具有不定号单点势的Anderson模型的Lifshitz尾
Lifshitz Tails for Anderson Models with Sign-Indefinite Single-Site Potentials
摘要：
研究了连续随机薛定谔算子\begin{equation*} H_{\om}=-\De+V_{0}+\sum_{i\in\Z^{d}}\om_{i}u(\cdot-i), \end{equation*}的谱极小值和Lifshitz尾，其中$V_{0}$是周期势，$\{\om_{i}\}_{i\in\Z^{d}}$是独立同分布随机变量，$u$是符号不定的杂质势.最近，在$u$的小支撑假设和$V_{0}$和$u$的反射对称假设下，该模型在谱底附近显示出Lifshitz尾.这里我们放弃了$V_{0}$和$u$的反射对称性假设。我们首先给出谱的底部的特征。然后，我们证明了存在的Lifshitz尾巴的政权的底部的频谱的特征是明确的。特别是，这个制度涵盖了反射对称的情况。
英文摘要：
We study the spectral minimum and Lifshitz tails for continuum random Schrödinger operators of the form \begin{equation*} H_{\om}=-\De+V_{0}+\sum_{i\in\Z^{d}}\om_{i}u(\cdot-i), \end{equation*} where $V_{0}$ is the periodic potential, $\{\om_{i}\}_{i\in\Z^{d}}$ are i.i.d random variables and $u$ is the sign-indefinite impurity potential. Recently, this model has been proven to exhibit Lifshitz tails near the bottom of the spectrum under the small support assuption of $u$ and the reflection symmetry assumption of $V_{0}$ and $u$. We here drop the reflection symmetry assumption of $V_{0}$ and $u$. We first give characterizations of the bottom of the spectrum. Then, we show the existence of Lifshitz tails in the regime where the characterization of the bottom of the spectrum is explicit. In particular, this regime covers the reflection symmetry case.
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