Must the Spectrum of a Random Schrödinger Operator Contain an Interval?
Must the Spectrum of a Random Schrödinger Operator Contain an Interval?
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DOI：
10.1007/s00220-022-04395-w
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发表时间：
2021-12
影响因子：
2.4
通讯作者：
D. Damanik;A. Gorodetski
中科院分区：
文献类型：
--
作者：
D. Damanik;A. Gorodetski
我们考虑Schrödinger算子，其中的势由独立的（不一定是同分布的）随机变量给出。我们要问，它的谱是否几乎肯定包含一个区间。对于具有解析抽样函数和丢芬图频率向量的摄动小拟周期势与由独立同分布随机变量给出的Anderson型项的和所给出的随机势，我们给出了肯定的答案（为支持单点分布，我们给出了一些小间隙假设）。证明是通过扩展经典安德森模型非典型实现的基态存在的结果来进行的，我们在这里也证明了这一点，这似乎是新的。
We consider Schrödinger operators inwhose potentials are given by independent (not necessarily identically distributed) random variables. We ask whether it is true that almost surely its spectrum contains an interval. We provide an affirmative answer in the case of random potentials given by a sum of a perturbatively small quasi-periodic potential with analytic sampling function and Diophantine frequency vector and a term of Anderson type, given by independent identically distributed random variables (with some small-gap assumption for the support of the single-site distribution). The proof proceeds by extending a result about the presence of ground states for atypical realizations of the classical Anderson model, which we prove here as well and which appears to be new.