Sparse Potentials With Fractional Hausdorff Dimension
Mathematical Physics
2007-05-23 v1 math.MP
Abstract
We construct non-random bounded discrete half-line Schr\" odinger operators which have purely singular continuous spectral measures with fractional Hausdorff dimension (in some interval of energies). To do this we use suitable sparse potentials. Our results also apply to whole line operators, as well as to certain random operators. In the latter case we prove and compute an exact dimension of the spectral measures.
Keywords
Cite
@article{arxiv.math-ph/0210054,
title = {Sparse Potentials With Fractional Hausdorff Dimension},
author = {Andrej Zlatos},
journal= {arXiv preprint arXiv:math-ph/0210054},
year = {2007}
}