论文标题
量子的光谱定位，量子较弱的随机增量相互作用
Spectral localization for quantum Hamiltonians with weak random delta interaction
论文作者
论文摘要
我们认为在多维欧几里得空间（或多维层）中具有负弱的laplacian。 扰动由晶格的总和组成，该晶格翻译由在同感的紧凑型歧管上支撑的三角洲相互作用，并由耦合常数调节，耦合常数是独立分布的随机变量乘以小型疾病参数的相同分布的随机变量。 我们确定所考虑的运算符的频谱几乎肯定是固定集，使其最小值的特征性，给出了初始长度尺度估计值和韦格纳估计，并得出结论，纯点光谱的小区域包含几乎确定的光谱底部。该区域的长度与小型疾病参数成正比。
We consider a negative Laplacian in multi-dimensional Euclidean space (or a multi-dimensional layer) with a weak disorder random perturbation. The perturbation consists of a sum of lattice translates of a delta interaction supported on a compact manifold of co-dimension one and modulated by coupling constants which are independent identically distributed random variables times a small disorder parameter. We establish that the spectrum of the considered operator is almost surely a fixed set, characerize its minimum, give an initial length scale estimate and the Wegner estimate and conclude that there is a small zone of a pure point spectrum containing the almost sure spectral bottom. The length of this zone is proportional to the small disorder parameter.
