The transformation of irreducible tensor operators under spherical functions

The irreducible tensor operators and their tensor products employing Racah algebra are studied. Transformation procedure of the coordinate system operators act on are introduced. The rotation matrices and their parametrization by the spherical coordinates of vector in the fixed and rotated coordinate systems are determined. A new way of calculation of the irreducible coupled tensor product matrix elements is suggested. As an example, the proposed technique is applied for the matrix element construction for two electrons in a field of a fixed nucleus.Comment: To appear in Int. J. Theor. Phy

Wave packet revivals and the energy eigenvalue spectrum of the quantum pendulum

The rigid pendulum, both as a classical and as a quantum problem, is an interesting system as it has the exactly soluble harmonic oscillator and the rigid rotor systems as limiting cases in the low- and high-energy limits respectively. The energy variation of the classical periodicity ($\tau$) is also dramatic, having the special limiting case of $\tau \to \infty$ at the 'top' of the classical motion (i.e. the separatrix.) We study the time-dependence of the quantum pendulum problem, focusing on the behavior of both the (approximate) classical periodicity and especially the quantum revival and superrevival times, as encoded in the energy eigenvalue spectrum of the system. We provide approximate expressions for the energy eigenvalues in both the small and large quantum number limits, up to 4th order in perturbation theory, comparing these to existing handbook expansions for the characteristic values of the related Mathieu equation, obtained by other methods. We then use these approximations to probe the classical periodicity, as well as to extract information on the quantum revival and superrevival times. We find that while both the classical and quantum periodicities increase monotonically as one approaches the 'top' in energy, from either above or below, the revival times decrease from their low- and high-energy values until very near the separatrix where they increase to a large, but finite value.Comment: 27 pages, 8 embedded .eps figures; to appear, Annals of Physic

Formation and control of electron molecules in artificial atoms: Impurity and magnetic-field effects

Interelectron interactions and correlations in quantum dots can lead to spontaneous symmetry breaking of the self-consistent mean field resulting in formation of Wigner molecules. With the use of spin-and-space unrestricted Hartree-Fock (sS-UHF) calculations, such symmetry breaking is discussed for field-free conditions, as well as under the influence of an external magnetic field. Using as paradigms impurity-doped (as well as the limiting case of clean) two-electron quantum dots (which are analogs to helium-like atoms), it is shown that the interplay between the interelectron repulsion and the electronic zero-point kinetic energy leads, for a broad range of impurity parameters, to formation of a singlet ground-state electron molecule, reminiscent of the molecular picture of doubly-excited helium. Comparative analysis of the conditional probability distributions for the sS-UHF and the exact solutions for the ground state of two interacting electrons in a clean parabolic quantum dot reveals that both of them describe formation of an electron molecule with similar characteristics. The self-consistent field associated with the triplet excited state of the two-electron quantum dot (clean as well as impurity-doped) exhibits symmetry breaking of the Jahn-Teller type, similar to that underlying formation of nonspherical open-shell nuclei and metal clusters. Furthermore, impurity and/or magnetic-field effects can be used to achieve controlled manipulation of the formation and pinning of the discrete orientations of the Wigner molecules. Impurity effects are futher illustrated for the case of a quantum dot with more than two electrons.Comment: Latex/Revtex, 10 pages with 4 gif figures. Small changes to explain the difference between Wigner and Jahn-Teller electron molecules. A complete version of the paper with high quality figures inside the text is available at http://shale.physics.gatech.edu/~costas/qdhelium.html For related papers, see http://www.prism.gatech.edu/~ph274c

An analysis of the FIR/RADIO Continuum Correlation in the Small Magellanic Cloud

The local correlation between far-infrared (FIR) emission and radio-continuum (RC) emission for the Small Magellanic Cloud (SMC) is investigated over scales from 3 kpc to 0.01 kpc. Here, we report good FIR/RC correlation down to ~15 pc. The reciprocal slope of the FIR/RC emission correlation (RC/FIR) in the SMC is shown to be greatest in the most active star forming regions with a power law slope of ~1.14 indicating that the RC emission increases faster than the FIR emission. The slope of the other regions and the SMC are much flatter and in the range of 0.63-0.85. The slopes tend to follow the thermal fractions of the regions which range from 0.5 to 0.95. The thermal fraction of the RC emission alone can provide the expected FIR/RC correlation. The results are consistent with a common source for ultraviolet (UV) photons heating dust and Cosmic Ray electrons (CRe-s) diffusing away from the star forming regions. Since the CRe-s appear to escape the SMC so readily, the results here may not provide support for coupling between the local gas density and the magnetic field intensity.Comment: 19 pages, 7 Figure

Magnetic Fields in the Milky Way

This chapter presents a review of observational studies to determine the magnetic field in the Milky Way, both in the disk and in the halo, focused on recent developments and on magnetic fields in the diffuse interstellar medium. I discuss some terminology which is confusingly or inconsistently used and try to summarize current status of our knowledge on magnetic field configurations and strengths in the Milky Way. Although many open questions still exist, more and more conclusions can be drawn on the large-scale and small-scale components of the Galactic magnetic field. The chapter is concluded with a brief outlook to observational projects in the near future.Comment: 22 pages, 5 figures, to appear in "Magnetic Fields in Diffuse Media", eds. E.M. de Gouveia Dal Pino and A. Lazaria

Observing Supermassive Black Holes across cosmic time: from phenomenology to physics

In the last decade, a combination of high sensitivity, high spatial resolution observations and of coordinated multi-wavelength surveys has revolutionized our view of extra-galactic black hole (BH) astrophysics. We now know that supermassive black holes reside in the nuclei of almost every galaxy, grow over cosmological times by accreting matter, interact and merge with each other, and in the process liberate enormous amounts of energy that influence dramatically the evolution of the surrounding gas and stars, providing a powerful self-regulatory mechanism for galaxy formation. The different energetic phenomena associated to growing black holes and Active Galactic Nuclei (AGN), their cosmological evolution and the observational techniques used to unveil them, are the subject of this chapter. In particular, I will focus my attention on the connection between the theory of high-energy astrophysical processes giving rise to the observed emission in AGN, the observable imprints they leave at different wavelengths, and the methods used to uncover them in a statistically robust way. I will show how such a combined effort of theorists and observers have led us to unveil most of the SMBH growth over a large fraction of the age of the Universe, but that nagging uncertainties remain, preventing us from fully understating the exact role of black holes in the complex process of galaxy and large-scale structure formation, assembly and evolution.Comment: 46 pages, 21 figures. This review article appears as a chapter in the book: "Astrophysical Black Holes", Haardt, F., Gorini, V., Moschella, U and Treves A. (Eds), 2015, Springer International Publishing AG, Cha

Global CO2 emissions from dry inland waters share common drivers across ecosystems

Many inland waters exhibit complete or partial desiccation, or have vanished due to global change, exposing sediments to the atmosphere. Yet, data on carbon dioxide (CO2) emissions from these sediments are too scarce to upscale emissions for global estimates or to understand their fundamental drivers. Here, we present the results of a global survey covering 196 dry inland waters across diverse ecosystem types and climate zones. We show that their CO2 emissions share fundamental drivers and constitute a substantial fraction of the carbon cycled by inland waters. CO2 emissions were consistent across ecosystem types and climate zones, with local characteristics explaining much of the variability. Accounting for such emissions increases global estimates of carbon emissions from inland waters by 6% (~0.12 Pg C y−1). Our results indicate that emissions from dry inland waters represent a significant and likely increasing component of the inland waters carbon cycle

Cotton in the new millennium: advances, economics, perceptions and problems

Cotton is the most significant natural fibre and has been a preferred choice of the textile industry and consumers since the industrial revolution began. The share of man-made fibres, both regenerated and synthetic fibres, has grown considerably in recent times but cotton production has also been on the rise and accounts for about half of the fibres used for apparel and textile goods. To cotton’s advantage, the premium attached to the presence of cotton fibre and the general positive consumer perception is well established, however, compared to commodity man-made fibres and high performance fibres, cotton has limitations in terms of its mechanical properties but can help to overcome moisture management issues that arise with performance apparel during active wear. This issue of Textile Progress aims to: i. Report on advances in cotton cultivation and processing as well as improvements to conventional cotton cultivation and ginning. The processing of cotton in the textile industry from fibre to finished fabric, cotton and its blends, and their applications in technical textiles are also covered. ii. Explore the economic impact of cotton in different parts of the world including an overview of global cotton trade. iii. Examine the environmental perception of cotton fibre and efforts in organic and genetically-modified (GM) cotton production. The topic of naturally-coloured cotton, post-consumer waste is covered and the environmental impacts of cotton cultivation and processing are discussed. Hazardous effects of cultivation, such as the extensive use of pesticides, insecticides and irrigation with fresh water, and consequences of the use of GM cotton and cotton fibres in general on the climate are summarised and the effects of cotton processing on workers are addressed. The potential hazards during cotton cultivation, processing and use are also included. iv. Examine how the properties of cotton textiles can be enhanced, for example, by improving wrinkle recovery and reducing the flammability of cotton fibre

Ultraluminous Infrared Galaxies

Ever since their discovery in the 1970's, UltraLuminous InfraRed Galaxies (ULIRGs; classically Lir>10^12Lsun) have fascinated astronomers with their immense luminosities, and frustrated them due to their singularly opaque nature, almost in equal measure. Over the last decade, however, comprehensive observations from the X-ray through to the radio have produced a consensus picture of local ULIRGs, showing that they are mergers between gas rich galaxies, where the interaction triggers some combination of dust-enshrouded starburst and AGN activity, with the starburst usually dominating. Very recent results have thrown ULIRGs even further to the fore. Originally they were thought of as little more than a local oddity, but the latest IR surveys have shown that ULIRGs are vastly more numerous at high redshift, and tantalizing suggestions of physical differences between high and low redshift ULIRGs hint at differences in their formation modes and local environment. In this review we look at recent progress on understanding the physics and evolution of local ULIRGs, the contribution of high redshift ULIRGs to the cosmic infrared background and the global history of star formation, and the role of ULIRGs as diagnostics of the formation of massive galaxies and large-scale structures.Comment: Review article, published in "Astrophysics Update 2 - topical and timely reviews on astronomy and astrophysics". Ed. John W. Mason. Springer/Praxis books. ISBN: 3-540-30312-X. 53 pages, 5 figures. Higher quality figures available on reques