论文标题
Schrödinger操作员的光谱具有随机扰动的偏僻势
The Spectrum of Schrödinger Operators with Randomly Perturbed Ergodic Potentials
论文作者
论文摘要
我们考虑$ \ ell^2（\ Mathbb {z}）$中的Schrödinger运算符，其电势由ergodic术语的总和和Anderson类型的随机术语给出。在假设沿着连接的紧凑型度量空间和连续采样函数的同态形态形态产生的假设中，我们表明，几乎确定的频谱以从未渗透的频谱和单位点分布的拓扑支持和单位分布的拓扑支持中明确描述的方式产生。特别是，假设后者是紧凑的，并且至少包含两个点，那么对几乎肯定的频谱的明确描述表明，它将始终由非排分紧凑间隔的有限结合给出。结果可以看作是对经典安德森模型范围的众所周知公式的泛滥。
We consider Schrödinger operators in $\ell^2(\mathbb{Z})$ whose potentials are given by the sum of an ergodic term and a random term of Anderson type. Under the assumption that the ergodic term is generated by a homeomorphism of a connected compact metric space and a continuous sampling function, we show that the almost sure spectrum arises in an explicitly described way from the unperturbed spectrum and the topological support of the single-site distribution. In particular, assuming that the latter is compact and contains at least two points, this explicit description of the almost sure spectrum shows that it will always be given by a finite union of non-degenerate compact intervals. The result can be viewed as a far reaching generalization of the well known formula for the spectrum of the classical Anderson model.
