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Footnotes and References
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.
K. Kraus: Ann. Phys. (N.Y.) 64, 311 (1971).
V. Gorini, A. Kossakowski and E. C. G. Sudarshan: J. Math. Phys. 17, 821 (1976).
G. Lindblad: Commun. Math. Phys. 48, 119 (1976).
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).
W. Happer: Rev. Mod. Phys. 44, 169 (1972) and references contained therein.
A. Omont: Progr. Quantum Electronics 5, 69 (1977) and references contained therein.
See, e.g., Ref. 7 and J.F. Papp and F.A. Franz, Phys Rev. A5, 1763 (1972).
V. Gorini, A. Frigerio, M. Verri, A. Kossakowski and E. C. G. Sudarshan: Rep. Math. Phys. 13, 149 (1978).
M. Verri and V. Gorini: Quantum dynamical semigroups and isotropic relaxation of two coupled spins, in preparation.
V. Gorini, G. Parravicini, E.C.G. Sudarshan and M. Verri, Positive and completely positive SU(2) — invariant dynamical semigroups, in preparation.
A superscript bar denotes complex conjugation.
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The statement in [17] 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.
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Gorini, V., Verri, M., Sudarshan, E.C.G. (1980). Quantum dynamical semigroups and complete positivity. An application to isotropic spin relaxation. In: Wolf, K.B. (eds) Group Theoretical Methods in Physics. Lecture Notes in Physics, vol 135. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-10271-X_314
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DOI: https://doi.org/10.1007/3-540-10271-X_314
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