The spectrum of a Schrödinger operator with small quasi-periodic potential is homogeneous

  • David Damanik

    Rice University, Houston, United States
  • Michael Goldstein

    University of Toronto, Canada
  • Milivoje Lukic

    Rice University, Houston, USA

Abstract

We consider the quasi-periodic Schrödinger operator

in , where the potential is given by

with a Diophantine frequency vector and exponentially decaying Fourier coefficients . In the regime of small we show that the spectrum of the operator is homogeneous in the sense of Carleson.

Cite this article

David Damanik, Michael Goldstein, Milivoje Lukic, The spectrum of a Schrödinger operator with small quasi-periodic potential is homogeneous. J. Spectr. Theory 6 (2016), no. 2, pp. 415–427

DOI 10.4171/JST/128