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 (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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc89-0-5,
author = {Franco Fagnola and Veronica Umanit\`a},
title = {On two quantum versions of the detailed balance condition},
journal = {Banach Center Publications},
volume = {89},
year = {2010},
pages = {105-119},
zbl = {1214.46046},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc89-0-5}
}
Franco Fagnola; Veronica Umanità. On two quantum versions of the detailed balance condition. Banach Center Publications, Tome 89 (2010) pp. 105-119. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc89-0-5/