Thomas Hupfer

The Absolute Continuity of the Integrated Density¶of States for Magnetic Schrödinger Operators¶with Certain Unbounded Random Potentials

Abstract:The object of the present study is the integrated density of states of a quantum particle in multi-dimensional Euclidean space which is characterized by a Schrödinger operator with magnetic field and a random potential which may be unbounded from above and below.In case that the magnetic field is constant and the random potential is ergodic and admits a so-called one-parameter decomposition, we prove the absolute continuity of the integrated density of states and provide explicit upper bounds on its derivative, the density of states.This local Lipschitz continuity of the integrated density of states is derived by establishing a Wegner estimate for finite-volume Schrödinger operators which holds for rather general magnetic fields and different boundary conditions.Examples of random potentials to which the results apply are certain alloy-type and Gaussian random potentials.Besides we show a diamagnetic inequality for Schrödinger operators with Neumann boundary conditions.

EXISTENCE AND UNIQUENESS OF THE INTEGRATED DENSITY OF STATES FOR SCHRÖDINGER OPERATORS WITH MAGNETIC FIELDS AND UNBOUNDED RANDOM POTENTIALS

The object of the present study is the integrated density of states of a quantum particle in multi-dimensional Euclidean space which is characterized by a Schrodinger operator with a constant magnetic field and a random potential which may be unbounded from above and from below. For an ergodic random potential satisfying a simple moment condition, we give a detailed proof that the infinite-volume limits of spatial eigenvalue concentrations of finite-volume operators with different boundary conditions exist almost surely. Since all these limits are shown to coincide with the expectation of the trace of the spatially localized spectral family of the infinite-volume operator, the integrated density of states is almost surely non-random and independent of the chosen boundary condition. Our proof of the independence of the boundary condition builds on and generalizes certain results obtained by S. Doi, A. Iwatsuka and T. Mine (Math. Z. 237 (2001) 335) and S. Nakamura (J. Funct. Anal. 173 (2001) 136).

Upper bounds on the density of states of single Landau levels broadened by Gaussian random potentials

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.

Stat6-Dependent Inhibition of Mincle Expression in Mouse and Human Antigen-Presenting Cells by the Th2 Cytokine IL-4

The C-type lectin receptors (CLRs) Mincle, Mcl, and Dectin-2 bind mycobacterial and fungal cell wall glycolipids and carbohydrates. Recently, we described that expression of these CLR is downregulated during differentiation of human monocytes to dendritic cells (DC) in the presence of GM-CSF and IL-4. Here, we demonstrate that the Th2 cytokine IL-4 specifically inhibits expression of Mincle, Mcl, and Dectin-2 in human antigen-presenting cells (APC). This inhibitory effect of IL-4 was observed across species, as murine macrophages and DC treated with IL-4 also downregulated these receptors. IL-4 blocked upregulation of Mincle and Mcl mRNA expression and cell surface protein by murine macrophages in response to the Mincle ligand Trehalose-6,6-dibehenate (TDB), whereas the TLR4 ligand LPS overcame inhibition by IL-4. Functionally, downregulation of Mincle expression by IL-4 was accompanied by reduced cytokine production upon stimulation with TDB. These inhibitory effects of IL-4 were dependent on the transcription factor Stat6. Together, our results show that the key Th2 cytokine IL-4 exerts a negative effect on the expression of Mincle and other Dectin-2 cluster CLR in mouse and human macrophages and DC, which may render these sentinel cells less vigilant for sensing mycobacterial and fungal ligands.

Polycrystalline SiC as Source Material for the Growth of Fluorescent SiC Layers

Polycrystalline doped SiC act as source for fluorescent SiC. We have studied the growth of individual grains with different polytypes in the source material. We show an evolution and orientation of grains of different polytypes in polycrystalline SiC ingots grown by the Physical Vapor Transport method. The grain influence on the growth rate of fluorescent SiC layers grown by a sublimation epitaxial process is discussed in respect of surface kinetics.

Modeling of the Mass Transport during Homo-Epitaxial Growth of Silicon Carbide by Fast Sublimation Epitaxy

Ballistic and diffusive growth regimes in the Fast Sublimation Growth Process of silicon carbide can be determined using suggested theoretical model for the mean free path calculations. The influences of temperature and inert gas pressure on the mass transport for the growth of epitaxial layers were analyzed theoretically and experimentally.