Abstract
We find the structure of generators of norm-continuous quantum Markov semigroups on \({\mathcal{B}({\rm h})}\) that are symmetric with respect to the scalar product tr (ρ 1/2 x*ρ 1/2 y) induced by a faithful normal invariant state ρ and satisfy two quantum generalisations of the classical detailed balance condition related with this non-commutative notion of symmetry: the so-called standard detailed balance condition and the standard detailed balance condition with an antiunitary time reversal.
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Communicated by M.B. Ruskai
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Fagnola, F., Umanità, V. Generators of KMS Symmetric Markov Semigroups on \({\mathcal{B}({\rm h})}\) Symmetry and Quantum Detailed Balance. Commun. Math. Phys. 298, 523–547 (2010). https://doi.org/10.1007/s00220-010-1011-1
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DOI: https://doi.org/10.1007/s00220-010-1011-1