论文标题
衰减潜在模型的特征向量的形状
Shape of eigenvectors for the decaying potential model
论文作者
论文摘要
我们认为具有衰减的随机电势的1DSchrödinger操作员，并研究特征值的关节缩放限制以及与基于Rifkind-Virag制定的相应特征功能相关的措施。结果，我们的行为完全不同，具体取决于潜在的衰减率$α> 0 $：限制措施等于（1）超临界情况的lebesgue度量（$α> 1/2 $），（2）衡量密度的措施与关键情况下的Brownian波动（$ a = 1/2 $）和（3）和（3）和（3）的量子均具有功能范围（3）和（3）。亚临界情况（$α<1/2 $）。该结果与先前关于光谱和统计特性的研究一致。
We consider the 1d Schrödinger operator with decaying random potential, and study the joint scaling limit of the eigenvalues and the measures associated with the corresponding eigenfunctions which is based on the formulation by Rifkind-Virag. As a result, we have completely different behavior depending on the decaying rate $α> 0$ of the potential : the limiting measure is equal to (1) Lebesgue measure for the super-critical case ($α> 1/2$), (2) a measure of which the density has power-law decay with Brownian fluctuation for critical case ($α=1/2$), and (3) the delta measure with its atom being uniformly distributed for the sub-critical case($α<1/2$). This result is consistent with previous study on spectral and statistical properties.
