Title

Generic continuous spectrum for multi-dimensional quasiperiodic Schrödinger operators with rough potentials

Document Type

Article

Publication Date

1-1-2018

Abstract

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

First Page

1635

Last Page

1645

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