Conjectures about certain parabolic Kazhdan--Lusztig polynomials

Irreducibility results for parabolic induction of representations of the general linear group over a local non-archimedean field can be formulated in terms of Kazhdan--Lusztig polynomials of type $A$. Spurred by these results and some computer calculations, we conjecture that certain alternating sums of Kazhdan--Lusztig polynomials known as parabolic Kazhdan--Lusztig polynomials satisfy properties analogous to those of the ordinary ones.Comment: final versio

An efficient basis set representation for calculating electrons in molecules

The method of McCurdy, Baertschy, and Rescigno, J. Phys. B, 37, R137 (2004) is generalized to obtain a straightforward, surprisingly accurate, and scalable numerical representation for calculating the electronic wave functions of molecules. It uses a basis set of product sinc functions arrayed on a Cartesian grid, and yields 1 kcal/mol precision for valence transition energies with a grid resolution of approximately 0.1 bohr. The Coulomb matrix elements are replaced with matrix elements obtained from the kinetic energy operator. A resolution-of-the-identity approximation renders the primitive one- and two-electron matrix elements diagonal; in other words, the Coulomb operator is local with respect to the grid indices. The calculation of contracted two-electron matrix elements among orbitals requires only O(N log(N)) multiplication operations, not O(N^4), where N is the number of basis functions; N = n^3 on cubic grids. The representation not only is numerically expedient, but also produces energies and properties superior to those calculated variationally. Absolute energies, absorption cross sections, transition energies, and ionization potentials are reported for one- (He^+, H_2^+ ), two- (H_2, He), ten- (CH_4) and 56-electron (C_8H_8) systems.Comment: Submitted to JC

Electron Traps in Ag-doped Li\u3csub\u3e2\u3c/sub\u3eB\u3csub\u3e4\u3c/sub\u3eO\u3csub\u3e7\u3c/sub\u3e Crystals: The role of Ag Interstitial Ions

Electron paramagnetic resonance (EPR) is used to establish models for electron traps in Ag-doped lithium tetraborate (Li2B4O7) crystals. When exposed at room temperature to ionizing radiation, electrons are trapped at interstitial Ag+ ions and holes are trapped at Ag+ ions on Li+ sites. The trapped electrons occupy a 5s1 orbital on the interstitial Ag ions (some of the unpaired spin density is also on neighboring ions). Three EPR spectra are assigned to electrons trapped at interstitial Ag ions. Their g values are near 1.99 and they have resolved hyperfine structure from 107Ag and 109Ag nuclei. The spectrum representing the largest concentration of trapped electrons has the unpaired spin shared by the interstitial Ag ion and an adjacent boron ion at its regular lattice site. A 10B enriched crystal verifies this assignment and an analysis of spin-Hamiltonian parameters yields information about the Ag and B orbitals occupied by the unpaired spin. The second spectrum has the unpaired spin shared equally by two Ag ions, one at an interstitial site and the other at an adjacent Li site. The third spectrum has a large Ag hyperfine interaction and a weak Li interaction. Optical absorption bands associated with the trapped electrons are observed between 225 and 500 nm. Thermal release of electrons from these traps is responsible for a prominent thermoluminescence peak near 150 °C, whereas optical release of the electrons at room temperature produces intense optically stimulated luminescence. Radiative recombination occurs at Ag2+ ions with emission peaking near 270 nm

Lambda-Cold Dark Matter, Stellar Feedback, and the Galactic Halo Abundance Pattern

(Abridged) The hierarchical formation scenario for the stellar halo requires the accretion and disruption of dwarf galaxies, yet low-metallicity halo stars are enriched in alpha-elements compared to similar, low-metallicity stars in dwarf spheroidal (dSph) galaxies. We address this primary challenge for the hierarchical formation scenario for the stellar halo by combining chemical evolution modelling with cosmologically-motivated mass accretion histories for the Milky Way dark halo and its satellites. We demonstrate that stellar halo and dwarf galaxy abundance patterns can be explained naturally within the LCDM framework. Our solution relies fundamentally on the LCDM model prediction that the majority of the stars in the stellar halo were formed within a few relatively massive, ~5 x 10^10 Msun, dwarf irregular (dIrr)-size dark matter halos, which were accreted and destroyed ~10 Gyr in the past. These systems necessarily have short-lived, rapid star formation histories, are enriched primarily by Type II supernovae, and host stars with enhanced [a/Fe] abundances. In contrast, dwarf spheroidal galaxies exist within low-mass dark matter hosts of ~10^9 Msun, where supernovae winds are important in setting the intermediate [a/Fe] ratios observed. Our model includes enrichment from Type Ia and Type II supernovae as well as stellar winds, and includes a physically-motivated supernovae feedback prescription calibrated to reproduce the local dwarf galaxy stellar mass - metallicity relation. We use representative examples of the type of dark matter halos we expect to host a destroyed ``stellar halo progenitor'' dwarf, a surviving dIrr, and a surviving dSph galaxy, and show that their derived abundance patterns, stellar masses, and gas masses are consistent with those observed for each type of system.Comment: 10 pages, 3 figures, version accepted by Ap

Identification of electron and hole traps in lithium tetraborate (Li2B4O7) crystals: Oxygen vacancies and lithium vacancies

Electron paramagnetic resonance (EPR) and electron-nuclear double resonance (ENDOR) are used to identify and characterize electrons trapped by oxygen vacancies and holes trapped by lithium vacancies in lithium tetraborate (Li2B4O7) crystals. Our study includes a crystal with the natural abundances of 10B and 11B and a crystal highly enriched with 10B. The as-grown crystals contain isolated oxygen vacancies, lithium vacancies, and copper impurities, all in nonparamagnetic charge states. During an irradiation at 77 K with 60 kV x-rays, doubly ionized oxygen vacancies trap electrons while singly ionized lithium vacancies and monovalent copper impurities trap holes. The vacancies return to their preirradiation charge states when the temperature of the sample is increased to approximately 90 K. Hyperfine interactions with 10B and 11B nuclei, observed between 13 and 40 K in the radiation-induced EPR and ENDOR spectra, provide models for the two vacancy-related defects. The electron trapped by an oxygen vacancy is localized primarily on only one of the two neighboring boron ions while the hole stabilized by a lithium vacancy is localized on a neighboring oxygen ion with nearly equal interactions with the two boron ions adjacent to the oxygen ion

Molecular Hydrogen and Global Star Formation Relations in Galaxies

(ABRIDGED) We use hydrodynamical simulations of disk galaxies to study relations between star formation and properties of the molecular interstellar medium (ISM). We implement a model for the ISM that includes low-temperature (T<10^4K) cooling, directly ties the star formation rate to the molecular gas density, and accounts for the destruction of H2 by an interstellar radiation field from young stars. We demonstrate that the ISM and star formation model simultaneously produces a spatially-resolved molecular-gas surface density Schmidt-Kennicutt relation of the form Sigma_SFR \propto Sigma_Hmol^n_mol with n_mol~1.4 independent of galaxy mass, and a total gas surface density -- star formation rate relation Sigma_SFR \propto Sigma_gas^n_tot with a power-law index that steepens from n_tot~2 for large galaxies to n_tot>~4 for small dwarf galaxies. We show that deviations from the disk-averaged Sigma_SFR \propto Sigma_gas^1.4 correlation determined by Kennicutt (1998) owe primarily to spatial trends in the molecular fraction f_H2 and may explain observed deviations from the global Schmidt-Kennicutt relation.Comment: Version accepted by ApJ, high-res version available at http://kicp.uchicago.edu/~brant/astro-ph/molecular_ism/rk2007.pd

Feedback-Driven Evolution of the Far-Infrared Spectral Energy Distributions of Luminous and Ultraluminous Infrared Galaxies

We calculate infrared spectral energy distributions (SEDs) from simulations of major galaxy mergers and study the effect of AGN and starburst driven feedback on the evolution of the SED as a function of time. We use a self-consistent three-dimensional radiative equilibrium code to calculate the emergent SEDs and to make images. To facilitate a simple description of our findings, we describe our results in reference to an approximate analytic solution for the far-IR SED. We focus mainly on the luminous infrared galaxy (LIRG) and ultraluminous infrared galaxy (ULIRG) phases of evolution. We contrast the SEDs of simulations performed with AGN feedback to simulations performed with starburst driven wind feedback. We find that the feedback processes critically determine the evolution of the SED. Changing the source of illumination (whether stellar or AGN) has virtually no impact on the reprocessed far-infrared SED. We find that AGN feedback is particularly effective at dispersing gas and rapidly injecting energy into the ISM. The observational signature of such powerful feedback is a warm SED. In general, simulations performed with starburst driven winds have colder spectra and reprocess more of their emission into the infrared, resulting in higher infrared to bolometric luminosities compared to (otherwise equivalent) simulations performed with AGN feedback. We depict our results in IRAS bands, as well as in Spitzer's MIPS bands, and in Herschel's PACS bands.Comment: Accepted to ApJ, 11 figures, 26 pages, added 2 figure