The absolute continuity of the integrated density of states for magnetic Schr\"odinger operators with certain 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 Schr{\"o}dinger 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 Schr\"odinger 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 Schr\"odinger operators with Neumann boundary conditions.Comment: This paper will appear in "Communications in Mathematical Physics". It is a revised version of the second part of the first version of math-ph/0010013, which in its second version only contains the (revised) first par

Existence and uniqueness of the integrated density of states for Schr\"odinger 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 Schr\"odinger 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 by S. Doi, A. Iwatsuka and T. Mine [Math. Z. {\bf 237} (2001) 335-371] and S. Nakamura [J. Funct. Anal. {\bf 173} (2001) 136-152].Comment: This paper is a revised version of the first part of the first version of math-ph/0010013. For a revised version of the second part, see math-ph/0105046. To appear in Reviews in Mathematical Physic

Herstellung von LATP für den Einsatz als Festkörperelektrolyt und dessen Eigenschaften

In dieser Arbeit wird das oxidische Material Li₁₊ₓAlₓTi₂₋ₓ(PO₄)₃ (LATP) im Detail auf seine Eignung als Festkörperelektrolyt untersucht. Ausgehend von der Rohmaterialherstellung von LATP mittels Sol-Gel-Methoden über die Pulveraufbereitung bis zur Sinterung vollkeramischer Proben wird der vollständige Herstellungsprozess von LATP abgebildet und analysiert

Die IL-4-abhängige Inhibition der Expression des Mustererkennungsrezeptors Mincle

Hintergrund und Ziele Die C-Typ-Lektin-Rezeptoren des Dectin-2-Clusters Mincle, MCL und Dectin-2 erkennen immunologisch Bestandteile der Zellwand von Mycobacterium tuberculosis, beispielsweise den mykobakteriellen Cordfaktor durch MCL und Mincle. Nach Erkennung des Liganden Cordfactor werden antibakterielle Effektorfunktionen des angeborenen Immunsystems aktiviert und die Expression der Rezeptoren erhöht. Es wurde beobachtet, dass das Zytokin Interleukin-4, welches mit einer alternativen Makrophagenaktivierung assoziiert ist, die Expression dieser Rezeptoren inhibiert. In der vorliegenden Arbeit soll dieser Effekt charakterisiert werden. Methoden Es erfolgte die Analyse humaner und muriner antigenpräsentierender Zellen (Monozyten, Makrophagen, dendritische Zellen) in Zellkultur. Untersuchungen erfolgten nach Stimulation mit Liganden für C-Typ-Lektin-Rezeptoren (Trehalosedibehenat, Trehalosedimykolat), Toll-Like-Rezeptor 4 (Lipopolysaccharid) und weiterer Zytokine (M-CSF, GM-CSF) in An- oder Abwesenheit von Interleukin-4. Der Einfluss auf die Expression verschiedener C-Typ-Lektine wurde mittels RT-PCR und Durchflusszytometrie untersucht. Die Analyse der funktionellen Zytokinantwort erfolgte mittels ELISA. Ergebnisse und Beobachtungen Interleukin-4 induzierte eine konzentrationsabhängige, anhaltende Inhibition der Expression von Mincle und anderen C-Typ-Lektinen des Dectin-2-Clusters sowohl auf humanen als auch murinen Zellen, wobei der Effekt sowohl auf Makrophagen als auch auf dendritischen Zellen nachzuweisen war. Unter Interleukin-4 zeigte sich eine Inhibition der induzierten mRNA-Expression von Mincle nach Stimulation mit dessen Liganden, nicht jedoch nach Stimulation mit dem Toll-Like-Rezeptor-Agonisten Lipopolysaccharid. Die Inhibition der mRNA-Expression übersetzte sich in eine reduzierte Proteinexpression und eine reduzierte funktionelle Antwort auf Mincle-abhängige Stimuli im Sinne einer reduzierten Produktion proinflammatorischer Zytokine. Der Effekt war abhängig von dem im Interleukin-4 Signalweg wichtigen Transkriptionsfaktor STAT6.   Schlussfolgerungen Interleukin-4 inhibiert die Expression der für die Erkennung von Mycobacterium tuberculosis wichtigen Mustererkennungsrezeptoren des Dectin-2-Clusters auf antigenpräsentierenden Zellen des angeborenen Immunsystems. Dieser Mechanismus könnte zu einer erhöhten Suszeptibilität und erhöhtem Reaktivierungsrisiko einer latenten Tuberkulose in einem von Th2-Zytokinen wie Interleukin-4 geprägten Milieu beitragen

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

The C-type lectin receptors (CLR) Mincle, Mcl and Dectin-2 bind mycobacterial and fungal cell wall glycolipids and carbohydrates. Recently, we described that expression of these CLR is down-regulated 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-2in human APC. This inhibitory effect of IL-4 was observed across species, as murine macrophages and DC treated with IL-4 also down-regulated these receptors. IL-4 blocked up-regulation 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, down-regulation 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

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

We study a non-relativistic charged particle on the Euclidean plane R^2 subject to a perpendicular constant magnetic field and an R^2-homogeneous random potential in the approximation that the corresponding random Landau Hamiltonian on the Hilbert space L^2(R^2) is restricted to the eigenspace of a single but arbitrary Landau level. For a wide class of 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.Comment: 16 pages, to appear in "Journal of Mathematical Physics

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