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

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 $C^2$ cosine type quasiperiodic Schrödinger operators with large coupling constants, Diophantine frequencies and Diophantine phases.

arXiv comment16 pages

References in corpus (3)

• Universal reflective-hierarchical structure of quasiperiodic eigenfunctions and sharp spectral transition in phase
• Ballistic transport for one-dimensional quasiperiodic Schrödinger operators
• Localization and Cantor spectrum for quasiperiodic discrete Schrödinger operators with asymmetric, smooth, cosine-like sampling functions