Wegner estimate for discrete alloy-type models

We study discrete alloy-type random Schr\"odinger operators on $\ell^2(\mathbb{Z}^d)$. Wegner estimates are bounds on the average number of eigenvalues in an energy interval of finite box restrictions of these types of operators. If the single site potential is compactly supported and the distribution of the coupling constant is of bounded variation a Wegner estimate holds. The bound is polynomial in the volume of the box and thus applicable as an ingredient for a localisation proof via multiscale analysis.Comment: Accepted for publication in AHP. For an earlier version see http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=09-10

Exploratory study of silicide, aluminide, and boride coatings for nitridation-oxidation protection of chromium alloys

Protective coatings for chromium alloys for use in advanced air breathing application

Understanding the Random Displacement Model: From Ground-State Properties to Localization

We give a detailed survey of results obtained in the most recent half decade which led to a deeper understanding of the random displacement model, a model of a random Schr\"odinger operator which describes the quantum mechanics of an electron in a structurally disordered medium. These results started by identifying configurations which characterize minimal energy, then led to Lifshitz tail bounds on the integrated density of states as well as a Wegner estimate near the spectral minimum, which ultimately resulted in a proof of spectral and dynamical localization at low energy for the multi-dimensional random displacement model.Comment: 31 pages, 7 figures, final version, to appear in Proceedings of "Spectral Days 2010", Santiago, Chile, September 20-24, 201

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

The weak localization for the alloy-type Anderson model on a cubic lattice

We consider alloy type random Schr\"odinger operators on a cubic lattice whose randomness is generated by the sign-indefinite single-site potential. We derive Anderson localization for this class of models in the Lifshitz tails regime, i.e. when the coupling parameter $\lambda$ is small, for the energies $E \le -C \lambda^2$.Comment: 45 pages, 2 figures. To appear in J. Stat. Phy

Localization on quantum graphs with random vertex couplings

We consider Schr\"odinger operators on a class of periodic quantum graphs with randomly distributed Kirchhoff coupling constants at all vertices. Using the technique of self-adjoint extensions we obtain conditions for localization on quantum graphs in terms of finite volume criteria for some energy-dependent discrete Hamiltonians. These conditions hold in the strong disorder limit and at the spectral edges

Localization for the random displacement model at weak disorder

This paper is devoted to the study of the random displacement model on $\R^d$. We prove that, in the weak displacement regime, Anderson and dynamical localization holds near the bottom of the spectrum under a generic assumption on the single site potential and a fairly general assumption on the support of the possible displacements. This result follows from the proof of the existence of Lifshitz tail and of a Wegner estimate for the model under scrutiny

Low lying spectrum of weak-disorder quantum waveguides

We study the low-lying spectrum of the Dirichlet Laplace operator on a randomly wiggled strip. More precisely, our results are formulated in terms of the eigenvalues of finite segment approximations of the infinite waveguide. Under appropriate weak-disorder assumptions we obtain deterministic and probabilistic bounds on the position of the lowest eigenvalue. A Combes-Thomas argument allows us to obtain so-called 'initial length scale decay estimates' at they are used in the proof of spectral localization using the multiscale analysis.Comment: Accepted for publication in Journal of Statistical Physics http://www.springerlink.com/content/0022-471

Control of the apple sawfly Hoplocampa testudinea Klug in organic fruit growing and possible side effects of control strategies on Aphelinus mali Haldeman and other beneficial insects

The effect of Quassia extract on eggs and larvae of the apple sawfly Hoplocampa testudinea was studied. The efficacy of this extract is mainly due to an oral toxicity to the neonate sawfly larvae. The main active ingredients, Quassin and Neoquassin, were tested separately. Wheras Quassin has a considerable efficacy also on older larvae, Neoquassin is less efficient in this case. While Quassin and Neoquassin are found in different Quassia sources in varying relations to each other and have different efficacy, they have to be considered separately in the definition of extract quality by the content of active ingredients. These findings mean, that the “egg maturity” is not important for application date. Nevertheless, the application must take place before the larvae hatch. It was shown that low rates of Quassin (4-6 g/ha) can show very good results in the field, in other cases the rates necessary for good efficacy are much higher. This corresponds to farmers experience. Several factors as application technique and the condition of the blossom must be taken in consideration and will be object of further studies. The side effects of Quassin, Neoquassin and Quassia extract on Aphelinus mali and other beneficial arthropods were tested. Quassia is harmless to all organisms tested