We study the multi-dimensional operator
where is the shift of the torus . When , we show the spectrum of is almost surely purely continuous for a.e. and generic continuous potentials. When , the same result holds for frequencies under an explicit arithmetic criterion. We also show that general multi-dimensional operators with measurable potentials do not have eigenvalue for generic .
Cite this article
Rui Han, Fan Yang, Generic continuous spectrum for multi-dimensional quasiperiodic Schrödinger operators with rough potentials. J. Spectr. Theory 8 (2018), no. 4, pp. 1635–1645DOI 10.4171/JST/238