ERGODICITY OF QUANTUM CELLULAR-AUTOMATA

We define a class of dynamical maps on the quasi-local algebra of a qu antum spin system, which are quantum analoges of probabilistic cellula r automata. We develop criteria for such a system to be ergodic, i.e., to possess a unique invariant state. Intuitively, ergodicity obtains if the local transition operators exhibit sufficiently large disorder. The ergodicity criteria also imply bounds for the exponential decay o f correlations in the unique invariant state. The main technical tool is a quantum version of oscillation norms, defined in the classical ca se as the sum over all sites of the variations of an observable with r espect to local spin flips.