Dynamical Systems Seminar

The Schrödinger operator is a fundamental model of a single-particle Hamiltonian in quantum mechanics. We show how to prove estimates on the size of the spectra of ergodic Schrödinger operators using cocycle techniques and uniform hyperbolicity. In particular, hyperbolicity across long blocks leads to exponentially small upper bounds on the size of the spectrum in suitable energy regions. We will review some of the relevant background.