Scattering from Sparse Potentials on Graphs

Анотація

We study the spectral structure of Schrödinger operators $H=\Delta+V$ for random potentials supported on sparse sets. In the past years examples of such operators whose spectra almost surely satisfy the following properties have been exhibited: Anderson localization holds outside spec($\Delta$), while the wave operators $\Omega^{\pm}(H,\Delta)$ exist inside this last set. We continue this program by presenting sparseness conditions under which $\Omega^{\pm}(\Delta,H)$ also exist.

Mathematics Subject Classification: 81Q10, 47B80.