Absolutely continuous spectrum for limit-periodic Schr\"odinger operators
Spectral Theory
2013-04-11 v1
Abstract
We show that a large class of limit-periodic Schr\"odinger operators has purely absolutely continuous spectrum in arbitrary dimensions. This result was previously known only in dimension one. The proof proceeds through the non-perturbative construction of limit-periodic extended states. An essential step is a new estimate of the probability (in quasi-momentum) that the Floquet Bloch operators have only simple eigenvalues.
Cite
@article{arxiv.1304.2805,
title = {Absolutely continuous spectrum for limit-periodic Schr\"odinger operators},
author = {Helge Krueger},
journal= {arXiv preprint arXiv:1304.2805},
year = {2013}
}