Non-random perturbations of the Anderson Hamiltonian (Q2275590)

Summary: The Anderson Hamiltonian \(H_0=-\Delta+V(x,\omega)\) is considered, where \(V\) is a random potential of Bernoulli type. The operator \(H_0\) is perturbed by a non-random, continuous potential \(-v(x) \leq 0\), decaying at infinity. It will be shown that the borderline between finitely, and infinitely many negative eigenvalues of the perturbed operator, is achieved with a decay of the potential \(-v(x)\) as \(O(\ln^{-2/d} |x|)\).