@Article{CiCP-15-712, author = {}, title = {Spectral Aspects of the Skew-Shift Operator: A Numerical Perspective}, journal = {Communications in Computational Physics}, year = {2014}, volume = {15}, number = {3}, pages = {712--732}, abstract = {

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).

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.120513.290813a}, url = {http://global-sci.org/intro/article_detail/cicp/7112.html} }