English

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.

Keywords

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}
}
R2 v1 2026-06-21T23:57:00.139Z