Entanglement conditions and polynomial identities

We develop a rather general approach to entanglement characterization based on convexity properties and polynomial identities. This approach is applied to obtain simple and efficient entanglement conditions which work equally well in both discrete as well as continuous-variable environments. Examples of violations of our conditions are presented.Comment: 5 pages, no figure

The Lerch Zeta Function II. Analytic Continuation

This is the second of four papers that study algebraic and analytic structures associated with the Lerch zeta function. In this paper we analytically continue it as a function of three complex variables. We that it is well defined as a multivalued function on the manifold M equal to C^3 with the hyperplanes corresponding to integer values of the two variables a and c removed. We show that it becomes single valued on the maximal abelian cover of M. We compute the monodromy functions describing the multivalued nature of this function on M, and determine various of their properties.Comment: 29 pages, 3 figures; v2 notation changes, homotopy action on lef

Evolution of unoccupied resonance during the synthesis of a silver dimer on Ag(111)

Silver dimers were fabricated on Ag(111) by single-atom manipulation using the tip of a cryogenic scanning tunnelling microscope. An unoccupied electronic resonance was observed to shift toward the Fermi level with decreasing atom-atom distance as monitored by spatially resolved scanning tunnelling spectroscopy. Density functional calculations were used to analyse the experimental observations and revealed that the coupling between the adsorbed atoms is predominantly direct rather than indirect via the Ag(111) substrate.Comment: 9 pages, 3 figure

A Comparison of the Red Green Blue Air Mass Imagery and Hyperspectral Infrared Retrieved Profiles

The Red Green Blue (RGB) Air Mass imagery is derived from multiple channels or paired channel differences. Multiple channel products typically provide additional information than a single channel can provide alone. The RGB Air Mass imagery simplifies the interpretation of temperature and moisture characteristics of air masses surrounding synoptic and mesoscale features. Despite the ease of interpretation of multiple channel products, the combination of channels and channel differences means the resulting product does not represent a quantity or physical parameter such as brightness temperature in conventional single channel satellite imagery. Without a specific quantity to reference, forecasters are often confused as to what RGB products represent. Hyperspectral infrared retrieved profiles of temperature, moisture, and ozone can provide insight about the air mass represented on the RGB Air Mass product and provide confidence in the product and representation of air masses despite the lack of a quantity to reference for interpretation. This study focuses on RGB Air Mass analysis of Hurricane Sandy as it moved north along the U.S. East Coast, while transitioning to a hybrid extratropical storm. Soundings and total column ozone retrievals were analyzed using data from the Cross-track Infrared and Advanced Technology Microwave Sounder Suite (CrIMSS) on the Suomi National Polar Orbiting Partnership satellite and the Atmospheric Infrared Sounder (AIRS) on the National Aeronautics and Space Administration Aqua satellite along with dropsondes that were collected from National Oceanic and Atmospheric Administration and Air Force research aircraft. By comparing these datasets to the RGB Air Mass, it is possible to capture quantitative information that could help in analyzing the synoptic environment enough to diagnose the onset of extratropical transition. This was done by identifying any stratospheric air intrusions (SAIs) that existed in the vicinity of Sandy as the wind field expanded and the cloud pattern evolved into an atypical pattern

SIC-POVMs and the Extended Clifford Group

We describe the structure of the extended Clifford Group (defined to be the group consisting of all operators, unitary and anti-unitary, which normalize the generalized Pauli group (or Weyl-Heisenberg group as it is often called)). We also obtain a number of results concerning the structure of the Clifford Group proper (i.e. the group consisting just of the unitary operators which normalize the generalized Pauli group). We then investigate the action of the extended Clifford group operators on symmetric informationally complete POVMs (or SIC-POVMs) covariant relative to the action of the generalized Pauli group. We show that each of the fiducial vectors which has been constructed so far (including all the vectors constructed numerically by Renes et al) is an eigenvector of one of a special class of order 3 Clifford unitaries. This suggests a strengthening of a conjuecture of Zauner's. We give a complete characterization of the orbits and stability groups in dimensions 2-7. Finally, we show that the problem of constructing fiducial vectors may be expected to simplify in the infinite sequence of dimensions 7, 13, 19, 21, 31,... . We illustrate this point by constructing exact expressions for fiducial vectors in dimensions 7 and 19.Comment: 27 pages. Version 2 contains some additional discussion of Zauner's original conjecture, and an alternative, possibly stronger version of the conjecture in version 1 of this paper; also a few other minor improvement

The Use of Red Green Blue Air Mass Imagery to Investigate the Role of Stratospheric Air in a Non-convective Wind Event

Non-convective wind events commonly occur with passing extratropical cyclones and have significant societal and economic impacts. Since non-convective winds often occur in the absence of specific phenomena such as a thunderstorm, tornado, or hurricane, the public are less likely to heed high wind warnings and continue daily activities. Thus non-convective wind events result in as many fatalities as straight line thunderstorm winds. One physical explanation for non-convective winds includes tropopause folds. Improved model representation of stratospheric air and associated non-convective wind events could improve non-convective wind forecasts and associated warnings. In recent years, satellite data assimilation has improved skill in forecasting extratropical cyclones; however errors still remain in forecasting the position and strength of extratropical cyclones as well as the tropopause folding process. The goal of this study is to determine the impact of assimilating satellite temperature and moisture retrieved profiles from hyperspectral infrared (IR) sounders (i.e. Atmospheric Infrared Sounder (AIRS), Cross-track Infrared and Microwave Sounding Suite (CrIMSS), and Infrared Atmospheric Sounding Interferometer (IASI)) on the model representation of the tropopause fold and an associated high wind event that impacted the Northeast United States on 09 February 2013. Model simulations using the Advanced Research Weather Research and Forecasting Model (ARW) were conducted on a 12-km grid with cycled data assimilation mimicking the operational North American Model (NAM). The results from the satellite assimilation run are compared to a control experiment (without hyperspectral IR retrievals), Modern Era-Retrospective Analysis for Research and Applications (MERRA) reanalysis, and Rapid Refresh analyses

Impact of the Assimilation of Hyperspectral Infrared Retrieved Profiles on Advanced Weather and Research Model Simulations of a Non-Convective Wind Event

Non-convective wind events commonly occur with passing extratropical cyclones and have significant societal and economic impacts. Since non-convective winds often occur in the absence of specific phenomena such as a thunderstorm, tornado, or hurricane, the public are less likely to heed high wind warnings and continue daily activities. Thus non-convective wind events result in as many fatalities as straight line thunderstorm winds. One physical explanation for non-convective winds includes tropopause folds. Improved model representation of stratospheric air and associated non-convective wind events could improve non-convective wind forecasts and associated warnings. In recent years, satellite data assimilation has improved skill in forecasting extratropical cyclones; however errors still remain in forecasting the position and strength of extratropical cyclones as well as the tropopause folding process. The goal of this study is to determine the impact of assimilating satellite temperature and moisture retrieved profiles from hyperspectral infrared (IR) sounders (i.e. Atmospheric Infrared Sounder (AIRS), Cross-track Infrared and Microwave Sounding Suite (CrIMSS), and Infrared Atmospheric Sounding Interferometer (IASI)) on the model representation of the tropopause fold and an associated high wind event that impacted the Northeast United States on 09 February 2013. Model simulations using the Advanced Research Weather Research and Forecasting Model (ARW) were conducted on a 12-km grid with cycled data assimilation mimicking the operational North American Model (NAM). The results from the satellite assimilation run are compared to a control experiment (without hyperspectral IR retrievals), 32-km North American Regional Reanalysis (NARR) interpolated to a 12-km grid, and 13-km Rapid Refresh analyses

Coisotropic deformations of algebraic varieties and integrable systems

Coisotropic deformations of algebraic varieties are defined as those for which an ideal of the deformed variety is a Poisson ideal. It is shown that coisotropic deformations of sets of intersection points of plane quadrics, cubics and space algebraic curves are governed, in particular, by the dKP, WDVV, dVN, d2DTL equations and other integrable hydrodynamical type systems. Particular attention is paid to the study of two- and three-dimensional deformations of elliptic curves. Problem of an appropriate choice of Poisson structure is discussed.Comment: 17 pages, no figure

Applications and generalizations of Fisher-Hartwig asymptotics

Fisher-Hartwig asymptotics refers to the large $n$ form of a class of Toeplitz determinants with singular generating functions. This class of Toeplitz determinants occurs in the study of the spin-spin correlations for the two-dimensional Ising model, and the ground state density matrix of the impenetrable Bose gas, amongst other problems in mathematical physics. We give a new application of the original Fisher-Hartwig formula to the asymptotic decay of the Ising correlations above $T_c$, while the study of the Bose gas density matrix leads us to generalize the Fisher-Hartwig formula to the asymptotic form of random matrix averages over the classical groups and the Gaussian and Laguerre unitary matrix ensembles. Another viewpoint of our generalizations is that they extend to Hankel determinants the Fisher-Hartwig asymptotic form known for Toeplitz determinants.Comment: 25 page

Light from Cascading Partons in Relativistic Heavy-Ion Collisions

We calculate the production of high energy photons from Compton and annihilation processes as well as fragmentation off quarks in the parton cascade model. The multiple scattering of partons is seen to lead to a substantial production of high energy photons, which rises further when parton multiplication due to final state radiation is included. The photon yield is found to be proportional to the number of collisions among the cascading partons.Comment: revised version: 4 pages, 4 figures, uses REVTEX