Efficient computation of high index Sturm-Liouville eigenvalues for problems in physics

Finding the eigenvalues of a Sturm-Liouville problem can be a computationally challenging task, especially when a large set of eigenvalues is computed, or just when particularly large eigenvalues are sought. This is a consequence of the highly oscillatory behaviour of the solutions corresponding to high eigenvalues, which forces a naive integrator to take increasingly smaller steps. We will discuss some techniques that yield uniform approximation over the whole eigenvalue spectrum and can take large steps even for high eigenvalues. In particular, we will focus on methods based on coefficient approximation which replace the coefficient functions of the Sturm-Liouville problem by simpler approximations and then solve the approximating problem. The use of (modified) Magnus or Neumann integrators allows to extend the coefficient approximation idea to higher order methods

Average output entropy for quantum channels

We study the regularized average Renyi output entropy \bar{S}_{r}^{\reg} of quantum channels. This quantity gives information about the average noisiness of the channel output arising from a typical, highly entangled input state in the limit of infinite dimensions. We find a closed expression for \beta_{r}^{\reg}, a quantity which we conjecture to be equal to \Srreg. We find an explicit form for \beta_{r}^{\reg} for some entanglement-breaking channels, and also for the qubit depolarizing channel $\Delta_{\lambda}$ as a function of the parameter $\lambda$. We prove equality of the two quantities in some cases, in particular we conclude that for $\Delta_{\lambda}$ both are non-analytic functions of the variable $\lambda$.Comment: 32 pages, several plots and figures; positivity condition added for Theorem on entanglement breaking channels; new result for entrywise positive channel

Partial covering of emission regions of Q 0528-250 by intervening H2_2 clouds

We present an analysis of the molecular hydrogen absorption system at z$_{\rm abs}$ = 2.811 in the spectrum of the blazar Q0528-250. We demonstrate that the molecular cloud does not cover the background source completely. The partial coverage reveals itself as a residual flux in the bottom of saturated H_2 absorption lines. This amounts to about (2.22$\pm$0.54)% of the continuum and does not depend on the wavelength. This value is small and it explains why this effect has not been detected in previous studies of this quasar spectrum. However, it is robustly detected and significantly higher than the zero flux level in the bottom of saturated lines of the Ly-alpha forest, (-0.21$\pm$0.22)%. The presence of the residual flux could be caused by unresolved quasar multicomponents, by light scattered by dust, and/or by jet-cloud interaction. The H$_2$ absorption system is very well described by a two-component model without inclusion of additional components when we take partial coverage into account. The derived total column densities in the H$_2$ absorption components A and B are logN(H$_2$)[cm$^{-2}$] = 18.10$\pm$0.02 and 17.82$\pm$0.02, respectively. HD molecules are present only in component B. Given the column density, logN(HD)= 13.33$\pm$0.02, we find N(HD)/2N(H$_2$)=(1.48$\pm$0.10)x10$^{-5}$, significantly lower than previous estimations. We argue that it is crucial to take into account partial coverage effects for any analysis of H$_2$ bearing absorption systems, in particular when studying the physical state of high-redshift interstellar medium.Comment: Accepted for MNRA

Neutral chlorine and molecular hydrogen at high redshift

Chlorine and molecular hydrogen are known to be tightly linked together in the cold phase of the local interstellar medium through rapid chemical reactions. We present here the first systematic study of this relation at high redshifts using H$_2$-bearing damped Ly$\alpha$ systems (DLAs) detected along quasar lines of sight. Using high-resolution spectroscopic data from VLT/UVES and Keck/HIRES, we report the detection of Cl$\,$I in 9 DLAs (including 5 new detections) out of 18 high-$z$ DLAs with $N($H$_2) \ge 10^{17.3}\,$cm$^{-2}$ (including a new H$_2$ detection at $z=3.09145$ towards J$\,$2100$-$0641) and present upper limits for the remaining 9 systems. We find a $\sim$5$\,\sigma$ correlation between $N$(Cl$\,$I) and $N$(H$_2$) with only $\sim$0.2$\,$dex dispersion over the range 18.1$\,<\,$log$\,N$(H$_2$)$\,<\,$20.1, thus probing column densities 10 times lower those seen towards nearby stars, roughly following the relation $N$(Cl$\,$I$) \approx 1.5\times10^{-6} \times N($H$_2)$. This relation between column densities is surprisingly the same at low and high redshift suggesting that the physical and chemical conditions are similar for a given H$_2$ (or Cl$\,$I) column density. In turn, the N({Cl\,I})/N({\rm H_2}) ratio is found to be uncorrelated with the overall metallicity in the DLA. Our results confirm that neutral chlorine is an excellent tracer of molecule-rich gas and show that the molecular fraction or/and metallicity in the H$_2$-bearing component of DLA could possibly be much higher than the line-of-sight average values usually measured in DLAs.Comment: 5 pages, 3 figures, Accepted for publication in A&A Letter

CO-dark molecular gas at high redshift: very large H2_2 content and high pressure in a low metallicity damped Lyman-alpha system

We present a detailed analysis of a H$_2$-rich, extremely strong intervening Damped Ly-$\alpha$ Absorption system (DLA) at $z_{\rm abs}=2.786$ towards the quasar J$\,$0843+0221, observed with the Ultraviolet and Visual Echelle Spectrograph on the Very Large Telescope. The total column density of molecular (resp. atomic) hydrogen is $\log N$(H$_2$)=$21.21\pm0.02$ (resp. $\log N$(H$\,$I)=$21.82\pm0.11$), making it to be the first case in quasar absorption lines studies with H$_2$ column density as high as what is seen in $^{13}$CO-selected clouds in the Milky-Way. We find that this system has one of the lowest metallicity detected among H$_2$-bearing DLAs, with $\rm [Zn/H]=-1.52^{+0.08}_{-0.10}$. This can be the reason for the marked differences compared to systems with similar H$_2$ column densities in the local Universe: $(i)$ the kinetic temperature, $T\sim$120~K, derived from the $J=0,1$ H$_2$ rotational levels is at least twice higher than expected; $(ii)$ there is little dust extinction with A$_V < 0.1$; $(iii)$ no CO molecules are detected, putting a constraint on the $X_{\rm CO}$ factor $X_{\rm CO}> 2\times 10^{23}$ cm$^{-2}$/(km/s\,K), in the very low metallicity gas. Low CO and high H$_2$ contents indicate that this system represents "CO-dark/faint" gas. We investigate the physical conditions in the H$_2$-bearing gas using the fine-structure levels of C$\,$I, C$\,$II, Si$\,$II and the rotational levels of HD and H$_2$. We find the number density to be about $n \sim 260-380\,$cm$^{-3}$, implying a high thermal pressure of $(3-5) \times 10^4\,$cm$^{-3}\,$K. We further identify a trend of increasing pressure with increasing total hydrogen column density. This independently supports the suggestion that extremely strong DLAs (with $\log\,$N(H) $\sim 22$) probe high-z galaxies at low impact parameters.Comment: 21 pages, 21 figures. Accepted for publication in MNRA

Intervening Metal Systems in GRB and QSO sight-lines: The Mgii and Civ Question

Prochter et al. 2006 recently found that the number density of strong intervening 0.5<z<2 MgII absorbers detected in gamma-ray burst (GRB) afterglow spectra is nearly 4 times larger than in QSO spectra. We have conducted a similar study using CIV absorbers. Our CIV sample, consisting of a total of 20 systems, is drawn from 3 high resolution and high to moderate S/N VLT/UVES spectra of 3 long-duration GRB afterglows, covering the redshift interval 1.6< z<3.1. The column density distribution and number density of this sample do not show any statistical difference with the same quantities measured in QSO spectra. We discuss several possibilities for the discrepancy between CIV and MgII absorbers and conclude that a higher dust extinction in the MgII QSO samples studied up to now would give the most straightforward solution. However, this effect is only important for the strong MgII absorbers. Regardless of the reasons for this discrepancy, this result confirms once more that GRBs can be used to detect a side of the universe that was unknown before, not necessarily connected with GRBs themselves, providing an alternative and fundamental investigative tool of the cosmic evolution of the universe.Comment: 21 pages, 4 figures, ApJ accepted, Revised after Referee Repor

Phase space measure concentration for an ideal gas

We point out that a special case of an ideal gas exhibits concentration of the volume of its phase space, which is a sphere, around its equator in the thermodynamic limit. The rate of approach to the thermodynamic limit is determined. Our argument relies on the spherical isoperimetric inequality of L\'{e}vy and Gromov.Comment: 15 pages, No figures, Accepted by Modern Physics Letters

Silicon nanoparticles and interstellar extinction

To examine a recently proposed hypothesis that silicon nanoparticles are the source of extended red emission (ERE) in the interstellar medium, we performed a detailed modeling of the mean Galactic extinction in the presence of silicon nanoparticles. For this goal we used the appropriate optical constants of nanosized Si, essentially different from those of bulk Si due to quantum confinement. It was found that a dust mixture of silicon nanoparticles, bare graphite grains, silicate core-organic refractory mantle grains and three-layer silicate-water ice-organic refractory grains works well in explaining the extinction and, in addition, results in the acceptable fractions of UV/visible photons absorbed by silicon nanoparticles: 0.071-0.081. Since these fractions barely agree with the fraction of UV/visible photons needed to excite the observed ERE, we conclude that the intrinsic photon conversion efficiency of the photoluminescence by silicon nanoparticles must be near 100%, if they are the source of the ERE.Comment: Latex2e, uses emulateapj.sty (included), multicol.sty, epsf.sty, 6 pages, 3 figures (8 Postscript files), accepted for publication in ApJ Letters, complete Postscript file is also available at http://physics.technion.ac.il/~zubko/eb.html#SNP

Deuterium at high-redshift: Primordial abundance in the zabs = 2.621 damped Ly-alpha system towards CTQ247

The detection of neutral deuterium in the low-metallicity damped Lyman-{\alpha} system at zabs = 2.621 towards the quasar CTQ247 is reported. Using a high signal-to-noise and high spectral resolution (R = 60000) spectrum from the Very Large Telescope Ultraviolet and Visual Echelle Spectrograph, we precisely measure the deuterium-to-oxygen ratio log N(DI)/N(OI) = 0.74+/-0.04, as well as the overall oxygen abundance, log N(OI)/N(HI)=-5.29+/-0.10 (or equivalently [O/H]=-1.99+/-0.10 with respect to the solar value). Assuming uniform metallicity throughout the system, our measurement translates to (D/H) = (2.8+0.8 -0.6)x10^-5. This ratio is consistent within errors (<0.4sigma) with the primordial ratio, (D/H)p = (2.59+/-0.15)x10^-5, predicted by standard Big-Bang Nucleosynthesis using the WMAP7 value of the cosmological density of baryons (100 Omega_b h^2 = 2.249+/-0.056). The DI absorption lines are observed to be broader than the OI absorption lines. From a consistent fit of the profiles we derive the turbulent broadening to be 5.2 km/s and the temperature of the gas to be T = 8800+/-1500 K, corresponding to a warm neutral medium.Comment: Accepted for publication in A&A Letter

Torsional nodeless vibrations of quaking neutron star restored by combined forces of shear elastic and magnetic field stresses

Within the framework of Newtonian magneto-solid-mechanics, relying on equations appropriate for a perfectly conducting elastic continuous medium threaded by a uniform magnetic field, the asteroseismic model of a neutron star undergoing axisymmetric global torsional nodeless vibrations under the combined action of Hooke's elastic and Lorentz magnetic forces is considered with emphasis on a toroidal Alfv\'en mode of differentially rotational vibrations about the dipole magnetic moment axis of the star. The obtained spectral equation for frequency is applied to $\ell$-pole identification of quasi-periodic oscillations (QPOs) of X-ray flux during the giant flares of SGR 1806-20 and SGR 1900+14. Our calculations suggest that detected QPOs can be consistently interpreted, within the framework of this model, as produced by global torsional nodeless vibrations of quaking magnetar if they are considered to be restored by the joint action of bulk forces of shear elastic and magnetic field stresses.Comment: 18 pages, 5 figures; accepted in Ap