Sparse Potentials With Fractional Hausdorff Dimension

Details Sparse Potentials With Fractional Hausdorff Dimension Sparse Potentials With Fractional Hausdorff Dimension

2002-10-30

arxiv.org/abs/math-ph/0210054v1

Physics

Mathematical Physics

Scientific paper

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.

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