David A. Meyer,
``Quantum lattice gases and their invariants'',
International Journal of Modern Physics C 8 (1997) 717-735,
quant-ph/9703027,
expanded version of a talk presented at the Sixth International Conference on Discrete Models for Fluid Mechanics, Boston, MA, 26-28 August 1996.

The one particle sector of the simplest one dimensional quantum lattice gas automaton has been observed to simulate both the (relativistic) Dirac and (nonrelativistic) Schrödinger equations, in different continuum limits. By analyzing the discrete analogues of plane waves in this sector we find conserved quantities corresponding to energy and momentum. We show that the Klein paradox obtains so that in some regimes the model must be considered to be relativistic and the negative energy modes interpreted as positive energy modes of antiparticles. With a formally similar approach---the Bethe ansatz---we find the evolution eigenfunctions in the two particle sector of the quantum lattice gas automaton and conclude by discussing consequences of these calculations and their extension to more particles, additional velocities, and higher dimensions.

PlainTeX (19 pages): PostScript (672K), PDF (297K).


Last modified: 14 april 1998