Seminar

Beyond Diophantine Wannier diagrams: gap labelling for Bloch-Landau Hamiltonians

Spectral Methods in Mathematical Physics

15 April 14:00 - 15:00

Massimo Moscolari - Sapienza University of Rome

In 1978 Wannier discovered a Diophantine relation expressing the integrated density of states of a gapped group of bands of the Hofstadter Hamiltonian as a linear function of the magnetic field flux with integer slope. I will show how to extend this relation to a gap labelling theorem for any 2D Bloch-Landau Hamiltonian operator and to certain non-covariant systems having slowly varying magnetic fields. The integer slope will be interpreted as the Chern character of the projection onto the space of occupied states. This is based on a joint work with H. Cornean and D. Monaco.
Then, I will briefly discuss the relation between the Chern character and the existence of a localized generalized Wannier basis for the space of occupied states of a generic 2D gapped quantum system, this is a work in progress with G. Marcelli and G. Panati.
Organizers
Søren Fournais
Aarhus University
Rupert Frank
LMU Munich
Benjamin Schlein
University of Zurich, UZH
Simone Warzel
TU Munich

Program
Contact

Rupert Frank

frank@math.lmu.de

Other
information

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