Journal of Statistical Physics

, Volume 82, Issue 3, pp 963–998

Ergodicity of quantum cellular automata

  • S. Richter
  • R. F. Werner

DOI: 10.1007/BF02179798

Cite this article as:
Richter, S. & Werner, R.F. J Stat Phys (1996) 82: 963. doi:10.1007/BF02179798


We define a class of dynamical maps on the quasi-local algebra of a quantum spin system, which are quantum analoges of probabilistic cellular automata. We develop criteria for such a system to be ergodic, i.e., to posses 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.

Key Words

Cellular automata interacting particle systems quantum spin systems approach to equilibrium oscillation norm 

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • S. Richter
    • 1
  • R. F. Werner
    • 2
  1. 1.Instituut voor Theoretische FysicaUniversiteit LeuvenHeverleeBelgium
  2. 2.FB Physik Universität OsnabrückOsnabrückGermany

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