arXiv:0707.2147 · Infinite Dimensional Analysis Quantum Probability and Related Topics

GENERATORS OF DETAILED BALANCE QUANTUM MARKOV SEMIGROUPS

Franco Fagnola, Veronica Umanità

Published Sep 1, 2007• 88 citations

Abstract

For a quantum Markov semigroup [Formula: see text] on the algebra [Formula: see text] with a faithful invariant state ρ, we can define an adjoint [Formula: see text] with respect to the scalar product determined by ρ. In this paper, we solve the open problems of characterizing adjoints [Formula: see text] that are also a quantum Markov semigroup and satisfy the detailed balance condition in terms of the operators H, Lk in the Gorini–Kossakowski–Sudarshan–Lindblad representation [Formula: see text] of the generator of [Formula: see text]. We study the adjoint semigroup with respect to both scalar products 〈a, b〉 = tr (ρa*b) and 〈a, b〉 = tr (ρ1/2a*ρ1/2 b).

DOI: 10.1142/s0219025707002762

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