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

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

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

Inverse Scattering for Gratings and Wave Guides

We consider the problem of unique identification of dielectric coefficients for gratings and sound speeds for wave guides from scattering data. We prove that the "propagating modes" given for all frequencies uniquely determine these coefficients. The gratings may contain conductors as well as dielectrics and the boundaries of the conductors are also determined by the propagating modes.Comment: 12 page

Ink dating using thermal desorption and gas chromatography / mass spectrometry: comparison of results obtained in two laboratories

Recent ink dating methods focused mainly on changes in solvent amounts occurring over time. A promising method was developed at the Landeskriminalamt of Munich using thermal desorption (TD) followed by gas chromatography / mass spectrometry (GC/MS) analysis. Sequential extractions of the phenoxyethanol present in ballpoint pen ink entries were carried out at two different temperatures. This method is applied in forensic practice and is currently implemented in several laboratories participating to the InCID group (International Collaboration on Ink Dating). However, harmonization of the method between the laboratories proved to be a particularly sensitive and time consuming task. The main aim of this work was therefore to implement the TD-GC/MS method at the Bundeskriminalamt (Wiesbaden, Germany) in order to evaluate if results were comparable to those obtained in Munich. At first validation criteria such as limits of reliable measurements, linearity and repeatability were determined. Samples were prepared in three different laboratories using the same inks and analyzed using two TDS-GC/MS instruments (one in Munich and one in Wiesbaden). The inter- and intra-laboratory variability of the ageing parameter was determined and ageing curves were compared. While inks stored in similar conditions yielded comparable ageing curves, it was observed that significantly different storage conditions had an influence on the resulting ageing curves. Finally, interpretation models, such as thresholds and trend tests, were evaluated and discussed in view of the obtained results. Trend tests were considered more suitable than threshold models. As both approaches showed limitations, an alternative model, based on the slopes of the ageing curves, was also proposed

An early evaluation of the 2050 Calculator international outreach programme

This paper presents the findings of an early evaluation of the UK Department of Energy and Climate Change’s 2050 Calculator International Outreach Programme. The programme supported eleven countries to develop their own versions of the 2050 Calculator. Drawing on interviews with stakeholders who were involved directly and indirectly in the development of the 2050 Calculators, this paper evaluates the process of developing these tools in different national contexts and discusses the lessons learnt so far. The findings discussed include the original motivations for involvement and how these evolved through the project, and the process of stakeholder engagement. The latter was expected to be a key benefit of the Calculator, and one which would open up debate about long term energy futures. While the teams developing the Calculators faced challenges, including data availability, political buy-in, and defining scenario trajectories, a flexible approach enabled countries to develop Calculators that were tailored to their national objectives and political environments. Overall, the 2050 Calculators have led to a wide range of benefits and there is ongoing commitment to develop new iterations and applications to use these Calculators to support planning of, and debate on, future energy and emissions trajectories

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

A Bayesian Approach to Inverse Quantum Statistics

A nonparametric Bayesian approach is developed to determine quantum potentials from empirical data for quantum systems at finite temperature. The approach combines the likelihood model of quantum mechanics with a priori information over potentials implemented in form of stochastic processes. Its specific advantages are the possibilities to deal with heterogeneous data and to express a priori information explicitly, i.e., directly in terms of the potential of interest. A numerical solution in maximum a posteriori approximation was feasible for one--dimensional problems. Using correct a priori information turned out to be essential.Comment: 4 pages, 6 figures, revte

The repulsion between localization centers in the Anderson model

In this note we show that, a simple combination of deep results in the theory of random Schr\"odinger operators yields a quantitative estimate of the fact that the localization centers become far apart, as corresponding energies are close together