Spectral Aspects of the Skew-Shift Operator: A Numerical Perspective (Communications in Computational Physics, 2014)
In this paper we perform a numerical study of the spectra, eigenstates, andLyapunov exponents of the skew-shift counterpart to Harper's equation. This studyis 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 numericscarried out at different scales are within agreement with the conjectures and show astriking 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).