How the Angle of Static Field Affects the Spectrum of Lattice Schrodinger Operator on $\mathbb{Z}^2$

Meina Gao; Siming Li; Yingte Sun

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arXiv · 2607.17720

How the Angle of Static Field Affects the Spectrum of Lattice Schrodinger Operator on $\mathbb{Z}^2$

Meina Gao·Siming Li·Yingte Sun

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Abstract

The spectral properties of the discrete Schrodinger operator on a two-dimensional lattice under uniform static fields are critically governed by the field direction: for angles parameterized by irrational frequencies, the operator is exponentially localized, and for a subset of such angles with asymptotically full Lebesgue measure, this localization persists under a given logarithmically decaying perturbation potential.

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Meina Gao, Siming Li, Yingte Sun. 2026-07-20. How the Angle of Static Field Affects the Spectrum of Lattice Schrodinger Operator on $\mathbb{Z}^2$. https://arxiv.org/abs/2607.17720

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