Magnetic Schrödinger operators and Mañé's critical value

2014/10/30 by Peter Herbrich, Herbrich, Peter
Mathematics · Physics and Astronomy · #Spectral Theory in Mathematical Physics #Quantum chaos and dynamical systems #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1410.8210

Abstract

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.

Citations

• The Geometries of 3-Manifolds
• Action minimizing invariant measures for positive definite Lagrangian systems

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