Generic continuous spectrum for multi-dimensional quasiperiodic Schrödinger operators with rough potentials
We study the multi-dimensional operator .H x u/ n D X u m C f .T n .x//u n ; jmnjD1 where T is the shift of the torus T d . When d D 2, we show the spectrum of H x is almost surely purely continuous for a.e. and generic continuous potentials. When d 3, 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.
Publication Source (Journal or Book title)
Journal of Spectral Theory
Han, R., & Yang, F. (2018). Generic continuous spectrum for multi-dimensional quasiperiodic Schrödinger operators with rough potentials. Journal of Spectral Theory, 8 (4), 1635-1645. https://doi.org/10.4171/JST/238