Quantum Mechanics Of Lattice Gas Automata I. One Particle Plane Waves And Potentials

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. PACS numbers: 03.65.-w, 02.70.-c, 11.55.Fv, 89.80.+h. KEY WORDS: quantum lattice gas; quantum cellular automaton; quantum computation. Phys. Rev. E 55 (1997) 5261--5269. Quantum mechanics of LGA I. David A. Meyer 1. Introduction The first quantum lattice gas automaton (QLGA) appeared as Feynman's path integral for a relativistic particle in 1 + 1 dimensions [1]; independently Riaza..