On the spectrum of quasi-periodic Schr\"odinger operators on $\mathbb{Z}^d$ with $C^2$-cosine type potentials

Abstract

In this paper, we establish the Anderson localization, strong dynamical localization and the $(\frac 12-)$-H\"older continuity of the integrated density of states (IDS) for some multi-dimensional discrete quasi-periodic (QP) Schr\"odinger operators with asymmetric $C^2$-cosine type potentials. We extend both the iteration scheme of \cite{CSZ23a} and the interlacing method of \cite{FV21} to handle asymmetric Rellich functions with collapsed gaps.