Spectral Aspects of the Skew-Shift Operator: A Numerical Perspective

摘要: In this paper we perform a numerical study of the spectra, eigenstates, and Lyapunov exponents skew-shift counterpart to Harper’s equation. This is motivated by various conjectures on spectral theory these ‘pseudo-random’ models, which are reviewed in detail initial sections paper. The numerics carried out at different scales within agreement with show striking difference compared features Almost Mathieu model. particular our establish small upper bound gaps spectrum (conjectured be absent).