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… (More)
We consider three-dimensional Schrödinger operators with constant magnetic fields and ergodic electric potentials. We study the strong-magnetic-field asymptotic behaviour of the integrated density of states, distinguishing between the asymptotics far from the Landau levels, and the asymptotics near a given Landau level.
We consider the three-dimensional Schrödinger operator with constant magnetic field, perturbed by an appropriate short-range electric potential, and investigate various asymptotic properties of the corresponding spectral shift function (SSF). First, we analyse the singularities of the SSF at the Landau levels. Further, we study the strong magnetic field… (More)
We consider a 2D Schrödinger operator H 0 with constant magnetic field, on a strip of finite width. The spectrum of H 0 is absolutely continuous, and contains a discrete set of thresholds. We perturb H 0 by an electric potential V which decays in a suitable sense at infinity, and study the spectral properties of the perturbed operator H = H 0 + V. First, we… (More)
We consider the unperturbed operator H 0 := (−i∇ − A) 2 + W , self-adjoint in L 2 (R 2). Here A is a magnetic potential which generates a constant magnetic field b > 0, and the edge potential W = W is a T-periodic non-constant bounded function depending only on the first coordinate x ∈ R of (x, y) ∈ R 2. Then the spectrum σ(H 0) of H 0 has a band structure,… (More)