论文标题
超对称群集扩展和对随机Schrödinger操作员的应用
Supersymmetric Cluster Expansions and Applications to Random Schrödinger Operators
论文作者
论文摘要
我们通过超对称形式主义研究离散的随机Schrödinger操作员。我们开发了一个集群的扩展，该群集在强和弱障碍方面融合。我们证明了这种疾病平均绿色功能的指数衰减以及状态的局部密度要么在弱点和能量处于未受干扰的频谱或强障碍和强度障碍和任何能量下的能量。作为一种应用，我们为状态的局部密度建立了LIFSHITZ-TAIL型估计，从而定位在弱障碍处。
We study discrete random Schrödinger operators via the supersymmetric formalism. We develop a cluster expansion that converges at both strong and weak disorder. We prove the exponential decay of the disorder-averaged Green's function and the smoothness of the local density of states either at weak disorder and at energies in proximity of the unperturbed spectrum or at strong disorder and at any energy. As an application, we establish Lifshitz-tail-type estimates for the local density of states and thus localization at weak disorder.
