静态场角度如何影响\(\mathbb{Z}^2\)上晶格薛定谔算子的谱
How the Angle of Static Field Affects the Spectrum of Lattice Schrodinger Operator on $\mathbb{Z}^2$
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中文总结 AI 辅助
研究二维晶格上离散薛定谔算子在均匀静态场下谱性质受场方向影响，通过无理频率参数化角度，发现特定角度下算子指数局域化，且在对数衰减微扰势下部分角度局域化仍持续。
中文摘要 AI 辅助
二维晶格上离散薛定谔算子在均匀静态场下的谱性质受场方向关键影响：对于由无理频率参数化的角度，算子是指数局域化的，且对于此类角度中具有渐近全勒贝格测度的子集，在给定对数衰减微扰势下这种局域化持续存在。
英文摘要
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.
