Subcritical behavior for quasi-periodic Schrödinger cocycles with trigonometric potentials

  • Christoph A. Marx

    Oberlin College, USA
  • Laura H. Shou

    Princeton University, USA
  • Jake L. Wellens

    Massachusetts Institute of Technology, Cambridge, USA

Abstract

We give a criterion implying subcritical behavior for quasi-periodic Schrödinger operators where the potential sampling function is given by a trigonometric polynomial. Subcritical behavior, in the sense of Avila’s global theory, is known to imply purely absolutely continuous spectrum for all irrational frequencies and all phases.

Cite this article

Christoph A. Marx, Laura H. Shou, Jake L. Wellens, Subcritical behavior for quasi-periodic Schrödinger cocycles with trigonometric potentials. J. Spectr. Theory 8 (2018), no. 1, pp. 123–163

DOI 10.4171/JST/192