Quantum dynamical semigroups and complete positivity. An application to isotropic spin relaxation
Part of the Lecture Notes in Physics book series (LNP, volume 135)
Canonical Transformation and Quantum Mechanics
KeywordsDensity Matrix Relaxation Rate Hyperfine Splitting Dynamical Semi Complete Positivity
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Footnotes and References
- 1.Here the derivative at the l.h.s of (1.1) is defined as where is the trace norm on (we denote by B* the adjoint of an operator B). The domain D(L) is the set of all for which dρ/dt exists.Google Scholar
- 5.For a partial result when L is unbounded see E. B. Davies, Generators of dynamical groups, semigroups, preprint (1977) For the classification of dynamical semigroups on arbitrary Von Neumann algebras and with bounded L see E. Christensen, Commun. Math. Phys. 62, 167 (1978).Google Scholar
- 10.M. Verri and V. Gorini: Quantum dynamical semigroups and isotropic relaxation of two coupled spins, in preparation.Google Scholar
- 11.V. Gorini, G. Parravicini, E.C.G. Sudarshan and M. Verri, Positive and completely positive SU(2) — invariant dynamical semigroups, in preparation.Google Scholar
- 12.A superscript bar denotes complex conjugation.Google Scholar
- 13.U. Fano and G. Racah: Irreducible tensorial sets, Academic Press, New York (1957).Google Scholar
- 14.A. Omont: J. Phys. 26, 26 (1965).Google Scholar
- 18.The statement in  that for isotropic relaxation of a single spin positivity and complete positivity are equivalent is false. Actually, the argument given there allows only to prove that positivity implies λ2J⩾0.Google Scholar
© Springer-Verlag 1980