München 2019 – scientific programme

Parts | Days | Selection | Search | Updates | Downloads | Help

MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 8: Quanteninformation und Kontrolle

MP 8.4: Talk

Wednesday, March 20, 2019, 15:30–15:50, HS 23

Quantum control in infinite dimensions and Banach-Lie algebras — •Michael Keyl — Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany

In finite dimensions, controllability of bilinear quantum control systems can be decided quite easily in terms of the “Lie algebra rank condition” (LARC), such that only the system Lie algebra has to be determined from a set of generators. In this paper we study how this idea can be lifted to infinite dimensions. To this end we look at control systems on an infinite dimensional Hilbert space, which are given by an unbounded drift Hamiltonian H₀ and bounded control Hamiltonians H₁, …, H_N. The drift H₀ is assumed to have empty continuous spectrum. We use recurrence methods and the theory of Abelian von Neumann algebras to develop a scheme, which allows to use an approximate version of LARC in order to check approximate controllability of the control system in question. Its power is demonstrated by looking at some examples. We recover in particular previous genericity results with a much easier proof. Finally several possible generalizations are outlined.