Point spectrum for quasi-periodic long range operators
Summary: We generalize Gordon type argument to quasi-periodic operators with finite range interaction and prove that these operators have no point spectrum when the rational approximation rate of the base frequency is relatively large. We also show that, for any irrational frequency, there are operators with infinite range interaction possessing point spectrum. This is a new phenomenon which can not happen in the finite range interaction case.
scientific article; zbMATH DE number 6424790