Arithmetic version of anderson localization for quasiperiodic Schrödinger operators with even cosine type potentials

2021/07/18 by Ge, Lingrui, You, Jiangong, Zhao, Xin
#Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2107.08547

Abstract

We propose a new method to prove Anderson localization for quasiperiodic Schrödinger operators and apply it to the quasiperiodic model considered by Sinai and Fröhlich-Spencer-Wittwer. More concretely, we prove Anderson localization for even C² cosine type quasiperiodic Schrödinger operators with large coupling constants, Diophantine frequencies and Diophantine phases.

Related

• Localization and Cantor spectrum for quasiperiodic discrete Schrödinger operators with asymmetric, smooth, cosine-like sampling functions
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