Quantum lattice gases and their invariants

Details Quantum lattice gases and their invariants Quantum lattice gases and their invariants

1997-03-16

arxiv.org/abs/quant-ph/9703027v1

Physics

Quantum Physics

19 pages, plain TeX, 11 PostScript figures included with epsf.tex (ignore the under/overfull \vbox error messages)

Scientific paper

10.1142/S0129183197000618

The one particle sector of the simplest one dimensional quantum lattice gas automaton has been observed to simulate both the (relativistic) Dirac and (nonrelativistic) Schroedinger 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.

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