A QCA IN 2+1 AND 3+1 DIMENSIONS

A quantum cellular automaton (QCA), originally proposed as a 1 + 1D co nfined automaton to model quantum mechanical type behavior, is further extended in this paper to 2 + 1 and 3 + 1 dimensional confinements. Q CA trajectories are fractal-like in space and time and can be characte rized by a fractal dimension d distinct from its topological dimension D. In addition, QCAs have the pronounced feature of having single spa ce time swaths which are continuous, though non-differentiable, over r ecurrence cycles in most cases of interest. This unique feature leads to identifying angular momentum states with the quasiparticle 'anyons' in 2 + 1D and hydrogen-like orbitals in the 3 + 1D case. It also emer ges from identifying QCA states with actual physical orbitals that pro perties such as spin and magnetic moments are no longer 'intrinsic' to orbital electrons but features of QCA/fermion space-time behavior in a fashion similar to the other orbital quantum numbers. Copyright (C) 1996 Elsevier Science Ltd