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

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

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

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

Comparing Chandra and SIRTF Observations for Obscured Starbursts and AGN at High Redshift

Tracking the star formation rate to high redshifts requires knowledge of the contribution from both optically visible and obscured sources. The dusty, optically-obscured galaxies can be located by X-ray and infrared surveys. To establish criteria for selecting such sources based only on X-ray and infrared surveys, we determine the ratio of infrared to X-ray brightness that would be observed by SIRTF and Chandra for objects with the same spectral shapes as nearby starbursts if seen at high redshift. The parameter IR/X is defined as IR/X = (flux density observed in SIRTF MIPS 24 $\mu$m filter in mJy)/(total flux observed within 0.5-2.0 keV in units of 10^-16 ergs\s\cm^2). Based on observations of NGC 4038/39 (``The Antennae''), NGC 3690+IC 694 (Arp 299 or Mkn 171), M 82, and Arp 220, nine starburst regions are compared using mid-infrared spectra taken by the Infrared Space Observatory (ISO) and X-ray spectra obtained with Chandra . The IR/X are determined as they would appear for 1<z<3. The mean IR/X over this redshift range is 1.3 and is not a significant function of redshift or luminosity, indicating that SIRTF surveys reaching 0.4 mJy at 24 $\mu$m should detect the same starbursts as deep CXO surveys detect at a flux of 0.3x10^-16 ergs/s/cm^2. The lower bound of IR/X for starbursts is about 0.2, suggesting that objects with IR/X smaller than this have an AGN X-ray component in addition to the starburst. Values of IR/X for the obscured AGN within NGC 1068, the Circinus galaxy, and NGC 6240 are also determined for comparison although interpretation is complicated by the circumnuclear starbursts in these galaxies. Any sources found in surveys having IR/X>4 would not match any of the objects considered.Comment: accepted for publication in Ap

The [CII] 158 um Line Deficit in Ultraluminous Infrared Galaxies Revisited

We present a study of the [CII] 157.74 um fine-structure line in a sample of 15 ultraluminous infrared (IR) galaxies (L_IR>10^12 Lsun; ULIRGs) using the Long Wavelength Spectrometer (LWS) on the Infrared Space Observatory (ISO). We confirm the observed order of magnitude deficit (compared to normal and starburst galaxies) in the strength of the [CII] line relative to the far-IR dust continuum emission found in our initial report (Luhman et al. 1998), but here with a sample that is twice as large. This result suggests that the deficit is a general phenomenon affecting 4/5 ULIRGs. We present an analysis using observations of generally acknowledged photodissociation region (PDR) tracers ([CII], [OI] 63 and 145 um, and FIR continuum emission), which suggests that a high UV flux G_o incident on a moderate density n PDR could explain the deficit. However, comparisons with other ULIRG observations, including CO (1-0), [CI] (1-0), and 6.2 um polycyclic aromatic hydrocarbon (PAH) emission, suggest that high G_o/n PDRs alone cannot produce a self-consistent solution that is compatible with all of the observations. We propose that non-PDR contributions to the FIR continuum can explain the apparent [CII] deficiency. Here, unusually high G_o and/or n physical conditions in ULIRGs as compared to those in normal and starburst galaxies are not required to explain the [CII] deficit. Dust-bounded photoionization regions, which generate much of the FIR emission but do not contribute significant [CII] emission, offer one possible physical origin for this additional non-PDR component. Such environments may also contribute to the observed suppression of FIR fine-structure emission from ionized gas and PAHs, as well as the warmer FIR colors found in ULIRGs. The implications for observations at higher redshifts are also revisited.Comment: to be published in The Astrophysical Journal, 58 page

Analysis of kaon spectra at SIS energies - what remains from the KN potential

We study the reaction Au+Au at 1.48 AGeV and analyze the influence of the KN optical potential on cm spectra and azimuthal distributions at mid-rapidity. We find a significant change of the yields but only slight changes in the shapes of the distributions when turning off the optical potential. However, the spectra show contributions from different reaction times, where early kaons contribute stronger to higher momenta and late kaons to lower momenta. Azimuthal distributions of the kaons at mid-rapidity show a strong centrality dependence. Their shape is influenced by the KN optical potential as well as by re-scattering.Comment: SQM 2003 proceedings, 4 figures, 6 page

Prototype design of a timing and fast control system in the CBM experiment

The Compressed Baryonic Matter (CBM) experiment is designed to handle interaction rates of up to 10 MHz and up to 1 TB/s of raw data generated. With triggerless streaming data acquisition in the experiment and beam intensity fluctuations, it is expected that occasional data bursts will surpass bandwidth capabilities of the Data Acquisition System (DAQ) system. In order to preserve integrity of event data, the bandwidth of DAQ must be throttled in an organised way with minimum information loss. The Timing and Fast Control (TFC) system provides a latency-optimised datapath for throttling commands and distributes a system clock together with a global timestamp. This paper describes a prototype design of the system with focus on synchronisation and its evaluation

Prototype design of a timing and fast control system in the CBM experiment

The Compressed Baryonic Matter (CBM) experiment is designed to handle interaction rates of up to 10 MHz and up to 1 TB/s of raw data generated. With triggerless streaming data acquisition in the experiment and beam intensity fluctuations, it is expected that occasional data bursts will surpass bandwidth capabilities of the Data Acquisition System (DAQ) system. In order to preserve integrity of event data, the bandwidth of DAQ must be throttled in an organised way with minimum information loss. The Timing and Fast Control (TFC) system provides a latency-optimised datapath for throttling commands and distributes a system clock together with a global timestamp. This paper describes a prototype design of the system with focus on synchronisation and its evaluation