Scattering from Sparse Potentials on Graphs

Анотація

We study the spectral structure of Schrödinger operators H = D+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(D), while the wave operators W± (H, D) exist inside this last set. We continue this program by presenting sparseness conditions under which W± (H, D) also exist.

Mathematics Subject Classification: 81Q10, 47B80.