Weyl-invariant random Hamiltonians and their relation to translational-invariant random potentials on Landau levels

Abstract

The authors construct and discuss classes of random Hamiltonians on the infinite-dimensional Hilbert space of a quantum system with a Euclidean configuration space. By construction, the corresponding probability distributions are invariant under the action of the Weyl group. For particular classes of Weyl-invariant random Hamiltonians they establish a relation to translational-invariant random potentials restricted to the Hilbert space of a single Landau level, that is, an eigenspace of the standard Hamiltonian for a charged particle confined to the plane and subjected to a perpendicular constant magnetic field.