1,031 research outputs found
Wegner estimate for discrete alloy-type models
We study discrete alloy-type random Schr\"odinger operators on
. 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 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 . 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 is small, for the energies
.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
. 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
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