Study of the Distillability of Werner States Using Entanglement Witnesses and Robust Semidefinite Programs

We use Robust Semidefinite Programs and Entanglement Witnesses to study the distillability of Werner states. We perform exact numerical calculations which show 2-undistillability in a region of the state space which was previously conjectured to be undistillable. We also introduce bases which yield interesting expressions for the {\em distillability witnesses} and for a tensor product of Werner states with arbitrary number of copies.Comment: 16 pages, 2 figure

On the Nodal Count Statistics for Separable Systems in any Dimension

We consider the statistics of the number of nodal domains aka nodal counts for eigenfunctions of separable wave equations in arbitrary dimension. We give an explicit expression for the limiting distribution of normalised nodal counts and analyse some of its universal properties. Our results are illustrated by detailed discussion of simple examples and numerical nodal count distributions.Comment: 21 pages, 4 figure

Swift J053041.9-665426, a new Be/X-ray binary pulsar in the Large Magellanic Cloud

We observed the newly discovered X-ray source Swift J053041.9-665426 in the X-ray and optical regime to confirm its proposed nature as a high mass X-ray binary. We obtained XMM-Newton and Swift X-ray data, along with optical observations with the ESO Faint Object Spectrograph, to investigate the spectral and temporal characteristics of Swift J053041.9-665426. The XMM-Newton data show coherent X-ray pulsations with a period of 28.77521(10) s (1 sigma). The X-ray spectrum can be modelled by an absorbed power law with photon index within the range 0.76 to 0.87. The addition of a black body component increases the quality of the fit but also leads to strong dependences of the photon index, black-body temperature and absorption column density. We identified the only optical counterpart within the error circle of XMM-Newton at an angular distance of ~0.8 arcsec, which is 2MASS J05304215-6654303. We performed optical spectroscopy from which we classify the companion as a B0-1.5Ve star. The X-ray pulsations and long-term variability, as well as the properties of the optical counterpart, confirm that Swift J053041.9-665426 is a new Be/X-ray binary pulsar in the Large Magellanic Cloud.Comment: 10 pages, 8 figures, accepted for publication in A&

Subtropical Real Root Finding

We describe a new incomplete but terminating method for real root finding for large multivariate polynomials. We take an abstract view of the polynomial as the set of exponent vectors associated with sign information on the coefficients. Then we employ linear programming to heuristically find roots. There is a specialized variant for roots with exclusively positive coordinates, which is of considerable interest for applications in chemistry and systems biology. An implementation of our method combining the computer algebra system Reduce with the linear programming solver Gurobi has been successfully applied to input data originating from established mathematical models used in these areas. We have solved several hundred problems with up to more than 800000 monomials in up to 10 variables with degrees up to 12. Our method has failed due to its incompleteness in less than 8 percent of the cases

Discovery of a 168.8 s X-ray pulsar transiting in front of its Be companion star in the Large Magellanic Cloud

We report the discovery of LXP169, a new high-mass X-ray binary (XRB) in the LMC. The optical counterpart has been identified and appears to exhibit an eclipsing light curve. We performed follow-up observations to clarify the eclipsing nature of the system. Energy spectra and time series were extracted from two XMM-Newton observations to search for pulsations, characterise the spectrum, and measure spectral and timing changes. Long-term X-ray variability was studied using archival ROSAT data. The XMM positions were used to identify the optical counterpart. We obtained UV to NIR photometry to characterise the companion, along with its 4000 d long I-band light curve. We observed LXP169 with Swift at two predicted eclipse times. We found a spin period of 168.8 s that did not change between two XMM observations. The X-ray spectrum, well characterised by a power law, was harder when the source was brighter. The X-ray flux of LXP169 is found to be variable by a factor of at least 10. The counterpart is highly variable on short and long timescales, and its photometry is that of an early-type star with a NIR excess. This classifies the source as a BeXRB pulsar. We observed a transit in the UV, thereby confirming that the companion star itself is eclipsed. We give an ephemeris for the transit of MJD 56203.877 + N*24.329. We propose and discuss the scenario where the matter captured from the companion's equatorial disc creates an extended region of high density around the neutron star (NS), which partially eclipses the companion as the NS transits in front of it. This is most likely the first time the compact object in an XRB is observed to eclipse its companion star. LXP169 would be the first eclipsing BeXRB, and a wealth of important information might be gained from additional observations, such as a measure of the possible Be disc/orbital plane misalignment, or the mass of the NS.Comment: Updated version of arXiv 1302.4665v1, accepted for publication in Astronomy and Astrophysics. 11 pages, 8 figures, 3 table

Discovery of SXP265, a Be/X-ray binary pulsar in the Wing of the Small Magellanic Cloud

We identify a new candidate for a Be/X-ray binary in the XMM-Newton slew survey and archival Swift observations that is located in the transition region of the Wing of the Small Magellanic Cloud and the Magellanic Bridge. We investigated and classified this source with follow-up XMM-Newton and optical observations. We model the X-ray spectra and search for periodicities and variability in the X-ray observations and the OGLE I-band light curve. The optical counterpart has been classified spectroscopically, with data obtained at the SAAO 1.9 m telescope, and photometrically, with data obtained using GROND at the MPG 2.2 m telescope. The X-ray spectrum is typical of a high-mass X-ray binary with an accreting neutron star. We detect X-ray pulsations, which reveal a neutron-star spin period of P = (264.516+-0.014) s. The source likely shows a persistent X-ray luminosity of a few 10^35 erg/s and in addition type-I outbursts that indicate an orbital period of ~146 d. A periodicity of 0.867 d, found in the optical light curve, can be explained by non-radial pulsations of the Be star. We identify the optical counterpart and classify it as a B1-2II-IVe star. This confirms SXP 265 as a new Be/X-ray binary pulsar originating in the tidal structure between the Magellanic Clouds.Comment: 11 pages, 12 figures, accepted for publication in MNRA

Searching for molecular outflows in Hyper-Luminous Infrared Galaxies

We present constraints on the molecular outflows in a sample of five Hyper-Luminous Infrared Galaxies using Herschel observations of the OH doublet at 119 {\mu}m. We have detected the OH doublet in three cases: one purely in emission and two purely in absorption. The observed emission profile has a significant blueshifted wing suggesting the possibility of tracing an outflow. Out of the two absorption profiles, one seems to be consistent with the systemic velocity while the other clearly indicates the presence of a molecular outflow whose maximum velocity is about ~1500 km/s. Our analysis shows that this system is in general agreement with previous results on Ultra-luminous Infrared Galaxies and QSOs, whose outflow velocities do not seem to correlate with stellar masses or starburst luminosities (star formation rates). Instead the galaxy outflow likely arises from an embedded AGN.Comment: Accepted for publication in MNRAS. 13 pages, 11 figures, 4 table

On the Invariant Theory of Weingarten Surfaces in Euclidean Space

We prove that any strongly regular Weingarten surface in Euclidean space carries locally geometric principal parameters. The basic theorem states that any strongly regular Weingarten surface is determined up to a motion by its structural functions and the normal curvature function satisfying a geometric differential equation. We apply these results to the special Weingarten surfaces: minimal surfaces, surfaces of constant mean curvature and surfaces of constant Gauss curvature.Comment: 16 page

Extraction of the electron mass from gg factor measurements on light hydrogenlike ions

The determination of the electron mass from Penning-trap measurements with $^{12}$C$^{5+}$ ions and from theoretical results for the bound-electron $g$ factor is described in detail. Some recently calculated contributions slightly shift the extracted mass value. Prospects of a further improvement of the electron mass are discussed both from the experimental and from the theoretical point of view. Measurements with $^4$He$^+$ ions will enable a consistency check of the electron mass value, and in future an improvement of the $^4$He nuclear mass and a determination of the fine-structure constant

AGN behind the SMC selected from radio and X-ray surveys

The XMM-Newton survey of the Small Magellanic Cloud (SMC) revealed 3053 X-ray sources with the majority expected to be active galactic nuclei (AGN) behind the SMC. However, the high stellar density in this field often does not allow assigning unique optical counterparts and hinders source classification. On the other hand, the association of X-ray point sources with radio emission can be used to select background AGN with high confidence, and to constrain other object classes like pulsar wind nebula. To classify X-ray and radio sources, we use clear correlations of X-ray sources found in the XMM-Newton survey with radio-continuum sources detected with ATCA and MOST. Deep radio-continuum images were searched for correlations with X-ray sources of the XMM-Newton SMC-survey point-source catalogue as well as galaxy clusters seen with extended X-ray emission. Eighty eight discrete radio sources were found in common with the X-ray point-source catalogue in addition to six correlations with extended X-ray sources. One source is identified as a Galactic star and eight as galaxies. Eight radio sources likely originate in AGN that are associated with clusters of galaxies seen in X-rays. One source is a PWN candidate. We obtain 43 new candidates for background sources located behind the SMC. A total of 24 X-ray sources show jet-like radio structures.Comment: 9 pages, 6 figures, accepted for publication in A&