Quantum mechanics of lattice gas automata. I. One particle plane waves and potentials
arXiv:quant-ph/9611005 · doi:10.1103/PhysRevE.55.5261
Abstract
Classical lattice gas automata effectively simulate physical processes such as diffusion and fluid flow (in certain parameter regimes) despite their simplicity at the microscale. Motivated by current interest in quantum computation we recently defined quantum lattice gas automata; in this paper we initiate a project to analyze which physical processes these models can effectively simulate. Studying the single particle sector of a one dimensional quantum lattice gas we find discrete analogues of plane waves and wave packets, and then investigate their behaviour in the presence of inhomogeneous potentials.
19 pages, plain TeX, 14 PostScript figures included with epsf.tex (ignore the under/overfull \vbox error messages), two additional large figures available upon request
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