Paper detail

Magnetic Schrödinger operators and Mañé's critical value

We study periodic magnetic Schrödinger operators on covers of closed manifolds in relation to Mañé's critical energy values of the corresponding classical Hamiltonian systems. In particular, we show that if the covering transformation group is amenable, then the bottom of the spectrum is bounded from above by Mañé's critical energy value. We also determine the spectra for various homogeneous spaces with left-invariant magnetic fields.