Lecture Event
Mañé's critical value and periodic magnetic Schrödinger operators
Dr. Peter Herbrich
22 May 2013, 15:30 – 16:30
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
data.
http://www.math.dartmouth.edu/~herbrich/
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