The quantum cellular automaton as a Markov process

The dynamical behavior of the Quantum Cellular Automaton (QCA) is described here as a Markov Process. Ergodicity and recurrence, emergent properties o f the discrete dynamical QCA system, are defined in the context of the char acteristic polynomial of the Markov transition matrix. Except for a few ano malous cases, the transition matrix can be used to predict recurrence times . Finally, a correspondence between recurrence and elementary particle mass is proposed as an example of an emergent property of the QCA system. (C) 1 999 Elsevier Science Ltd. All rights reserved.