TY - JOUR
T1 - Spectral Aspects of the Skew-Shift Operator: A Numerical Perspective
AU - Eric Bourgain-Chang
JO - Communications in Computational Physics
VL - 3
SP - 712
EP - 732
PY - 2014
DA - 2014/03
SN - 15
DO - http://doi.org/10.4208/cicp.120513.290813a
UR - https://global-sci.org/intro/article_detail/cicp/7112.html
KW - 
AB - <p style="text-align: justify;">In this paper we perform a numerical study of the spectra, eigenstates, and
Lyapunov exponents of the skew-shift counterpart to Harper&#39;s equation. This study
is motivated by various conjectures on the spectral theory of these &#39;pseudo-random&#39; 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).</p>