Ergodicity of quantum cellular automata

Details Ergodicity of quantum cellular automata Ergodicity of quantum cellular automata

1995-04-03

arxiv.org/abs/cond-mat/9504001v1

Physics

Condensed Matter

plain TeX, 37 pages, no figures

Scientific paper

10.1007/BF02179798

We define a class of dynamical maps on the quasi-local algebra of a quantum spin system, which are quantum analogues of probabilistic cellular 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 of correlations in the unique invariant state. The main technical tool is a quantum version of oscillation norms, defined in the classical case as the sum over all sites of the variations of an observable with respect to local spin-flips.

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