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## Banach Center Publications

2010 | 89 | 1 | 105-119
Tytuł artykułu

### On two quantum versions of the detailed balance condition

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EN
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EN
Quantum detailed balance conditions are often formulated as relationships between the generator of a quantum Markov semigroup and the generator of a dual semigroup with respect to a certain scalar product defined by an invariant state. In this paper we survey some results describing the structure of norm continuous quantum Markov semigroups on ℬ(h) satisfying a quantum detailed balance condition when the duality is defined by means of pre-scalar products on ℬ(h) of the form $⟨x,y⟩_s: = tr(ρ^{1-s}x*ρ^{s}y)$ (s ∈ [0,1]) in order to compare the resulting quantum versions of the classical detailed balance condition. Moreover, we discuss the structure of generators of a quantum Markov semigroup which commute with the modular automorphism because this condition appears when we consider pre-scalar products with s ≠ 1/2.
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Numer
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105-119
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Daty
wydano
2010
Twórcy
autor
• Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy
autor
• Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, I-16146 Genova, Italy
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