Details
| Original language | English |
|---|---|
| Pages (from-to) | 963–998 |
| Journal | Journal of Statistical Physics |
| Volume | 82 (1996) |
| Publication status | Published - 3 Apr 1995 |
| Externally published | Yes |
Abstract
Keywords
- cond-mat
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In: Journal of Statistical Physics, Vol. 82 (1996), 03.04.1995, p. 963–998.
Research output: Contribution to journal › Article › Research › peer review
}
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 -