Lifshitz Tails in Constant Magnetic Fields

Abstract

We consider the 2D Landau Hamiltonian $H$ perturbed by a random alloy-type potential, and investigate the Lifshitz tails, i.e. the asymptotic behavior of the corresponding integrated density of states (IDS) near the edges in the spectrum of $H$. If a given edge coincides with a Landau level, we obtain different asymptotic formulae for power-like, exponential sub-Gaussian, and super-Gaussian decay of the one-site potential. If the edge is away from the Landau levels, we impose a rational-flux assumption on the magnetic field, consider compactly supported one-site potentials, and formulate a theorem which is analogous to a result obtained in the case of a vanishing magnetic field.

References in corpus (1)

• Integrated density of states and Wegner estimates for random Schrödinger Operators

Cited by in corpus (6)

• The Integrated Density of States for Random Schroedinger Operators
• Lifshitz tails for alloy type models in a constant magnetic field
• Recent developments in quantum mechanics with magnetic fields
• Applications of the landscape function for Schrödinger operators with singular potentials and irregular magnetic fields
• Regularity of the density of states for random Dirac operators
• Surface Lifshits tails for random quantum Hamiltonians