AI 中文总结
本文基于各向同性α-稳定Lévy过程理论，证明了分数随机薛定谔算子积分态密度的存在性，并确定其谱右端Lifshitz尾部的渐近行为，凸显自相似性的核心作用。
AI 中文摘要
我们基于各向同性$\alpha$-稳定Lévy过程的理论，证明了具有高斯势的分数随机薛定谔算子的积分态密度（IDS）的存在性。进一步，我们证明了该IDS表现出Lifshitz尾部，并确定了其谱右端的渐近行为。各向同性$\alpha$-稳定Lévy过程是自相似的但不连续的，因此自相似性对于这些量子算子而言是一个基本概念。
英文摘要
We proof the existence of the Integrated Density of States (IDS) for fractional random Schrödinger operators with Gaussian potential based on the theory of isotropic $α$-stable Lévy processes. Further we show that the IDS exhibits Lifshitz tails and determine its asymptotics at the right end of the spectrum. Isotropic$α$-stable Lévy processes are self-similar but not continuous. Thus self-similarity is a fundamental concept for these quantum operators.
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