (MSC2010)
Software:
FFTW
PDF BibTeX Cite
Full Text: DOI
References:
[1] Chen, Annual Review of Fluid Mechanics 30 (1) pp 329– (1998) · Zbl 1398.76180
[2] PHYS REPORTS 222 pp 145– (1992)
[3] Physica. D 69 pp 327– (1993) · Zbl 0798.76080
[4] PHYS REV E 53 pp 1969– (1996)
[5] PHYS REV E 75 pp 066704– (2007)
[6] PHYS REV D 49 pp 6920– (1994)
[7] J STATIST PHYS 85 pp 551– (1996) · Zbl 0952.37501
[8] 4 pp 980– (2008)
[9] J COMPUT PHYS 146 pp 282– (1998) · Zbl 0919.76068
[10] PHYS REV E 83 pp 046706– (2011)
[11] J STATIST MECH 2009 pp 06004P– (2009)
[12] Physica. D 43 pp 105– (1990) · Zbl 0713.65044
[13] Proceedings of the IEEE 93 pp 216– (2005)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.