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...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).展开更多
文摘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).
