Effective inter-band coupling in MgB2 due to anharmonic phonons

We investigate the origin of the inter-band coupling in MgB2 by focusing on its unusual phononic features, namely, the strong anharmonicity of the phonons and the presence of both linear and quadratic electron-phonon interactions of the Su-Schrieffer-Heeger (SSH) type. The bare electronic Hamiltonian has two bands with intra- and inter-band hopping, which lead to two decoupled hybridized bands. The phonon Hamiltonian including the anharmonic terms is diagonalized approximately by a squeezing transformation, which causes the softening of the phonon frequency. The linear SSH coupling amplitude is reduced, consistently with the estimates from first-principle calculations. Additionally, the quadratic coupling generates an effective phonon-induced interaction between the hybridized bands, which is non-vanishing even in the limit of vanishing inter-bare-band hopping amplitude.Comment: 11 page

A model Hamiltonian for MgB2 which takes into account its unusual phononic features

Taking as a starting point the results of LDA calculations, which show that in MgB2 the phonons have a strong quartic anharmonicity and that the bond-stretching electron-phonon interaction (EPI) has both a linear and a large quadratic component, we propose a model Hamiltonian which succesfully matches a number of experimental evidences. We relate the single critical temperature for both superconducting gaps to a phonon-induced inter-band coupling whose amplitude increases with temperature. We also obtain phonon frequencies and linewidths depending on the band filling, as well as band energies and hybridization amplitudes depending on the phonon number.Comment: 19 pages, no figures, accepted on The European Physical Journal

Generalizations of the Familywise Error Rate

Consider the problem of simultaneously testing null hypotheses H_1,...,H_s. The usual approach to dealing with the multiplicity problem is to restrict attention to procedures that control the familywise error rate (FWER), the probability of even one false rejection. In many applications, particularly if s is large, one might be willing to tolerate more than one false rejection provided the number of such cases is controlled, thereby increasing the ability of the procedure to detect false null hypotheses. This suggests replacing control of the FWER by controlling the probability of k or more false rejections, which we call the k-FWER. We derive both single-step and stepdown procedures that control the k-FWER, without making any assumptions concerning the dependence structure of the p-values of the individual tests. In particular, we derive a stepdown procedure that is quite simple to apply, and prove that it cannot be improved without violation of control of the k-FWER. We also consider the false discovery proportion (FDP) defined by the number of false rejections divided by the total number of rejections (defined to be 0 if there are no rejections). The false discovery rate proposed by Benjamini and Hochberg [J. Roy. Statist. Soc. Ser. B 57 (1995) 289-300] controls E(FDP). Here, we construct methods such that, for any \gamma and \alpha, P{FDP>\gamma}\le\alpha. Two stepdown methods are proposed. The first holds under mild conditions on the dependence structure of p-values, while the second is more conservative but holds without any dependence assumptions.Comment: Published at http://dx.doi.org/10.1214/009053605000000084 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Role of the particle's stepping cycle in an asymmetric exclusion process: A model of mRNA translation

Messenger RNA translation is often studied by means of statistical-mechanical models based on the Asymmetric Simple Exclusion Process (ASEP), which considers hopping particles (the ribosomes) on a lattice (the polynucleotide chain). In this work we extend this class of models and consider the two fundamental steps of the ribosome's biochemical cycle following a coarse-grained perspective. In order to achieve a better understanding of the underlying biological processes and compare the theoretical predictions with experimental results, we provide a description lying between the minimal ASEP-like models and the more detailed models, which are analytically hard to treat. We use a mean-field approach to study the dynamics of particles associated with an internal stepping cycle. In this framework it is possible to characterize analytically different phases of the system (high density, low density or maximal current phase). Crucially, we show that the transitions between these different phases occur at different parameter values than the equivalent transitions in a standard ASEP, indicating the importance of including the two fundamental steps of the ribosome's biochemical cycle into the model.Comment: 9 pages, 9 figure

The effect of stellar migration on Galactic chemical evolution: a heuristic approach

In the last years, stellar migration in galactic discs has been the subject of several investigations. However, its impact on the chemical evolution of the Milky Way still needs to be fully quantified. In this paper, we aim at imposing some constraints on the significance of this phenomenon by considering its influence on the chemical evolution of the Milky Way thin disc. We do not investigate the physical mechanisms underlying the migration of stars. Rather, we introduce a simple, heuristic treatment of stellar migration in a detailed chemical evolution model for the thin disc of the Milky Way, which already includes radial gas flows and reproduces several observational constraints for the solar vicinity and the whole Galactic disc. When stellar migration is implemented according to the results of chemo-dynamical simulations by Minchev et. al. (2013) and finite stellar velocities of 1 km s$^{-1}$ are taken into account, the high-metallicity tail of the metallicity distribution function of long-lived thin-disc stars is well reproduced. By exploring the velocity space, we find that the migrating stars must travel with velocities in the range 0.5 -2 km s$^{-1}$ to properly reproduce the high-metallicity tail of the metallicity distribution. We confirm previous findings by other authors that the observed spread in the age-metallicity relation of solar neighbourhood stars can be explained by the presence of stars which originated at different Galactocentric distances, and we conclude that the chemical properties of stars currently observed in the solar vicinity do suggest that stellar migration is present to some extent.Comment: Accepted for publication by Ap

Two years of monitoring Supergiant Fast X-ray Transients with Swift

We present two years of intense Swift monitoring of three SFXTs, IGR J16479-4514, XTE J1739-302, and IGR J17544-2619 (since October 2007). Out-of-outburst intensity-based X-ray (0.3-10keV) spectroscopy yields absorbed power laws with by hard photon indices (G~1-2). Their outburst broad-band (0.3-150 keV) spectra can be fit well with models typically used to describe the X-ray emission from accreting NSs in HMXBs. We assess how long each source spends in each state using a systematic monitoring with a sensitive instrument. These sources spend 3-5% of the total in bright outbursts. The most probable flux is 1-2E-11 erg cm^{-2} s^{-1} (2-10 keV, unabsorbed), corresponding to luminosities in the order of a few 10^{33} to 10^{34} erg s^{-1} (two orders of magnitude lower than the bright outbursts). The duty-cycle of inactivity is 19, 39, 55%, for IGR J16479-4514, XTE J1739-302, and IGR J17544-2619, respectively. We present a complete list of BAT on-board detections further confirming the continued activity of these sources. This demonstrates that true quiescence is a rare state, and that these transients accrete matter throughout their life at different rates. X-ray variability is observed at all timescales and intensities we can probe. Superimposed on the day-to-day variability is intra-day flaring which involves variations up to one order of magnitude that can occur down to timescales as short as ~1ks, and whichcan be explained by the accretion of single clumps composing the donor wind with masses M_cl~0.3-2x10^{19} g. (Abridged)Comment: Accepted for publication in MNRAS. 17 pages, 11 figures, 8 table

On Optimality of Stepdown and Stepup Multiple Test Procedures

Consider the multiple testing problem of testing k null hypotheses, where the unknown family of distributions is assumed to satisfy a certain monotonicity assumption. Attention is restricted to procedures that control the familywise error rate in the strong sense and which satisfy a monotonicity condition. Under these assumptions, we prove certain maximin optimality results for some well-known stepdown and stepup procedures.Comment: Published at http://dx.doi.org/10.1214/009053605000000066 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org