TY - JOUR

T1 - Ergodicity of quantum cellular automata

AU - Richter, Susanne

AU - Werner, Reinhard F.

N1 - plain TeX, 37 pages, no figures

PY - 1995/4/3

Y1 - 1995/4/3

N2 - 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.

AB - 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.

KW - cond-mat

U2 - 10.1007/BF02179798

DO - 10.1007/BF02179798

M3 - Article

VL - 82 (1996)

SP - 963

EP - 998

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

ER -