Quantum detailed balance conditions with time reversal: the finite-dimensional case

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

Abstrakty

EN

We classify generators of quantum Markov semigroups 𝓣 on 𝓑 (h), with h finite-dimensional and with a faithful normal invariant state ρ satisfying the standard quantum detailed balance condition with an anti-unitary time reversal θ commuting with ρ, namely $tr(ρ^{1/2}xρ^{1/2}𝓣_t(y)) = tr(ρ^{1/2}θy*θρ^{1/2}𝓣_t(θx*θ))$ for all x,y ∈ 𝓑 and t ≥ 0.
Our results also show that it is possible to find a standard form for the operators in the Lindblad representation of the generators extending the standard form of generators of quantum Markov semigroups satisfying the usual quantum detailed balance condition with non-symmetric multiplications $x ↦ ρ^{s}xρ^{1-s}$ (s ∈ [0,1], s ≠ 1/2) whose generators must commute with the modular group associated with ρ. This supports our conclusion that the most appropriate non-commutative version of the classical detailed balance condition is the above standard quantum detailed balance condition with an anti-unitary time reversal.

Kategorie tematyczne

• 81S25: Quantum stochastic calculus
• 82B10: Quantum equilibrium statistical mechanics (general)
• 47D06: One-parameter semigroups and linear evolution equations
• 82C10: Quantum dynamics and nonequilibrium statistical mechanics (general)
• 47D07: Markov semigroups and applications to diffusion processes
• 46L55: Noncommutative dynamical systems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2011
• Tom: 96
• Numer: 1
• Strony: 159-174

Daty

wydano

2011

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/bc96-0-10