Splitting of the Low Landau Levels into a Set of Positive Lebesgue Measure under Small Periodic Perturbations
Abstract
We study the spectral properties of a twodimensional Schrödinger operator with a uniform magnetic field and a small external periodic field:<FORMULA FORM="DISPLAY" DISC="MATH"> where<FORMULA FORM="DISPLAY" DISC="MATH"> and , are small parameters. Representing as the direct integral of onedimensional quasiperiodic difference operators with longrange potential and employing recent results of E.I.Dinaburg about Anderson localization for such operators (we assume to be typical irrational) we construct the full set of generalised eigenfunctions for the low Landau bands. We also show that the Lebesgue measure of the low bands is positive and proportional in the main order to .
 Publication:

Communications in Mathematical Physics
 Pub Date:
 1997
 DOI:
 10.1007/s002200050217
 Bibcode:
 1997CMaPh.189..559D