On two quantum versions of the detailed balance condition

Franco 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 -