On nonperturbative localization with quasiperiodic potential
Abstract
The two main results of the article are concerned with Anderson Localization for onedimensional lattice Schroedinger operators with quasiperiodic potentials with d frequencies. First, in the case d = 1 or 2, it is proved that the spectrum is purepoint with exponentially decaying eigenfunctions for all potentials (defined in terms of a trigonometric polynomial on the ddimensional torus) for which the Lyapounov exponents are strictly positive for all frequencies and all energies. Second, for every nonconstant realanalytic potential and with a Diophantine set of d frequencies, a lower bound is given for the Lyapounov exponents for the same potential rescaled by a sufficiently large constant.
 Publication:

arXiv eprints
 Pub Date:
 October 2000
 arXiv:
 arXiv:mathph/0011053
 Bibcode:
 2000math.ph..11053B
 Keywords:

 Mathematical Physics;
 Mathematics  Spectral Theory
 EPrint:
 45 pages, published version, abstract added in migration