Schrödinger operators with random sparse potentials. Existence of wave operators
The existence of wave operators is proved for operator pairs of the form \(\{-\Delta,-\Delta+V_\omega\}\) in \(L^2(\mathbb{R}^d)\), \(d\geq 3\). The \(V_\omega\) are bounded random sparse potentials, not necessarily decaying. The proof is based on a criterion given by Hörmander. For deterministic potentials, this criterion was already used to prove the wave operator existence for potentials which are not decaying in some directions.
scientific article; zbMATH DE number 2091494