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

Evidence for vivianite formation and its contribution to long-term phosphorus retention in a recent lake sediment: a novel analytical approach

Vivianite, Fe3(PO4)2 · 8 H2O, is a ferrous iron phosphate mineral which forms in waterlogged soils and sediments. The phosphorus (P) bound in its crystal lattice is considered to be immobilised because vivianite is stable under anoxic, reducing, sedimentary conditions. Thus, vivianite formation can make a major contribution to P retention during early diagenesis. Much remains unknown about vivianite in sediments, because technical challenges have rendered direct identification and quantification difficult. To identify vivianite and assess its significance for P burial during early diagenesis we studied the consequences of a 1992/1993 in-lake application of FeCl3 and Fe(OH)3 aimed at restoring Lake Groß-Glienicke (Berlin, Germany). In a novel approach, we firstly applied a heavy-liquid separation to the iron-rich surface sediments which allowed direct identification of vivianite by X-ray diffraction in the high-density (ρ > 2.3 g cm−3) sediment fraction. Secondly, we assessed the contribution of vivianite to P retention, combining results from chemical digestion with magnetic susceptibility data derived from magnetic hysteresis measurements. Scanning electron microscopy revealed that the dark blue spherical vivianite nodules were 40–180 μm in diameter, and formed of platy- and needle-shaped crystal aggregates. Although equilibrium calculations indicated supersaturation of vivianite throughout the upper 30 cm of the sediment, the vivianite deposits were homogeneously distributed within, and restricted to, the upper 23 cm only. Thus, supersaturated pore water alone cannot serve as a reliable predictor for the in situ formation of vivianite. In Lake Groß -Glienicke, vivianite formation continues to be triggered by the artificial iron amendment more than 20 yr ago, significantly contributing to P retention in surface sediments

Lifshitz Tails in Constant Magnetic Fields

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

Non-inversion conservation tillage as an underestimated driver of tillage erosion

Tillage erosion is a widely underestimated process initiating soil degradation especially in case of large agricultural fields located in rolling topography. It is often assumed that, conservation, non-inversion tillage causes less tillage erosion than conventional inversion tillage. In this study, tillage erosion was determined on three paired plots comparing non-inversion chisel versus inversion mouldboard tillage. The experiments were performed at three sites in Northeast Germany with gentle, moderate, and steep slope, while tillage depth (0.25 m) and speed (≈ 6 km h−1) were kept constant during all experiments. The results indicate that non-inversion tillage produces significantly more soil movement compared to inversion tillage. The soil translocation distance was by a factor of 1.3–2.1 larger in case of chisel tillage. The largest difference in translocation distance and tillage transport coefficient (ktil) was found on the gentle slope exhibiting the lowest soil cohesion. Our results together with an evaluation of ktil values derived from literature and standardised for 0.25 m tillage depth contradict the general assumption that non-inversion tillage reduces tillage erosion. In tillage erosion dominated areas, non-inversion tillage applied with high tillage speed and depth potentially increases tillage erosion and fails its purpose to serve as soil conservation measure

LpL^p-approximation of the integrated density of states for Schr\"odinger operators with finite local complexity

We study spectral properties of Schr\"odinger operators on \RR^d. The electromagnetic potential is assumed to be determined locally by a colouring of the lattice points in \ZZ^d, with the property that frequencies of finite patterns are well defined. We prove that the integrated density of states (spectral distribution function) is approximated by its finite volume analogues, i.e.the normalised eigenvalue counting functions. The convergence holds in the space $L^p(I)$ where $I$ is any finite energy interval and $1\leq p< \infty$ is arbitrary.Comment: 15 pages; v2 has minor fixe

Hijacking the mustard-oil bomb: How a glucosinolate-sequestering flea beetle copes with plant myrosinases

Myrosinase enzymes play a key role in the chemical defense of plants of the order Brassicales. Upon herbivory, myrosinases hydrolyze the β-S-linked glucose moiety of glucosinolates, the characteristic secondary metabolites of brassicaceous plants, which leads to the formation of different toxic hydrolysis products. The specialist flea beetle, Phyllotreta armoraciae, is capable of accumulating high levels of glucosinolates in the body and can thus at least partially avoid plant myrosinase activity. In feeding experiments with the myrosinase-deficient Arabidopsis thaliana tgg1 × tgg2 (tgg) mutant and the corresponding Arabidopsis Col-0 wild type, we investigated the influence of plant myrosinase activity on the metabolic fate of ingested glucosinolates in adult P. armoraciae beetles. Arabidopsis myrosinases hydrolyzed a fraction of ingested glucosinolates and thereby reduced the glucosinolate sequestration rate by up to 50% in adult beetles. These results show that P. armoraciae cannot fully prevent glucosinolate hydrolysis; however, the exposure of adult beetles to glucosinolate hydrolysis products had no impact on the beetle’s energy budget under our experimental conditions. To understand how P. armoraciae can partially prevent glucosinolate hydrolysis, we analyzed the short-term fate of ingested glucosinolates and found them to be rapidly absorbed from the gut. In addition, we determined the fate of ingested Arabidopsis myrosinase enzymes in P. armoraciae. Although we detected Arabidopsis myrosinase protein in the feces, we found only traces of myrosinase activity, suggesting that P. armoraciae can inactivate plant myrosinases in the gut. Based on our findings, we propose that the ability to tolerate plant myrosinase activity and a fast glucosinolate uptake mechanism represent key adaptations of P. armoraciae to their brassicaceous host plants

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

Case study on the efficacy of a lanthanum-enriched clay (Phoslock®) in controlling eutrophication in Lake Het Groene Eiland (The Netherlands)

Lake Het Groene Eiland was created in the beginning of 2008 by construction of dikes for isolating it from the surrounding 220-ha water body. This so-called claustrum of 5 ha was treated using lanthanum-modified clay (Phoslock®) to control eutrophication and mitigate cyanobacterial nuisance. Cyanobacteria chlorophyll-a were significantly lower in the claustrum than those in the reference water body, where a massive bloom developed in summer, 2008. However, PO4-P and TP did not statistically differ in these two waters. TN and NO3-N were significantly lower in the claustrum, where dense submerged macrophytes beds developed. Lanthanum concentrations were elevated after the applications of the modified clay in the claustrum, but filterable lanthanum dropped rapidly below the Dutch standard of 10.1 μg l−1. During winter, dozens of Canada geese resided at the claustrum. Geese droppings contained an average of 2 mg PO4-P g−1 dry weight and 12 mg NH3-N g−1 dry weight and might present a growing source of nutrients to the water. Constructing the claustrum enabled unrestricted bathing in subsequent three summers, as no swimming bans had to be issued due to cyanobacteria blooms. However, the role of the modified clay in this positive outcome remains unclear, and longevity of the measures questionable.

Detection of triplex PCR for the modified qualitative soybean and maize genetically

A molecular screening method based on multiplex PCR that involves amplification of specific soybean or maize sequences from plant DNA (lectin or zein) and the amplification of 35S promoter and NOS terminator,for the detection of genetically modified soybean and maize was developed. The new method is proposed,for the simulicmeous cletcctimt of tree genetic elements in the.same run as reliable method for rapid detection of genetically, modified plants with sensitivity of 0.1%