# On two quantum versions of the detailed balance condition

Franco Fagnola; Veronica Umanità

Banach Center Publications (2010)

- Volume: 89, Issue: 1, page 105-119
- ISSN: 0137-6934

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topFranco Fagnola, and Veronica Umanità. "On two quantum versions of the detailed balance condition." Banach Center Publications 89.1 (2010): 105-119. <http://eudml.org/doc/282380>.

@article{FrancoFagnola2010,

abstract = {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.},

author = {Franco Fagnola, Veronica Umanità},

journal = {Banach Center Publications},

keywords = {quantum detailed balance; quantum Markov semigroup; Lindblad representation},

language = {eng},

number = {1},

pages = {105-119},

title = {On two quantum versions of the detailed balance condition},

url = {http://eudml.org/doc/282380},

volume = {89},

year = {2010},

}

TY - JOUR

AU - Franco Fagnola

AU - Veronica Umanità

TI - On two quantum versions of the detailed balance condition

JO - Banach Center Publications

PY - 2010

VL - 89

IS - 1

SP - 105

EP - 119

AB - 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.

LA - eng

KW - quantum detailed balance; quantum Markov semigroup; Lindblad representation

UR - http://eudml.org/doc/282380

ER -

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