Abstract
We study the spectral structure of Schrödinger operators H = ΔA + 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(Δ), while the wave operators Ω±(H, Δ) exist inside this last set. We continue this program by presenting sparseness conditions under which Ω±(H,Δ) also exist.
| Original language | English |
|---|---|
| Pages (from-to) | 151-170 |
| Number of pages | 20 |
| Journal | Journal of Mathematical Physics, Analysis, Geometry |
| Volume | 4 |
| Issue number | 1 |
| Publication status | Published - Dec 1 2008 |
Keywords
- Random schrödinger operators
- Scattering theory
- Spectral analysis
ASJC Scopus subject areas
- Analysis
- Mathematical Physics
- Geometry and Topology