Symmetry and Localization for Magnetic Schrödinger Operators: Landau Levels, Gabor Frames and All That

  title={Symmetry and Localization for Magnetic Schr{\"o}dinger Operators: Landau Levels, Gabor Frames and All That},
  author={Massimo Moscolari and Gianluca Panati},
  journal={Acta Applicandae Mathematicae},
We investigate the relation between broken time-reversal symmetry and localization of the electronic states, in the explicitly tractable case of the Landau model. We first review, for the reader’s convenience, the symmetries of the Landau Hamiltonian and the relation of the latter with the Segal-Bargmann representation of Quantum Mechanics. We then study the localization properties of the Landau eigenstates by applying an abstract version of the Balian-Low Theorem to the operators corresponding… 

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