Quantum Lattice Gases and Their Invariants

David A. Meyer ()
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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

International Journal of Modern Physics C (IJMPC), 1997, vol. 08, issue 04, 717-735

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.

Keywords: Quantum Lattice Gas; Conserved Quantities; Exactly Solvable Model; Quantum Computation (search for similar items in EconPapers)
Date: 1997
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DOI: 10.1142/S0129183197000618

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