Berlin 2015 – scientific programme
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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 2: Quanteninformation
MP 2.3: Talk
Tuesday, March 17, 2015, 11:35–11:55, HFT-FT 101
Fixpoint engineering and reachability in open Markovian quantum systems — •Thomas Schulte-Herbrüggen1, Corey O’Meara1, Gunther Dirr2, and Luca Arceci1,3 — 1Dept. Chem., TU-München — 2Math. Inst., University of Würzburg — 3Dept. Mathematics, TU-München
Lie groups and Lie semigroups with their symmetries provide a unified framework to pinpoint the dynamic behaviour of closed and open quantum systems under all kinds of controls.
Recently, we showed that all Markovian quantum maps can be represented by Lie semigroups. These semigroups come with the geometry of affine maps, whose translational parts determine the respective fixed points. We exploit this geometry for dissipative fixed-point engineering of unique target states. We extend our results from pure to mixed target states.
Finally, we elucidate the findings by their relation to control problems: particular light is shed on reachability and open-loop versus closed-loop control design.