Göttingen 2012 – wissenschaftliches Programm

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 17: Quanteninformation II

MP 17.1: Vortrag

Donnerstag, 1. März 2012, 15:00–15:25, ZHG 003

Mathematical Quantum Systems Theory for Engineers: Theory and Applications with a Focus on Fermions — •Thomas Schulte-Herbrüggen¹, Robert Zeier¹, Zoltan Zimboras², and Michael Keyl² — ¹TU-Munich, Dept. Chem. — ²ISI Torino, Italy

The dynamic properties of closed (or open) quantum systems is presented in a unified way via dynamic system Lie algebras (or Lie wedges).

For the quantum engineer, these algebras (or cones) encapsulate all directions a quantum system can be steered along. This is of central importance in quantum simulation and implementation of quantum information processing. We give a number of examples including systems of spins, bosons, and in particular fermions building on [1].

Applications to controllability, reachability, and observability are given. Relations to generalising notions in the mathematical field of C-numerical ranges are pointed out, which go beyond [2, 3].
References:
[1] R. Zeier and T. Schulte-Herbrüggen, J. Math. Phys. 52 (2011) 113510 [doi:10.1063/1.3657939]

[2] T. Schulte-Herbrüggen, S. Glaser, G. Dirr, and U. Helmke, Rev. Math. Phys. 22 (2010) 597–667 [doi:10.1142/S0129055X10004053]

[3] T. Schulte-Herbrüggen et al., Lin. Multilin. Alg. 56 (2008) 3–26 [doi:10.1080/03081080701544114]