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 H0=Δ+V(x,ω)H_0=-\Delta+V(x,\omega) is considered, where VV is a random potential of Bernoulli type. The operator H0H_0 is perturbed by a non-random, continuous potential v(x)0-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)-v(x) as O(ln2/dx)O(\ln^{-2/d} |x|).

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