Uniform spectral properties of one-dimensional quasicrystals, III. $α$-continuity

Details Uniform spectral properties of one-dimensional quasicrystals, III. $α$-continuity Uniform spectral properties of one-dimensional quasicrystals, III. $α$-continuity

1999-10-12

arxiv.org/abs/math-ph/9910017v1

Physics

Mathematical Physics

12 pages

Scientific paper

10.1007/s002200000203

We study the spectral properties of discrete one-dimensional Schr\"odinger operators with Sturmian potentials. It is shown that the point spectrum is always empty. Moreover, for rotation numbers with bounded density, we establish purely $\alpha$-continuous spectrum, uniformly for all phases. The proofs rely on the unique decomposition property of Sturmian potentials, a mass-reproduction technique based upon a Gordon-type argument, and on the Jitomirskaya-Last extension of the Gilbert-Pearson theory of subordinacy.

Affiliated with

Also associated with

No associations

Rating

Uniform spectral properties of one-dimensional quasicrystals, III. $α$-continuity does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Uniform spectral properties of one-dimensional quasicrystals, III. $α$-continuity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Uniform spectral properties of one-dimensional quasicrystals, III. $α$-continuity will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-446525