The Exponential Localization and Structure of the Spectrum for 1d QuasiPeriodic Discrete SCHRÖDINGER Operators
Abstract
We discuss main mechanisms of the exponential localization of the eigenfunctions for onedimensional quasiperiodic Schrödinger operators with the potential of the form V(α + nω), where V(α) is a nondegenerate C^{2}function on the ddimensional torus, and ω ∈ &R;^{d} is a typical vector with rationally incommensurate components. The exponential localization is proved so far for d ≤ 2. We emphasize the different nature of the support of the spectral measure for d = 1 and for d > 1.
 Publication:

Reviews in Mathematical Physics
 Pub Date:
 1991
 DOI:
 10.1142/S0129055X91000096
 Bibcode:
 1991RvMaP...3..241C