Non-random perturbations of the Anderson Hamiltonian

  • Stanislav Molchanov

    Moscow State University, Russian Federation
  • Boris Vainberg

    University of North Carolina-Charlotte, United States


The Anderson Hamiltonian is considered, where is a random potential of Bernoulli type. The operator is perturbed by a non-random, continuous potential , 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 as .

Cite this article

Stanislav Molchanov, Boris Vainberg, Non-random perturbations of the Anderson Hamiltonian. J. Spectr. Theory 1 (2011), no. 2, pp. 179–195

DOI 10.4171/JST/8