On the spectrum and Lyapunov exponent of limit periodic Schrodinger operators

Details On the spectrum and Lyapunov exponent of limit periodic Schrodinger operators On the spectrum and Lyapunov exponent of limit periodic Schrodinger operators

2008-07-28

arxiv.org/abs/0807.4339v1

Mathematics

Dynamical Systems

12 pages. To appear in Communications in Mathematical Physics

Scientific paper

We exhibit a dense set of limit periodic potentials for which the corresponding one-dimensional Schr\"odinger operator has a positive Lyapunov exponent for all energies and a spectrum of zero Lebesgue measure. No example with those properties was previously known, even in the larger class of ergodic potentials. We also conclude that the generic limit periodic potential has a spectrum of zero Lebesgue measure.

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