Absolutely continuous spectrum of one random elliptic operator
This paper concerns the differential operator \(H_0=-\Delta +\tau \xi(x)| x| ^{-\varepsilon}(-\Delta_\theta)\), perturbed by a random potential \(V\) (the same as that in Anderson's model). Here, \(\varepsilon>0\), \(\tau>0\), \(\Delta_\theta\) is the Laplace--Beltrami operator on the unit sphere, and \(\xi\) the characteristic function of the unit ball. The author proves that the operator \(H_0\pm V\) has absolutely continuous spectrum all over the positive half-line \([0,\infty)\), if the dimension \(d\geq 5\) and \(\varepsilon<2/(d+1)\).
scientific article; zbMATH DE number 5318666
scientific article