ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
We study a nonrelativistic charged particle on the Euclidean plane R2 subject to a perpendicular constant magnetic field and an R2-homogeneous random potential in the approximation that the corresponding random Landau Hamiltonian on the Hilbert space L2(R2) is restricted to the eigenspace of a single but arbitrary Landau level. For a wide class of R2-homogeneous Gaussian random potentials we rigorously prove that the associated restricted integrated density of states is absolutely continuous with respect to the Lebesgue measure. We construct explicit upper bounds on the resulting derivative, the restricted density of states. As a consequence, any given energy is seen to be almost surely not an eigenvalue of the restricted random Landau Hamiltonian. © 2001 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.1401138
