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.

我们考虑\(\ell ^2({\mathbb Z})\)中的薛定谔算子其势由遍历项和 Anderson 类型的随机项的总和给出。假设遍历项是由连接的紧致度量空间和连续采样函数的同胚生成的，我们证明了几乎确定的光谱以一种明确描述的方式从未扰动的光谱和单点的拓扑支持中产生分配。特别地，假设后者是紧致的并且至少包含两个点，这种对几乎确定谱的明确描述表明它总是由非退化紧致区间的有限并集给出。结果可以看作是对经典安德森模型的广为人知的频谱公式的深远推广。