Abstract
We extend the concept of quantum dynamical entropyh φ (γ) to cover the case of a completely positive map γ. Forh φ (γ) = 0 we examine the limit
calling the turning point β0 between zero and infiniteh φ (N, γ, β) the “entropic dimension”D N (γ). The application of this theory to a solvable irreversible quantum dynamical semigroup on a one-dimensional fermion lattice provides any value ofD N (γ) between 0 and 1.
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References
P. Cornfeld, S. V. Fomin, and Ya. G. Sinai,Ergodic Theory (Springer, Berlin, 1982).
A. Connes and E. Størmer,Acta Math. 134:289 (1975).
A. Connes,C. R. Acad. Sci. Paris 301:1 (1985).
A. Connes, H. Narnhofer, and W. Thirring,Commun. Math. Phys. 112:691 (1987).
H. Narnhofer and W. Thirring,Lett. Math. Phys. 14:89 (1987).
T. Hudetz, Space time dynamical entropy of quantum systems, University of Vienna preprint UWThPh-1988-6;Lett. Math. Phys., to appear.
S. Goldstein,Commun. Math. Phys. 39:303 (1975).
H. Narnhofer and W. Thirring,Lett. Math. Phys. 15:261 (1988).
E. Lieb and D. W. Robinson,Commun. Math. Phys. 28:251 (1972).
E. B. Davies,Commun. Math. Phys. 55:231 (1977).
E. B. Davies,Quantum Theory of Open Systems (Academic Press, New York, 1976).
G. Lindblad,Commun. Math. Phys. 48:119 (1976).
F. Benatti, Thesis, SISSA, Trieste, Italy (1988).
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Benatti, F., Narnhofer, H. Entropic dimension for completely positive maps. J Stat Phys 53, 1273–1298 (1988). https://doi.org/10.1007/BF01023869
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DOI: https://doi.org/10.1007/BF01023869