Würzburg 2018 – wissenschaftliches Programm
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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 10: Quantum Systems, Symmetries and Scattering
MP 10.3: Vortrag
Donnerstag, 22. März 2018, 14:40–15:00, Z6 - SR 1.012
Quantum Systems Theory Viewed from Lie Semigroups — •Thomas Schulte-Herbrüggen1, Robert Zeier1, and Gunther Dirr2 — 1TU-München, Lichtenbergstraße 4, 85747 Garching — 2Uni-Würzburg, Math. Inst., Emil-Fischer-Straße 40, 97074 Würzburg
The solutions to the celebrated Kossakowski-Lindblad equation extended by coherent controls yield Markovian quantum maps. More precisely, the set of all its solutions forms a semigroup of cptp maps taking the specific form of a Lie semigroup [1].
Non-trivial symmetries of these semigroups are shown to preclude accessibility in Markovian dissipative systems. This is the open-system analogue to closed systems, where triviality of (quadratic) symmetries of the Hamiltonian part suffices to decide that the system is fully controllable [2-3].
These findings are placed into a unifying Lie frame of quantum systems and control theory alongside with illustrating examples [4].
[1] Rep. Math. Phys. 64 (2009), 93.
[2] J. Math. Phys. 52 (2011), 113510 and 56 (2015), 081702.
[3] Phys. Rev. A 92 (2015), 042309.
[4] Open Sys. Inf. Dynamics 24 (2017), 1750001 [in press].