arXiv subjects
Publications and source records attributed to Eric Bourgain-Chang.
In this Note, we consider 1D lattice Schrodinger operators with deterministic strongly mixing potentials with very small coupling. We describe a scheme to establish positiv- ity of the Lyapunov exponent from a statement at some fixed scale. The required input may then be derived from Furstenberg theory, if the underlying dynamics are sufficiently mixing, or verified directly by numerical means.
In this paper we perform a numerical study of the spectra, eigenstates, and Lyapunov exponents of the skew-shift counterpart to Harper's equation. This study is motivated by various conjectures on the spectral theory of these 'pseudo-random' models, which are reviewed in detail in the initial sections of the paper. The numerics carried out at different scales are within agreement with the conjectures and show a striking difference compared with the spectral features of the Almost Mathieu model. In particular our numerics establish a small upper bound on the gaps in the spectrum (conjectured to be absent).