On two quantum versions of the detailed balance condition

• Autorzy: Franco Fagnola , Veronica Umanità
• Języki publikacji: EN

Abstrakty

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.

Kategorie tematyczne

• 81S25: Quantum stochastic calculus
• 82B10: Quantum equilibrium statistical mechanics (general)
• 82C10: Quantum dynamics and nonequilibrium statistical mechanics (general)
• 46L55: Noncommutative dynamical systems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2010
• Tom: 89
• Numer: 1
• Strony: 105-119

Daty

wydano

2010

Twórcy

autor

Franco Fagnola

• Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy

autor

Veronica Umanità

• Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, I-16146 Genova, Italy

Identyfikatory

DOI

10.4064/bc89-0-5