Global Bounds for the Lyapunov Exponent and the Integrated Density of States of Random Schr\"odinger Operators in One Dimension

In this article we prove an upper bound for the Lyapunov exponent $\gamma(E)$ and a two-sided bound for the integrated density of states $N(E)$ at an arbitrary energy $E>0$ of random Schr\"odinger operators in one dimension. These Schr\"odinger operators are given by potentials of identical shape centered at every lattice site but with non-overlapping supports and with randomly varying coupling constants. Both types of bounds only involve scattering data for the single-site potential. They show in particular that both $\gamma(E)$ and $N(E)-\sqrt{E}/\pi$ decay at infinity at least like $1/\sqrt{E}$. As an example we consider the random Kronig-Penney model.Comment: 9 page

The Density of States and the Spectral Shift Density of Random Schroedinger Operators

In this article we continue our analysis of Schroedinger operators with a random potential using scattering theory. In particular the theory of Krein's spectral shift function leads to an alternative construction of the density of states in arbitrary dimensions. For arbitrary dimension we show existence of the spectral shift density, which is defined as the bulk limit of the spectral shift function per unit interaction volume. This density equals the difference of the density of states for the free and the interaction theory. This extends the results previously obtained by the authors in one dimension. Also we consider the case where the interaction is concentrated near a hyperplane.Comment: 1 figur

The First INTEGRAL AGN Catalog

We present the first INTEGRAL AGN catalog, based on observations performed from launch of the mission in October 2002 until January 2004. The catalog includes 42 AGN, of which 10 are Seyfert 1, 17 are Seyfert 2, and 9 are intermediate Seyfert 1.5. The fraction of blazars is rather small with 5 detected objects, and only one galaxy cluster and no star-burst galaxies have been detected so far. A complete subset consists of 32 AGN with a significance limit of 7 sigma in the INTEGRAL/ISGRI 20-40 keV data. Although the sample is not flux limited, the distribution of sources shows a ratio of obscured to unobscured AGN of 1.5 - 2.0, consistent with luminosity dependent unified models for AGN. Only four Compton-thick AGN are found in the sample. Based on the INTEGRAL data presented here, the Seyfert 2 spectra are slightly harder (Gamma = 1.95 +- 0.01) than Seyfert 1.5 (Gamma = 2.10 +- 0.02) and Seyfert 1 (Gamma = 2.11 +- 0.05).Comment: 17 pages, 12 figures, accepted for publication in Ap

SLˉ(4,R)\bar{SL}(4,R) Embedding for a 3D World Spinor Equation

A generic-curved spacetime Dirac-like equation in 3D is constructed. It has, owing to the $\bar{SL}(n,R)$ group deunitarizing automorphism, a physically correct unitarity and flat spacetime particle properties. The construction is achieved by embedding $\bar{SL}(3,R)$ vector operator $X_{\mu}$, that plays a role of Dirac's $\gamma_{\mu}$ matrices, into $\bar{SL}(4,R)$. Decomposition of the unitary irreducible spinorial $\bar{SL}(4,R)$ representations gives rise to an explicit form of the infinite $X_{\mu}$ matrices

Simplicity of eigenvalues in Anderson-type models

We show almost sure simplicity of eigenvalues for several models of Anderson-type random Schr\"odinger operators, extending methods introduced by Simon for the discrete Anderson model. These methods work throughout the spectrum and are not restricted to the localization regime. We establish general criteria for the simplicity of eigenvalues which can be interpreted as separately excluding the absence of local and global symmetries, respectively. The criteria are applied to Anderson models with matrix-valued potential as well as with single-site potentials supported on a finite box.Comment: 20 page

Globalising assessment: an ethnography of literacy assessment, camels and fast food in the Mongolian Gobi

What happens when standardised literacy assessments travel globally? The paper presents an ethnographic account of adult literacy assessment events in rural Mongolia. It examines the dynamics of literacy assessment in terms of the movement and re-contextualisation of test items as they travel globally and are received locally by Mongolian respondents. The analysis of literacy assessment events is informed by Goodwin’s ‘participation framework’ on language as embodied and situated interactive phenomena and by Actor Network Theory. Actor Network Theory (ANT) is applied to examine literacy assessment events as processes of translation shaped by an ‘assemblage’ of human and non-human actors (including the assessment texts)

Differentiable potentials and metallic states in disordered one-dimensional systems

We provide evidence that as a general rule Anderson localization effects become weaker as the degree of differentiability of the disordered potential increases. In one dimension a band of metallic states exists provided that the disordered potential is sufficiently correlated and has some minimum degree of differentiability. Several examples are studied in detail. In agreement with the one parameter scaling theory the motion in the metallic region is ballistic if the spectral density is smooth. Finally, we study the most promising settings to observe these results in the context of cold atoms.Comment: 5 pages, 3 figures, journal versio

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