München 2019 – wissenschaftliches Programm
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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 8: Quanteninformation und Kontrolle
MP 8.2: Vortrag
Mittwoch, 20. März 2019, 14:40–15:00, HS 23
Exploring the Limits of Quantum Dynamics – I: Lie-Algebraic Frame and Recent Results — •Thomas Schulte-Herbrüggen1, Frederik vom Ende1, Gunther Dirr2, and Michael Keyl3 — 1Technical University of Munich (TUM) — 2University of Würzburg — 3Free University of Berlin (FUB)
Quantum systems theory emerges from a rigorous Lie-theoretical framework for answering questions of "what one can do" with a given quantum dynamical system in terms of controllability, accessibility, reachability, stabilisability, and simulability. It thus describes both potential and limits of dynamical systems, e.g., in quantum technology.
The broad class of bilinear quantum control systems is of the form Ẋ(t) = −(i adH0 + Γ + i∑j uj(t) adHj) X(t), where the drift is governed by the system Hamiltonian H0 and eventually a (Markovian) dissipator Γ, while the control Hamiltonians Hj are switched by (piecewise constant) amplitudes uj(t). The class thus comprises coherently controlled Schrödinger (or Liouville) equations of closed systems as well as controlled Markovian master equations of GKS-Lindblad form.
We symmetry-characterise this class of dynamical systems to explore "what one can do" and give recent examples taking the dynamics of closed or open systems to their (symmetry-induced) experimental limits.