Possible evolution of dim radio quiet neutron star 1E 1207.4-5209 based on a B-decay model

Dim radio-quiet neutron star (DRQNS) 1E 1207.4-5209 is one of the most heavily examined isolated neutron stars. Wide absorption lines were observed in its spectrum obtained by both XMM-Newton and Chandra X-ray satellites. These absorption lines can be interpreted as a principal frequency centered at 0.7 keV and its harmonics at 1.4, 2.1 and possibly 2.8 keV. The principal line can be formed by resonant proton cyclotron scattering leading to a magnetic field which is two orders of magnitude larger than the perpendicular component of the surface dipole magnetic field (B) found from the rotation period (P) and the time rate of change in the rotation period (\.{P}) of 1E 1207.4-5209. Besides, age of the supernova remnant (SNR) G296.5+10.0 which is physically connected to 1E 1207.4-5209 is two orders of magnitude smaller than the characteristic age ($\tau$=P/2\.{P}) of the neutron star. These huge differences between the magnetic field values and the ages can be explained based on a B-decay model. If the decay is assumed to be exponential, the characteristic decay time turns out to be several thousand years which is three orders of magnitude smaller than the characteristic decay time of radio pulsars represented in an earlier work. The lack of detection of radio emission from DRQNSs and the lack of point sources and pulsar wind nebulae in most of the observed SNRs can also be partly explained by such a very rapid exponential decay. The large difference between the characteristic decay times of DRQNSs and radio pulsars must be related to the differences in the magnetic fields, equation of states and masses of these isolated neutron stars.Comment: 13 pages, 1 figur

Sturm-Liouville operators on time scales

We establish the connection between Sturm-Liouville equations on time scales and Sturm--Liouville equations with measure-valued coefficients. Based on this connection we generalize several results for Sturm-Liouville equations on time scales which have been obtained by various authors in the past.Comment: 12 page

An integrable discretization of KdV at large times

An "exact discretization" of the Schroedinger operator is considered and its direct and inverse scattering problems are solved. It is shown that a differential-difference nonlinear evolution equation depending on two arbitrary constants can be solved by using this spectral transform and that for a special choice of the constants it can be considered an integrable discretization of the KdV equation at large times. An integrable difference-difference equation is also obtained.Comment: 12 page

Synoptic Sky Surveys and the Diffuse Supernova Neutrino Background: Removing Astrophysical Uncertainties and Revealing Invisible Supernovae

The cumulative (anti)neutrino production from all core-collapse supernovae within our cosmic horizon gives rise to the diffuse supernova neutrino background (DSNB), which is on the verge of detectability. The observed flux depends on supernova physics, but also on the cosmic history of supernova explosions; currently, the cosmic supernova rate introduces a substantial (+/-40%) uncertainty, largely through its absolute normalization. However, a new class of wide-field, repeated-scan (synoptic) optical sky surveys is coming online, and will map the sky in the time domain with unprecedented depth, completeness, and dynamic range. We show that these surveys will obtain the cosmic supernova rate by direct counting, in an unbiased way and with high statistics, and thus will allow for precise predictions of the DSNB. Upcoming sky surveys will substantially reduce the uncertainties in the DSNB source history to an anticipated +/-5% that is dominated by systematics, so that the observed high-energy flux thus will test supernova neutrino physics. The portion of the universe (z < 1) accessible to upcoming sky surveys includes the progenitors of a large fraction (~ 87%) of the expected 10-26 MeV DSNB event rate. We show that precision determination of the (optically detected) cosmic supernova history will also make the DSNB into a strong probe of an extra flux of neutrinos from optically invisible supernovae, which may be unseen either due to unexpected large dust obscuration in host galaxies, or because some core-collapse events proceed directly to black hole formation and fail to give an optical outburst.Comment: 11 pages, 6 figure

A discrete Schrodinger spectral problem and associated evolution equations

A recently proposed discrete version of the Schrodinger spectral problem is considered. The whole hierarchy of differential-difference nonlinear evolution equations associated to this spectral problem is derived. It is shown that a discrete version of the KdV, sine-Gordon and Liouville equations are included and that the so called `inverse' class in the hierarchy is local. The whole class of related Darboux and Backlund transformations is also exhibited.Comment: 14 pages, LaTeX2

An Alternative Interpretation of Recent ARPES Measurements on TiSe2

Recently there has been a renewed interest in the charge density wave transition of TiSe2, fuelled by the possibility that this transition may be driven by the formation of an excitonic insulator or even an excitonic condensate. We show here that the recent ARPES measurements on TiSe2 can also be interpreted in terms of an alternative scenario, in which the transition is due to a combination of Jahn-Teller effects and exciton formation. The hybrid exciton-phonons which cause the CDW formation interpolate between a purely structural and a purely electronic type of transition. Above the transition temperature, the electron-phonon coupling becomes ineffective but a finite mean-field density of excitons remains and gives rise to the observed diffuse ARPES signals.Comment: 4 pages, 2 figure

Scattering Theory for Jacobi Operators with Steplike Quasi-Periodic Background

We develop direct and inverse scattering theory for Jacobi operators with steplike quasi-periodic finite-gap background in the same isospectral class. We derive the corresponding Gel'fand-Levitan-Marchenko equation and find minimal scattering data which determine the perturbed operator uniquely. In addition, we show how the transmission coefficients can be reconstructed from the eigenvalues and one of the reflection coefficients.Comment: 14 page

High-pressure x-ray diffraction study on the structure and phase transitions of the defect-stannite ZnGa2Se4 and defect-chalcopyrite CdGa2S4

X-ray diffraction measurements on the sphalerite-derivatives ZnGa2Se4 and CdGa2S4 have been performed upon compression up to 23 GPa in a diamond-anvil cell. ZnGa2Se4 exhibits a defect tetragonal stannite-type structure (I-42m) up to 15.5 GPa and in the range from 15.5 GPa to 18.5 GPa the low-pressure phase coexists with a high-pressure phase, which remains stable up to 23 GPa. In CdGa2S4, we find the defect tetragonal chalcopyrite-type structure (I-4) is stable up to 17 GPa. Beyond this pressure a pressure-induced phase transition takes place. In both materials, the high-pressure phase has been characterized as a defect-cubic NaCl-type structure (Fm-3m). The occurrence of the pressure induced phase transitions is apparently related with an increase of the cation disorder on the semiconductors investigated. In addition, the results allow the evaluation of the axial compressibility and the determination of the equation of state for each compound. The obtained results are compared with those previously reported for isomorphic digallium sellenides. Finally, a systematic study of the pressure-induced phase transition in twenty-three different sphalerite-related ABX2 and AB2X4 compounds indicates that the transition pressure increases as the ratio of the cationic radii and anionic radii of the compounds increases.Comment: 34 pages, 3 tables, 6 figure

Mimicking diffuse supernova antineutrinos with the Sun as a source

Measuring the electron antineutrino component of the cosmic diffuse supernova neutrino background (DSNB) is the next ambitious goal for low-energy neutrino astronomy. The largest flux is expected in the lowest accessible energy bin. However, for E < 15 MeV a possible signal can be mimicked by a solar electron antineutrino flux that originates from the usual 8B neutrinos by spin-flavor oscillations. We show that such an interpretation is possible within the allowed range of neutrino electromagnetic transition moments and solar turbulent field strengths and distributions. Therefore, an unambiguous detection of the DSNB requires a significant number of events at E > 15 MeV.Comment: 4 pages, 1 figur

Neutrino Spectrum from SN 1987A and from Cosmic Supernovae

The detection of neutrinos from SN 1987A by the Kamiokande-II and Irvine-Michigan-Brookhaven detectors provided the first glimpse of core collapse in a supernova, complementing the optical observations and confirming our basic understanding of the mechanism behind the explosion. One long-standing puzzle is that, when fitted with thermal spectra, the two independent detections do not seem to agree with either each other or typical theoretical expectations. We assess the compatibility of the two data sets in a model-independent way and show that they can be reconciled if one avoids any bias on the neutrino spectrum stemming from theoretical conjecture. We reconstruct the neutrino spectrum from SN 1987A directly from the data through non-parametric inferential statistical methods and present predictions for the Diffuse Supernova Neutrino Background based on SN 1987A data. We show that this prediction cannot be too small (especially in the 10-18 MeV range), since the majority of the detected events from SN 1987 were above 18 MeV (including 6 events above 35 MeV), suggesting an imminent detection in operational and planned detectors.Comment: 9 pages, 4 figures; Matches version published in Phys. Rev.