Non-random perturbations of the Anderson Hamiltonian

Details Non-random perturbations of the Anderson Hamiltonian Non-random perturbations of the Anderson Hamiltonian

2010-02-22

arxiv.org/abs/1002.4220v2

Mathematics

Spectral Theory

Minor changes in the introductory section 2

Scientific paper

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 $-w(x) \leq 0$, 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 $-w(x)$ as $O(\ln^{-2/d} |x|)$.

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