Scaling of the Thue-Morse diffraction measure

We revisit the well-known and much studied Riesz product representation of the Thue-Morse diffraction measure, which is also the maximal spectral measure for the corresponding dynamical spectrum in the complement of the pure point part. The known scaling relations are summarised, and some new findings are explained

A critical Ising model on the Labyrinth

A zero-field Ising model with ferromagnetic coupling constants on the so-called Labyrinth tiling is investigated. Alternatively, this can be regarded as an Ising model on a square lattice with a quasi-periodic distribution of up to eight different coupling constants. The duality transformation on this tiling is considered and the self-dual couplings are determined. Furthermore, we analyze the subclass of exactly solvable models in detail parametrizing the coupling constants in terms of four rapidity parameters. For those, the self-dual couplings correspond to the critical points which, as expected, belong to the Onsager universality class.Comment: 25 pages, 6 figure

Lx-SFR relation in star forming galaxies

We compare the results of Grimm et al. (2003) and Ranalli et al. (2003) on the Lx-SFR relation in normal galaxies. Based on the Lx-stellar mass dependence for LMXBs, we show, that low SFR (SFR<1 Msun/year) galaxies in the Ranalli et al. sample are contaminated by the X-ray emission from low mass X-ray binaries, unrelated to the current star formation activity. The most important conclusion from our comparison is, however, that after the data are corrected for the ``LMXB contamination'', the two datasets become consistent with each other, despite of their different content, variability effects, difference in the adopted source distances, X-ray flux and star formation rate determination and in the cosmological parameters used in interpreting the HDF-N data. They also agree well, both in the low and high SFR regimes, with the predicted Lx-SFR dependence derived from the parameters of the ``universal'' HMXB luminosity function. This encouraging result emphasizes the potential of the X-ray luminosity as an independent star formation rate indicator for normal galaxies.Comment: revised, accepted for publication in MNRAS Letter

Recent progress in mathematical diffraction

A brief summary of recent developments in mathematical diffraction theory is given. Particular emphasis is placed on systems with aperiodic order and continuous spectral components. We restrict ourselves to some key results and refer to the literature for further details

Trigonometric R Matrices related to `Dilute' Birman--Wenzl--Murakami Algebra

Explicit expressions for three series of $R$ matrices which are related to a ``dilute'' generalisation of the Birman--Wenzl--Murakami are presented. Of those, one series is equivalent to the quantum $R$ matrices of the $D^{(2)}_{n+1}$ generalised Toda systems whereas the remaining two series appear to be new.Comment: 5 page

Anomaly Cancelation in Field Theory and F-theory on a Circle

We study the manifestation of local gauge anomalies of four- and six-dimensional field theories in the lower-dimensional Kaluza-Klein theory obtained after circle compactification. We identify a convenient set of transformations acting on the whole tower of massless and massive states and investigate their action on the low-energy effective theories in the Coulomb branch. The maps employ higher-dimensional large gauge transformations and precisely yield the anomaly cancelation conditions when acting on the one-loop induced Chern-Simons terms in the three- and five-dimensional effective theory. The arising symmetries are argued to play a key role in the study of the M-theory to F-theory limit on Calabi-Yau manifolds. For example, using the fact that all fully resolved F-theory geometries inducing multiple Abelian gauge groups or non-Abelian groups admit a certain set of symmetries, we are able to generally show the cancelation of pure Abelian or pure non-Abelian anomalies in these models.Comment: 48 pages, 2 figures; v2: typos corrected, comments on circle fluxes adde

Suppression of Phase Decoherence in a Single Atomic Qubit

We study the suppression of noise-induced phase decoherence in a single atomic qubit by employing pulse sequences. The atomic qubit is composed of a single neutral atom in a far-detuned optical dipole trap and the phase decoherence may originate from the laser intensity and beam pointing fluctuations as well as magnetic field fluctuations. We show that suitable pulse sequences may prolongate the qubit coherence time substantially as comparing to the conventional spin echo pulse.Comment: 4 pages, 3 figure

Statistical properties of the combined emission of a population of discrete sources: astrophysical implications

We study the statistical properties of the combined emission of a population of discrete sources (e.g. X-ray emission of a galaxy due to its X-ray binaries population). Namely, we consider the dependence of their total luminosity L_tot=SUM(L_k) and of fractional rms_tot of their variability on the number of sources N or, equivalently, on the normalization of the luminosity function. We show that due to small number statistics a regime exists, in which L_tot grows non-linearly with N, in an apparent contradiction with the seemingly obvious prediction =integral(dN/dL*L*dL) ~ N. In this non-linear regime, the rms_tot decreases with N significantly more slowly than expected from the rms ~ 1/sqrt(N) averaging law. For example, for a power law luminosity function with a slope of a=3/2, in the non-linear regime, L_tot ~ N^2 and the rms_tot does not depend at all on the number of sources N. Only in the limit of N>>1 do these quantities behave as intuitively expected, L_tot ~ N and rms_tot ~ 1/sqrt(N). We give exact solutions and derive convenient analytical approximations for L_tot and rms_tot. Using the total X-ray luminosity of a galaxy due to its X-ray binary population as an example, we show that the Lx-SFR and Lx-M* relations predicted from the respective ``universal'' luminosity functions of high and low mass X-ray binaries are in a good agreement with observations. Although caused by small number statistics the non-linear regime in these examples extends as far as SFR<4-5 Msun/yr and log(M*/Msun)<10.0-10.5, respectively.Comment: MNRAS, accepted for publicatio

Inequality in human development : an empirical assessment of thirty-two countries

One of the most frequent critiques of the HDI is that is does not take into account inequality within countries in its three dimensions. In this paper, we apply a simply approach to compute the three components and the overall HDI for quintiles of the income distribution. This allows a comparison of the level in human development of the poor with the level of the non-poor within countries, but also across countries. This is an application of the method presented in Grimm et al. (2008) to a sample of 21 low and middle income countries and 11 industrialized countries. In particular the inclusion of the industrialized countries, which were not included in the previous work, implies to deal with a number of additional challenges, which we outline in this paper. Our results show that inequality in human development within countries is high, both in developed and industrialized countries. In fact, the HDI of the lowest quintiles in industrialized countries is often below the HDI of the richest quintile in many middle income countries. We also find, however, a strong overall negative correlation between the level of human development and inequality in human development

Tuning the scattering length with an optically induced Feshbach resonance

We demonstrate optical tuning of the scattering length in a Bose-Einstein condensate as predicted by Fedichev {\em et al.} [Phys. Rev. Lett. {\bf 77}, 2913 (1996)]. In our experiment atoms in a $^{87}$Rb condensate are exposed to laser light which is tuned close to the transition frequency to an excited molecular state. By controlling the power and detuning of the laser beam we can change the atomic scattering length over a wide range. In view of laser-driven atomic losses we use Bragg spectroscopy as a fast method to measure the scattering length of the atoms.Comment: submitted to PRL, 5 pages, 5 figure