Mañé's critical value and periodic magnetic Schrödinger operators
Dr. Peter Herbrich
21.5.2013, 14:30 Uhr – 15:30 Uhr
Vortrag im Rahmen des Forschungsseminars "Geometrische Analysis und Spektraltheorie"
The talk will deal with lifted magnetic elds on covers of closed manifolds. In particular, the spectra of corresponding periodic magnetic Schrodinger operators can be related to Ma~ne's critical energy values of the corresponding classical Hamiltonian systems. Namely, if the covering transformation group is amenable, then the bottom of the spectrum is bounded from above by Ma~ne's critical value. In the special case of abelian covers, the spectral analysis reduces
to the study of shifted magnetic potentials on the compact quotient which parallels the behaviour of Ma~ne's critical value of the corresponding classical systems. The talk will nish with examples of magnetic elds on homogeneous spaces, which facilitate comparisons between the classical and the quantum