Quantum mechanics of lattice gas automata. II. Boundary conditions and other inhomogeneities

Abstract

We continue our analysis of the physics of quantum lattice gas automata (QLGA). Previous work has been restricted to periodic or infinite lattices; simulation of more realistic physical situations requires finite sizes and non-periodic boundary conditions. Furthermore, envisioning a QLGA as a nanoscale computer architecture motivates consideration of inhomogeneities in the `substrate'; this translates into inhomogeneities in the local evolution rules. Concentrating on the one particle sector of the model, we determine the various boundary conditions and rule inhomogeneities which are consistent with unitary global evolution. We analyze the reflection of plane waves from boundaries, simulate wave packet refraction across inhomogeneities, and conclude by discussing the extension of these results to multiple particles.