随机单调Hamilton算子的Lifshitz渐近性
Lifshitz asymptotics for Hamiltonians monotone in the randomness
摘要：
在随机Schroedinger算子的谱分析的各个方面，关于随机性的单调性起着关键作用。特别是，如果这种单调性存在于模型中，则积分态密度（IDS）的连续性属性和低能量行为都可以更好地理解。本文给出了两类随机势的IDS的Lifshitz型界。其中之一是一个轻微的推广的模型，其中一个Lifshitz界是在最近的联合文件中与维尔纳基尔希[KV]。第二种是呼吸型势，它是区间的特征函数之和。虽然第二个模型很简单，但似乎不能用[KV]的方法来处理。的模型和证据的动机是由完善的方法开发所谓的合金型电位。
英文摘要：
In various aspects of the spectral analysis of random Schroedinger operators monotonicity with respect to the randomness plays a key role. In particular, both the continuity properties and the low energy behaviour of the integrated density of states (IDS) are much better understood if such a monotonicity is present in the model than if not. In this note we present Lifshitz-type bounds on the IDS for two classes of random potentials. One of them is a slight generalisation of a model for which a Lifshitz bound was derived in a recent joint paper with Werner Kirsch [KV]. The second one is a breather type potential which is a sum of characteristic functions of intervals. Although the second model is very simple, it seems that it cannot be treated by the methods of [KV]. The models and the proofs are motivated by well-established methods developed for so called alloy type potentials.
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