Existence of Atoms and Molecules in the Mean-Field Approximation of No-Photon Quantum Electrodynamics

The Bogoliubov-Dirac-Fock (BDF) model is the mean-field approximation of no-photon Quantum Electrodynamics. The present paper is devoted to the study of the minimization of the BDF energy functional under a charge constraint. An associated minimizer, if it exists, will usually represent the ground state of a system of $N$ electrons interacting with the Dirac sea, in an external electrostatic field generated by one or several fixed nuclei. We prove that such a minimizer exists when a binding (HVZ-type) condition holds. We also derive, study and interpret the equation satisfied by such a minimizer. Finally, we provide two regimes in which the binding condition is fulfilled, obtaining the existence of a minimizer in these cases. The first is the weak coupling regime for which the coupling constant $\alpha$ is small whereas $\alpha Z$ and the particle number $N$ are fixed. The second is the non-relativistic regime in which the speed of light tends to infinity (or equivalently $\alpha$ tends to zero) and $Z$, $N$ are fixed. We also prove that the electronic solution converges in the non-relativistic limit towards a Hartree-Fock ground state.Comment: Final version, to appear in Arch. Rat. Mech. Ana

Ground state properties of graphene in Hartree-Fock theory

We study the Hartree-Fock approximation of graphene in infinite volume, with instantaneous Coulomb interactions. First we construct its translation-invariant ground state and we recover the well-known fact that, due to the exchange term, the effective Fermi velocity is logarithmically divergent at zero momentum. In a second step we prove the existence of a ground state in the presence of local defects and we discuss some properties of the linear response to an external electric field. All our results are non perturbative.Comment: 27 page

The Thermodynamic Limit of Quantum Coulomb Systems: A New Approach

We present two recent works on the thermodynamic limit of quantum Coulomb systems, in which we provided a general method allowing to show the existence of the limit for many different models.Comment: Talk given by M.L. at QMath10, 10th Quantum Mathematics International Conference, Moeciu (Romania) in September 200

A superburst from GX 3+1

I found one long X-ray flare from the X-ray burster GX 3+1 in almost 6 years of observations with the RXTE All Sky Monitor (ASM). The event had a peak flux of about 1.1 Crab (1.5-12 keV), lasted between 4.4 and 16.2 hours and exhibited a fluence of more than about 5x10^{41} erg for a source distance of 5 kpc. During the exponential-like decay, with an exponential decay time of 1.6 hours, spectral softening is seen. The total ASM effective exposure time on GX 3+1 is estimated to be around a year. The flare bears all the characteristics of the recently discovered so-called superbursts in other X-ray burst sources.Comment: 4 pages, 1 figure, accepted for A&A Letter

Femoral Arterial Thrombosis After Cardiac Catheterization In Infancy: Impact of Doppler Ultrasound for Diagnosis

Femoral arterial thrombosis (FAT) is a nonnegligible complication after cardiac catheterization (CC) in infancy. The aim of this study was to evaluate the impact of Doppler ultrasound (US) for diagnostic work-up after catheterization. We compared standard follow-up (FU) without Doppler US by relying on clinical signs of FAT with advanced FU using Doppler US of the femoral vessels. Between January and December 2009, we evaluated the rate of FAT in infants <12months of age using a multicenter, prospective observational survey. We analysed 171 patients [mean age 4.1±3.3 (SD) months; mean body weight 5.3±1.8kg] from 6 participating centres. The mean duration of catheter studies was 57.7±38.0min. The overall rate of FAT based on clinical diagnosis was 4.7% and was comparable in both groups [3.4% undergoing standard FU vs. 7.4% undergoing advanced FU (p=0.15)]. However, the overall rate of thrombosis as screened by Doppler US was greater at 7.1%, especially in patients after advanced FU [18.5% advanced vs. standard FU 1.7% (p<0.01)]. In conclusion, FAT remains a relevant and underestimated complication after catheterization in young infants when relying only on clinical signs of FAT. Therefore, to start effective treatment as soon as possible, we recommend Doppler US to be performed the day after C

Coupled HBO and NBO variations in the Z source GX 5-1: inner accretion disk as the location of QPOs

The simultaneous and coupled evolution of horizontal branch oscillation (HBO) and normal branch oscillation (NBO) in Z-type sources suggests that the production of HBO is connected to NBO and is caused by changes in the physical/radiative properties of the inner accretion disk, although there is a lack of substantial spectral evidence to support this. In this {\it Letter}, we present the results of an analysis of a RXTE observation of a Z source GX~5-1, where the 6 Hz NBO is simultaneously detected along with a HBO at 51 Hz. The variations in the intensity and the associated power density spectrum indicate that the HBO and NBO are strongly coupled, originating from the same location in the inner accretion disk. The absence of HBO and NBO in the lower energy bands, an increase in the rms amplitude with energy and a smooth transition among them suggest that they are produced in the hot inner regions of the accretion disk. Based on a spectral analysis, we found a signature of changing or physically modified inner disk front during the coupled HBO and NBO evolution. We explore the various models to explain the observed phenomenon and propose that the NBO is affiliated to the oscillations in the thick/puffed-up inner region of the accretion disk.Comment: 9 pages, 4 figures, Accepted for publication in ApJ Letter

Length–weight relations for 19 freshwater fish species (Actinopterygii) from the lowland Elbe River, Germany

Monthly and mean length–weight relations (LWRs) were calculated for 19 freshwater fish species from the middle section of the lowland Elbe River (Germany): Abramis brama (Linnaeus, 1758); Alburnus alburnus (Linnaeus, 1758); Anguilla anguilla (Linnaeus, 1758); Ballerus ballerus (Linnaeus, 1758); Blicca bjoerkna (Linnaeus, 1758); Cobitis taenia Linnaeus, 1758; Esox lucius Linnaeus, 1758; Gobio gobio (Linnaeus, 1758); Gymnocephalus cernua (Linnaeus, 1758); Leuciscus aspius (Linnaeus, 1758); Leuciscus idus (Linnaeus, 1758); Leuciscus leuciscus (Linnaeus, 1758); Lota lota (Linnaeus, 1758); Perca fluviatilis Linnaeus, 1758; Romanogobio albipinnatus (Lukasch, 1933); Rutilus rutilus (Linnaeus, 1758); Sander lucioperca (Linnaeus, 1758); Scardinius erythrophthalmus (Linnaeus, 1758); and Squalius cephalus (Linnaeus, 1758). The values of the exponent b in the LWR W = aTLb ranged from 2.882 (Lota lota) to 3.517 (Cobitis taenia) and the correlation coefficient (r2) was greater than 0.96 for all species except for Cobitis taenia with 0.93. The relations allow for the accurate estimation of weight from length data with reduced handling times of fish in the field while enabling comparisons with other regions and future studies. The calculated LWRs together with species-specific abundance and catch data will be useful for fisheries modeling and estimating population status and related fish species protection, especially for the endangered species in the Elbe River

Ground state properties of graphene in Hartree-Fock theory

Abstract. We study the Hartree-Fock approximation of graphene in infinite volume, with instantaneous Coulomb interactions. First we construct its translation-invariant ground state and we recover the well-known fact that, due to the exchange term, the effective Fermi velocity is logarithmically divergent at zero momentum. In a second step we prove the existence of a ground state in the presence of local defects and we discuss some properties of the linear response to an external electric field. All our results are non perturbative. c 2012, by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes

An Approximation for the rp-Process

Hot (explosive) hydrogen burning or the Rapid Proton Capture Process (rp-process) occurs in a number of astrophysical environments. Novae and X-ray bursts are the most prominent ones, but accretion disks around black holes and other sites are candidates as well. The expensive and often multidimensional hydro calculations for such events require an accurate prediction of the thermonuclear energy generation, while avoiding full nucleosynthesis network calculations. In the present investigation we present an approximation scheme applicable in a temperature range which covers the whole range of all presently known astrophysical sites. It is based on the concept of slowly varying hydrogen and helium abundances and assumes a kind of local steady flow by requiring that all reactions entering and leaving a nucleus add up to a zero flux. This scheme can adapt itself automatically and covers situations at low temperatures, characterized by a steady flow of reactions, as well as high temperature regimes where a $(p,\gamma)-(\gamma,p)$-equilibrium is established. In addition to a gain of a factor of 15 in computational speed over a full network calculation, and an energy generation accurate to more than 15 %, this scheme also allows to predict correctly individual isotopic abundances. Thus, it delivers all features of a full network at a highly reduced cost and can easily be implemented in hydro calculations.Comment: 18 pages, LaTeX using astrobib and aas2pp4, includes PostScript figures; Astrophysical Journal, in press. PostScript source also available at http://quasar.physik.unibas.ch/preps.htm

Hydrodynamic Models of Type I X-Ray Bursts: Metallicity Effects

Type I X-ray bursts are thermonuclear stellar explosions driven by charged-particle reactions. In the regime for combined H/He-ignition, the main nuclear flow is dominated by the rp-process (rapid proton-captures and beta+ decays), the 3 alpha-reaction, and the alpha-p-process (a suite of (alpha,p) and (p,gamma) reactions). The main flow is expected to proceed away from the valley of stability, eventually reaching the proton drip-line beyond A = 38. Detailed analysis of the relevant reactions along the main path has only been scarcely addressed, mainly in the context of parameterized one-zone models. In this paper, we present a detailed study of the nucleosynthesis and nuclear processes powering type I X-ray bursts. The reported 11 bursts have been computed by means of a spherically symmetric (1D), Lagrangian, hydrodynamic code, linked to a nuclear reaction network that contains 325 isotopes (from 1H to 107Te), and 1392 nuclear processes. These evolutionary sequences, followed from the onset of accretion up to the explosion and expansion stages, have been performed for 2 different metallicities to explore the dependence between the extension of the main nuclear flow and the initial metal content. We carefully analyze the dominant reactions and the products of nucleosynthesis, together with the the physical parameters that determine the light curve (including recurrence times, ratios between persistent and burst luminosities, or the extent of the envelope expansion). Results are in qualitative agreement with the observed properties of some well-studied bursting sources. Leakage from the predicted SbSnTe-cycle cannot be discarded in some of our models. Production of 12C (and implications for the mechanism that powers superbursts), light p-nuclei, and the amount of H left over after the bursting episodes will also be discussed.Comment: 78 pages (pdf), including 34 figures. Accepted for publication in The Astrophysical Journal Suppl. Serie