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

作　　者：Eric Bourgain-Chang 

机构地区：[1]Mechanical Engineering Department,University of California,Berkeley,CA 94720,USA

出　　处：《Communications in Computational Physics》2014年第3期712-732,共21页计算物理通讯（英文）

摘　　要：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).

关 键 词：Schrödinger operator skew-shift SPECTRUM localization 

分 类 号：O17[理学—数学]