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

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

Year:    2014

Communications in Computational Physics, Vol. 15 (2014), Iss. 3 : pp. 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).

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.120513.290813a

Communications in Computational Physics, Vol. 15 (2014), Iss. 3 : pp. 712–732

Published online:    2014-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    21

Keywords: