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arXiv · 2603.07180

Anderson localization and Hölder continuity of the integrated density of states for analytic quasiperiodic Schrödinger operators

Hongyi Cao·Yunfeng Shi·Zhifei Zhang
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Abstract

We establish both Anderson localization and Hölder continuity of the integrated density of states for quasiperiodic Schrödinger operators on $\mathbb{Z}^d$ with any non-constant analytic potential and any Diophantine frequency in the perturbative regime. Our proof is based on a new method for controlling Green's functions and eliminating double resonances, in the spirit of multi-scale analysis. To the best of our knowledge, this is the first multi-scale analysis approach that works for fixed Diophantine frequencies and potentials beyond the cosine type.

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Hongyi Cao, Yunfeng Shi, Zhifei Zhang. 2026-04-13. Anderson localization and Hölder continuity of the integrated density of states for analytic quasiperiodic Schrödinger operators. https://arxiv.org/abs/2603.07180

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