Rigged Hilbert Space Approach to the Schrodinger Equation

It is shown that the natural framework for the solutions of any Schrodinger equation whose spectrum has a continuous part is the Rigged Hilbert Space rather than just the Hilbert space. The difficulties of using only the Hilbert space to handle unbounded Schrodinger Hamiltonians whose spectrum has a continuous part are disclosed. Those difficulties are overcome by using an appropriate Rigged Hilbert Space (RHS). The RHS is able to associate an eigenket to each energy in the spectrum of the Hamiltonian, regardless of whether the energy belongs to the discrete or to the continuous part of the spectrum. The collection of eigenkets corresponding to both discrete and continuous spectra forms a basis system that can be used to expand any physical wave function. Thus the RHS treats discrete energies (discrete spectrum) and scattering energies (continuous spectrum) on the same footing.Comment: 27 RevTex page

Quantum mechanical potentials related to the prime numbers and Riemann zeros

Prime numbers are the building blocks of our arithmetic, however, their distribution still poses fundamental questions. Bernhard Riemann showed that the distribution of primes could be given explicitly if one knew the distribution of the non-trivial zeros of the Riemann $\zeta(s)$ function. According to the Hilbert-P{\'o}lya conjecture there exists a Hermitean operator of which the eigenvalues coincide with the real part of the non-trivial zeros of $\zeta(s)$. This idea encourages physicists to examine the properties of such possible operators, and they have found interesting connections between the distribution of zeros and the distribution of energy eigenvalues of quantum systems. We apply the Mar{\v{c}}henko approach to construct potentials with energy eigenvalues equal to the prime numbers and to the zeros of the $\zeta(s)$ function. We demonstrate the multifractal nature of these potentials by measuring the R{\'e}nyi dimension of their graphs. Our results offer hope for further analytical progress.Comment: 7 pages, 5 figures, 2 table

Multicenter prospective clinical study to evaluate children short-term neurodevelopmental outcome in congenital heart disease (children NEURO-HEART) : study protocol

Altres ajuts: RETICS funded by the PN 2018-2021 (Spain).Congenital heart disease (CHD) is the most prevalent congenital malformation affecting 1 in 100 newborns. While advances in early diagnosis and postnatal management have increased survival in CHD children, worrying long-term outcomes, particularly neurodevelopmental disability, have emerged as a key prognostic factor in the counseling of these pregnancies. Eligible participants are women presenting at 20 to < 37 weeks of gestation carrying a fetus with CHD. Maternal/neonatal recordings are performed at regular intervals, from the fetal period to 24 months of age, and include: placental and fetal hemodynamics, fetal brain magnetic resonance imaging (MRI), functional echocardiography, cerebral oxymetry, electroencephalography and serum neurological and cardiac biomarkers. Neurodevelopmental assessment is planned at 12 months of age using the ages and stages questionnaire (ASQ) and at 24 months of age with the Bayley-III test. Target recruitment is at least 150 cases classified in three groups according to three main severe CHD groups: transposition of great arteries (TGA), Tetralogy of Fallot (TOF) and Left Ventricular Outflow Tract Obstruction (LVOTO). The results of NEURO-HEART study will provide the most comprehensive knowledge until date of children's neurologic prognosis in CHD and will have the potential for developing future clinical decisive tools and improving preventive strategies in CHD. , on 4th December 2016 (retrospectively registered)

Multicenter prospective clinical study to evaluate children short-term neurodevelopmental outcome in congenital heart disease (children NEURO-HEART): study protocol.

BACKGROUND: Congenital heart disease (CHD) is the most prevalent congenital malformation affecting 1 in 100 newborns. While advances in early diagnosis and postnatal management have increased survival in CHD children, worrying long-term outcomes, particularly neurodevelopmental disability, have emerged as a key prognostic factor in the counseling of these pregnancies. METHODS: Eligible participants are women presenting at 20 to < 37 weeks of gestation carrying a fetus with CHD. Maternal/neonatal recordings are performed at regular intervals, from the fetal period to 24 months of age, and include: placental and fetal hemodynamics, fetal brain magnetic resonance imaging (MRI), functional echocardiography, cerebral oxymetry, electroencephalography and serum neurological and cardiac biomarkers. Neurodevelopmental assessment is planned at 12 months of age using the ages and stages questionnaire (ASQ) and at 24 months of age with the Bayley-III test. Target recruitment is at least 150 cases classified in three groups according to three main severe CHD groups: transposition of great arteries (TGA), Tetralogy of Fallot (TOF) and Left Ventricular Outflow Tract Obstruction (LVOTO). DISCUSSION: The results of NEURO-HEART study will provide the most comprehensive knowledge until date of children's neurologic prognosis in CHD and will have the potential for developing future clinical decisive tools and improving preventive strategies in CHD

Long-term multi-wavelength variability and correlation study of Markarian 421 from 2007 to 2009

We study the multi-band variability and correlations of the TeV blazar Mrk 421 on year time scales, which can bring additional insight on the processes responsible for its broadband emission. We observed Mrk 421 in the very high energy (VHE) gamma-ray range with the Cherenkov telescope MAGIC-I from March 2007 to June 2009 for a total of 96 hours of effective time after quality cuts. The VHE flux variability is quantified with several methods, including the Bayesian Block algorithm, which is applied to data from Cherenkov telescopes for the first time. The 2.3 year long MAGIC light curve is complemented with data from the Swift/BAT and RXTE/ASM satellites and the KVA, GASP-WEBT, OVRO, and Mets\"ahovi telescopes from February 2007 to July 2009, allowing for an excellent characterisation of the multi-band variability and correlations over year time scales. Mrk 421 was found in different gamma-ray emission states during the 2.3 year long observation period. Flares and different levels of variability in the gamma-ray light curve could be identified with the Bayesian Block algorithm. The same behaviour of a quiet and active emission was found in the X-ray light curves measured by Swift/BAT and the RXTE/ASM, with a direct correlation in time. The behaviour of the optical light curve of GASP-WEBT and the radio light curves by OVRO and Mets\"ahovi are different as they show no coincident features with the higher energetic light curves and a less variable emission. The fractional variability is overall increasing with energy. The comparable variability in the X-ray and VHE bands and their direct correlation during both high- and low-activity periods spanning many months show that the electron populations radiating the X-ray and gamma-ray photons are either the same, as expected in the Synchrotron-Self-Compton mechanism, or at least strongly correlated, as expected in electromagnetic cascades.Comment: Corresponding authors: Ann-Kristin Overkemping ([email protected]), Marina Manganaro ([email protected]), Diego Tescaro ([email protected]), To be published in Astronomy&Astrophysics (A&A), 12 pages, 9 figure

Avian influenza virus (H11N9) in migratory shorebirds wintering in the Amazon region, Brazil

Aquatic birds are the natural reservoir for avian influenza viruses (AIV). Habitats in Brazil provide stopover and wintering sites for water birds that migrate between North and South America. The current study was conducted to elucidate the possibility of the transport of influenza A viruses by birds that migrate annually between the Northern and Southern Hemispheres. In total, 556 orotracheal/cloacal swab samples were collected for influenza A virus screening using real-time RT-PCR (rRT-PCR). The influenza A virus-positive samples were subjected to viral isolation. Four samples were positive for the influenza A matrix gene by rRT-PCR. From these samples, three viruses were isolated, sequenced and characterized. All positive samples originated from a single bird species, the ruddy turnstone (Arenaria interpres), that was caught in the Amazon region at Caeté Bay, Northeast Pará, at Ilha de Canelas. To our knowledge, this is the first isolation of H11N9 in the ruddy turnstone in South America. (Résumé d'auteur

Detection of very high energy gamma-ray emission from the gravitationally-lensed blazar QSO B0218+357 with the MAGIC telescopes

Context. QSO B0218+357 is a gravitationally lensed blazar located at a redshift of 0.944. The gravitational lensing splits the emitted radiation into two components, spatially indistinguishable by gamma-ray instruments, but separated by a 10-12 day delay. In July 2014, QSO B0218+357 experienced a violent flare observed by the Fermi-LAT and followed by the MAGIC telescopes. Aims. The spectral energy distribution of QSO B0218+357 can give information on the energetics of z ~ 1 very high energy gamma- ray sources. Moreover the gamma-ray emission can also be used as a probe of the extragalactic background light at z ~ 1. Methods. MAGIC performed observations of QSO B0218+357 during the expected arrival time of the delayed component of the emission. The MAGIC and Fermi-LAT observations were accompanied by quasi-simultaneous optical data from the KVA telescope and X-ray observations by Swift-XRT. We construct a multiwavelength spectral energy distribution of QSO B0218+357 and use it to model the source. The GeV and sub-TeV data, obtained by Fermi-LAT and MAGIC, are used to set constraints on the extragalactic background light. Results. Very high energy gamma-ray emission was detected from the direction of QSO B0218+357 by the MAGIC telescopes during the expected time of arrival of the trailing component of the flare, making it the farthest very high energy gamma-ray sources detected to date. The observed emission spans the energy range from 65 to 175 GeV. The combined MAGIC and Fermi-LAT spectral energy distribution of QSO B0218+357 is consistent with current extragalactic background light models. The broad band emission can be modeled in the framework of a two zone external Compton scenario, where the GeV emission comes from an emission region in the jet, located outside the broad line region.Comment: 11 pages, 6 figures, accepted for publication in A&