维数至少三的弱无序Anderson模型的绝对连续谱
Absolutely Continuous Spectrum for Weak-Disorder Anderson Models in Dimensions at Least Three
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具体内容
稿件研究ℤd上带独立均匀格点势的Anderson算子。作者声称对每个固定维数d≥3和每个固定足够小的正无序强度，该算子几乎必然在一个开能量区间上具有非零权重的纯绝对连续谱；该区间可依赖于d但与无序强度无关。作者称这解决了Simon问题1中关于该模型的纯绝对连续能量范围问题。该手稿为AI产生，尚未经独立审查或同行评议。
- 对d≥3和足够小正无序强度研究ℤd上Anderson算子。
- 声称几乎必然在开能量区间上具有非零权重的纯绝对连续谱。
- 区间可依赖d但与无序强度无关，作者称解决Simon问题1的相关问题。
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英文原始摘要
For each fixed dimension d ≥ 3 and each fixed sufficiently small positive disorder strength, we prove that the Anderson operator on ℤd with independent uniform site potentials almost surely has purely absolutely continuous spectrum with nonzero weight on an open energy interval. The interval may depend on d but is independent of the disorder strength. This settles the purely absolutely continuous energy-range question in Simon's Problem 1 for this model.
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