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Quantum Lattice Gases and Their Invariants

Author

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  • David A. Meyer

    (Project in Geometry and Physics, Department of Mathematics, University of California/San Diego, La Jolla, CA 92093-0112, USA)

Abstract

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 Betheansatz— we find the evolution eigenfunctions in thetwo-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.

Suggested Citation

  • David A. Meyer, 1997. "Quantum Lattice Gases and Their Invariants," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 8(04), pages 717-735.
    • Handle: RePEc:wsi:ijmpcx:v:08:y:1997:i:04:n:s0129183197000618
    DOI: 10.1142/S0129183197000618
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