Abstract
For a quantum dynamical semigroup possessing a faithful normal stationary state, some conditions are discussed, which ensure the uniqueness of the equilibrium state and/or the approach to equilibrium for arbitrary initial condition.
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References
Spohn, H., ‘An Algebraic Condition for the Approach to Equilibrium for an Open N-Level System’, preprint München 1976, to appear in Lett. Math. Phys.
DaviesE.B., Commun. Math. Phys. 19, 83 (1970).
Evans, D.E., ‘Irreducible Quantum Dynamical Semigroups’, preprint ISBN 82-533-0288-3, University of Oslo, No. 15, 1976.
DaviesE.B., Commun. Math. Phys. 39, 91 (1974).
LindbladG., Commun. Math. Phys. 48, 119 (1976).
Evans, D.E. and Lewis, J.T., ‘Completely Positive Maps on the CCR Algebra’, preprint DIAS-TP-76-14, to appear in Commun. Math. Phys.; Theorems 3 and 4. Notice that, even though these theorems are formulated for the CCR algebra, their proofs make use only of general properties of completely positive maps.
Hille, E. and Phillips, R., Functional Analysis and Semi-Groups, Providence, R.I., 1957; Theorems 18.6.2 and 18.6.3.
Dixmier, J., Les C *-algèbres et leurs représentations, Paris 1969, Proposition 2.5.I.
RadinC., Commun. Math. Phys. 21, 291 (1971); Example 5.
KadisonR.V., Ann. Math. 56, 494 (1952).
Kossakowski, A., Frigerio, A., Gorini, V., and Verri, M., ‘Quantum Detailed Balance and KMS Condition’, preprint IFUM 201/FT, University of Milan, 1977.
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A fellowship from the Italian Ministry of Public Education is acknowledged.
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Frigerio, A. Quantum dynamical semigroups and approach to equilibrium. Lett Math Phys 2, 79–87 (1977). https://doi.org/10.1007/BF00398571
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DOI: https://doi.org/10.1007/BF00398571