Virtual turning points and bifurcation of Stokes curves for higher order ordinary differential equations

For a higher order linear ordinary differential operator P, its Stokes curve bifurcates in general when it hits another turning point of P. This phenomenon is most neatly understandable by taking into account Stokes curves emanating from virtual turning points, together with those from ordinary turning points. This understanding of the bifurcation of a Stokes curve plays an important role in resolving a paradox recently found in the Noumi-Yamada system, a system of linear differential equations associated with the fourth Painleve equation.Comment: 7 pages, 4 figure

Topological superconductivity and Majorana fermions in hybrid structures involving cuprate high-T_c superconductors

The possibility of inducing topological superconductivity with cuprate high-temperature superconductors (HTSC) is studied for various heterostructures. We first consider a ballistic planar junction between a HTSC and a metallic ferromagnet. We assume that inversion symmetry breaking at the tunnel barrier gives rise to Rashba spin-orbit coupling in the barrier and allows equal-spin triplet superconductivity to exist in the ferromagnet. Bogoliubov-de Gennes equations are obtained by explicitly modeling the barrier, and taking account of the transport anisotropy in the HTSC. By making use of the self-consistent boundary conditions and solutions for the barrier and HTSC regions, an effective equation of motion for the ferromagnet is obtained where Andreev scattering at the barrier is incorporated as a boundary condition for the ferromagnetic region. For a ferromagnet layer deposited on a (100) facet of the HTSC, triplet p-wave superconductivity is induced. For the layer deposited on a (110) facet, the induced gap does not have the p-wave orbital character, but has an even orbital symmetry and an odd dependence on energy. For the layer on the (001) facet, an exotic f-wave superconductivity is induced. We also consider the induced triplet gap in a one-dimensional half-metallic nanowire deposited on a (001) facet of a HTSC. We find that for a wire axis along the a-axis, a robust triplet p-wave gap is induced. For a wire oriented 45 degrees away from the a-axis the induced triplet p-wave gap vanishes. For the appropriately oriented wire, the induced p-wave gap should give rise to Majorana fermions at the ends of the half-metallic wire. Based on our result, topological superconductivity in a semi-conductor nanowire may also be possible given that it is oriented along the a-axis of the HTSC.Comment: 14 pages, 4 figure

Studying the WHIM with Gamma Ray Bursts

We assess the possibility to detect and characterize the physical state of the missing baryons at low redshift by analyzing the X-ray absorption spectra of the Gamma Ray Burst [GRB] afterglows, measured by a micro calorimeters-based detector with 3 eV resolution and 1000 cm2 effective area and capable of fast re-pointing, similar to that on board of the recently proposed X-ray satellites EDGE and XENIA. For this purpose we have analyzed mock absorption spectra extracted from different hydrodynamical simulations used to model the properties of the Warm Hot Intergalactic Medium [WHIM]. These models predict the correct abundance of OVI absorption lines observed in UV and satisfy current X-ray constraints. According to these models space missions like EDGE and XENIA should be able to detect about 60 WHIM absorbers per year through the OVII line. About 45 % of these have at least two more detectable lines in addition to OVII that can be used to determine the density and the temperature of the gas. Systematic errors in the estimates of the gas density and temperature can be corrected for in a robust, largely model-independent fashion. The analysis of the GRB absorption spectra collected in three years would also allow to measure the cosmic mass density of the WHIM with about 15 % accuracy, although this estimate depends on the WHIM model. Our results suggest that GRBs represent a valid, if not preferable, alternative to Active Galactic Nuclei to study the WHIM in absorption. The analysis of the absorption spectra nicely complements the study of the WHIM in emission that the spectrometer proposed for EDGE and XENIA would be able to carry out thanks to its high sensitivity and large field of view.Comment: 16 pages, 16 figures, accepted for publication by Ap

Thermodynamics of the Coma Cluster Outskirts

We present results from a large mosaic of Suzaku observations of the Coma Cluster, the nearest and X-ray brightest hot, dynamically active, non-cool core system, focusing on the thermodynamic properties of the ICM on large scales. For azimuths not aligned with an infalling subcluster towards the southwest, our measured temperature and X-ray brightness profiles exhibit broadly consistent radial trends, with the temperature decreasing from about 8.5 keV at the cluster center to about 2 keV at a radius of 2 Mpc, which is the edge of our detection limit. The SW merger significantly boosts the surface brightness, allowing us to detect X-ray emission out to ~2.2 Mpc along this direction. Apart from the southwestern infalling subcluster, the surface brightness profiles show multiple edges around radii of 30-40 arcmin. The azimuthally averaged temperature profile, as well as the deprojected density and pressure profiles, all show a sharp drop consistent with an outward propagating shock front located at 40 arcmin, corresponding to the outermost edge of the giant radio halo observed at 352 MHz with the WSRT. The shock front may be powering this radio emission. A clear entropy excess inside of r_500 reflects the violent merging events linked with these morphological features. Beyond r_500, the entropy profiles of the Coma Cluster along the relatively relaxed directions are consistent with the power-law behavior expected from simple models of gravitational large-scale structure formation. The pressure is also in agreement at these radii with the expected values measured from SZ data from the Planck satellite. However, due to the large uncertainties associated with the Coma Cluster measurements, we cannot yet exclude an entropy flattening in this system consistent with that seen in more relaxed cool core clusters.Comment: submitted to ApJ; revised after first referee repor

Hole burning in a nanomechanical resonator coupled to a Cooper pair box

We propose a scheme to create holes in the statistical distribution of excitations of a nanomechanical resonator. It employs a controllable coupling between this system and a Cooper pair box. The success probability and the fidelity are calculated and compared with those obtained in the atom-field system via distinct schemes. As an application we show how to use the hole-burning scheme to prepare (low excited) Fock states.Comment: 7 pages, 10 figure

Large-scale Motions in the Perseus Galaxy Cluster

By combining large-scale mosaics of ROSAT PSPC, XMM-Newton, and Suzaku X-ray observations, we present evidence for large-scale motions in the intracluster medium of the nearby, X-ray bright Perseus Cluster. These motions are suggested by several alternating and interleaved X-ray bright, low-temperature, low-entropy arcs located along the east-west axis, at radii ranging from ~10 kpc to over a Mpc. Thermodynamic features qualitatively similar to these have previously been observed in the centers of cool core clusters, and were successfully modeled as a consequence of the gas sloshing/swirling motions induced by minor mergers. Our observations indicate that such sloshing/swirling can extend out to larger radii than previously thought, on scales approaching the virial radius.Comment: 6 pages, 6 figures, accepted for publication in Ap

Studying the Warm-Hot Intergalactic Medium in Emission

We assess the possibility to detect the warm-hot intergalactic medium (WHIM) in emission and to characterize its physical conditions and spatial distribution through spatially resolved X-ray spectroscopy, in the framework of the recently proposed DIOS, EDGE, Xenia, and ORIGIN missions, all of which are equipped with microcalorimeter-based detectors. For this purpose we analyze a large set of mock emission spectra, extracted from a cosmological hydrodynamical simulation. These mock X-ray spectra are searched for emission features showing both the OVII K alpha triplet and OVIII Ly alpha line, which constitute a typical signature of the warm hot gas. Our analysis shows that 1 Ms long exposures and energy resolution of 2.5 eV will allow us to detect about 400 such features per deg^2 with a significance >5 sigma and reveals that these emission systems are typically associated with density ~100 above the mean. The temperature can be estimated from the line ratio with a precision of ~20%. The combined effect of contamination from other lines, variation in the level of the continuum, and degradation of the energy resolution reduces these estimates. Yet, with an energy resolution of 7 eV and all these effects taken into account, one still expects about 160 detections per deg^2. These line systems are sufficient to trace the spatial distribution of the line-emitting gas, which constitute an additional information, independent from line statistics, to constrain the poorly known cosmic chemical enrichment history and the stellar feedback processes.Comment: 19 pages, 10 figures, ApJ in press; revised version according to revie