Classical Behavior of the Integrated Density of States for the Uniform Magnetic Field and a Randomly Perturbed Lattice

N. Ueki

2011, v.17, №3, 347-368

ABSTRACT

For the Schrodinger operators on $L^2(R^2)$ and $L^2(R^3)$ with the uniform magnetic field and the scalar potentials located at all sites of a randomly perturbed lattice, the asymptotic behavior of the integrated density of states at the infimum of the spectrum is investigated. The randomly perturbed lattice is the model considered by Fukushima and this describes an intermediate situation between the ordered lattice and the Poisson random field. In this paper the scalar potentials are assumed to decay slowly and its effect to the leading term of the asymptotics are determined explicitly. As the perturbed lattice tends to the Poisson model, the determined leading term tends to that for the Poisson model.

Keywords: Lifshitz tails,magnetic Schrodinger operator