A New Proof of the Sharp Gordon's Lemma: No Eigenvalues for Schr\"odinger Operators with Almost Repetition Potentials

Abstract

Building on the work of Jitomirskaya-Simon and Jitomirskaya-Liu, who established the absence of eigenvalues for Schr\"odinger operators with almost reflective repetition potentials, we provide a new proof of the sharp Gordon's lemma, which asserts the absence of eigenvalues for Schr\"odinger operators with almost repetition potentials.