论文标题
Anderson的本地化，$ 1 $ -D-dschrödinger操作员具有白噪声潜力
Anderson localization for the $1$-d Schrödinger operator with white noise potential
论文作者
论文摘要
我们考虑在$ \ mathbb {r} $上使用随机的schrödinger操作员，通过用白噪声扰动拉普拉斯式获得。我们证明了安德森本地化为该操作员所包含的：几乎肯定的频谱度量是纯粹的点，而本征函数则是指数性的。我们给出了两个单独的证据。我们还介绍了操作员的详细构造，并将其与抛物线安德森模型联系起来。最后，我们讨论了噪音平滑的情况。
We consider the random Schrödinger operator on $\mathbb{R}$ obtained by perturbing the Laplacian with a white noise. We prove that Anderson localization holds for this operator: almost surely the spectral measure is pure point and the eigenfunctions are exponentially localized. We give two separate proofs of this result. We also present a detailed construction of the operator and relate it to the parabolic Anderson model. Finally, we discuss the case where the noise is smoothed out.
