Showing papers on "Almost Mathieu operator published in 1983"

Almost periodic Schrödinger operators: III. The absolutely continuous spectrum in one dimension

Abstract: We studyH=−d2/dx2+V(x) withV(x) limit periodic, e.g.V(x)=Σancos(x/2n) with Σ∣an∣<∞. We prove that for a genericV (and for generican in the explicit example), σ(H) is a Cantor (≡ nowhere dense, perfect) set. For a dense set, the spectrum is both Cantor and purely absolutely continuous and therefore purely recurrent absolutely continuous.