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Generators of KMS Symmetric Markov Semigroups on \({\mathcal{B}({\rm h})}\) Symmetry and Quantum Detailed Balance

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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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Authors and Affiliations

  1. Departiment of Mathematics, Politecnico di Milano, P. L. da Vinci 32, I-20133, Milano, Italy

    Franco Fagnola

  2. Departiment of Mathematics, University of Genoa, V. Dodecaneso 35, I-16146, Genova, Italy

    Veronica Umanità

Authors
  1. Franco Fagnola
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  2. Veronica Umanità
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Correspondence to Franco Fagnola.

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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

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