An official website of the United States government
Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher.
Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?
Some links on this page may take you to non-federal websites. Their policies may differ from this site.
-
We analyze the spectrum of a discrete Schrödinger operator with a potential given by a periodic variant of the Anderson model. In order to do so, we study the uniform hyperbolicity of a Schrödinger cocycle generated by the SL(2,R) transfer matrices. In the specific case of the potential generated by an alternating sequence of random values, we show that the almost sure spectrum consists of at most 4 intervals.more » « less
-
null (Ed.)Abstract We consider separable 2D discrete Schrödinger operators generated by 1D almost Mathieu operators. For fixed Diophantine frequencies, we prove that for sufficiently small couplings the spectrum must be an interval. This complements a result by J. Bourgain establishing that for fixed couplings the spectrum has gaps for some (positive measure) Diophantine frequencies. Our result generalizes to separable multidimensional discrete Schrödinger operators generated by 1D quasiperiodic operators whose potential is analytic and whose frequency is Diophantine. The proof is based on the study of the thickness of the spectrum of the almost Mathieu operator and utilizes the Newhouse Gap Lemma on sums of Cantor sets.more » « less
