Jitomirskaya S.
Anderson Localization for the Almost Mathieu Equation: A
Nonperturbative Proof.
(22K, LaTeX)
ABSTRACT. We prove that for any diophantine rotation angle and a.e. phase the almost
Mathieu operator has pure point spectrum with exponentially decaying
eigenfunctions if the coupling constant is greater than 15. We also prove the
existence of some pure point spectrum for any coupling constant greater
than 5.4.