Surface embedding, topology and dualization for spin networks

Spin networks are graphs derived from 3nj symbols of angular momentum. The surface embedding, the topology and dualization of these networks are considered. Embeddings into compact surfaces include the orientable sphere S^2 and the torus T, and the not orientable projective space P^2 and Klein's bottle K. Two families of 3nj graphs admit embeddings of minimal genus into S^2 and P^2. Their dual 2-skeletons are shown to be triangulations of these surfaces.Comment: LaTeX 17 pages, 6 eps figures (late submission to arxiv.org

The discretised harmonic oscillator: Mathieu functions and a new class of generalised Hermite polynomials

We present a general, asymptotical solution for the discretised harmonic oscillator. The corresponding Schr\"odinger equation is canonically conjugate to the Mathieu differential equation, the Schr\"odinger equation of the quantum pendulum. Thus, in addition to giving an explicit solution for the Hamiltonian of an isolated Josephon junction or a superconducting single-electron transistor (SSET), we obtain an asymptotical representation of Mathieu functions. We solve the discretised harmonic oscillator by transforming the infinite-dimensional matrix-eigenvalue problem into an infinite set of algebraic equations which are later shown to be satisfied by the obtained solution. The proposed ansatz defines a new class of generalised Hermite polynomials which are explicit functions of the coupling parameter and tend to ordinary Hermite polynomials in the limit of vanishing coupling constant. The polynomials become orthogonal as parts of the eigenvectors of a Hermitian matrix and, consequently, the exponential part of the solution can not be excluded. We have conjectured the general structure of the solution, both with respect to the quantum number and the order of the expansion. An explicit proof is given for the three leading orders of the asymptotical solution and we sketch a proof for the asymptotical convergence of eigenvectors with respect to norm. From a more practical point of view, we can estimate the required effort for improving the known solution and the accuracy of the eigenvectors. The applied method can be generalised in order to accommodate several variables.Comment: 18 pages, ReVTeX, the final version with rather general expression

The SAMI Galaxy Survey: Gas Streaming and Dynamical M/L in Rotationally Supported Systems

Line-of-sight velocities of gas and stars can constrain dark matter (DM) within rotationally supported galaxies if they trace circular orbits extensively. Photometric asymmetries may signify non-circular motions, requiring spectra with dense spatial coverage. Our integral-field spectroscopy of 178 galaxies spanned the mass range of the SAMI Galaxy Survey. We derived circular speed curves (CSCs) of gas and stars from non-parametric Diskfit fits out to $r\sim2r_e$. For 12/14 with measured H I profiles, ionized gas and H I maximum velocities agreed. We fitted mass-follows-light models to 163 galaxies by approximating the radial starlight profile as nested, very flattened mass homeoids viewed as a S\'ersic form. Fitting broad-band SEDs to SDSS images gave median stellar mass/light 1.7 assuming a Kroupa IMF vs. 2.6 dynamically. Two-thirds of the dynamical mass/light measures were consistent with star+remnant IMFs. One-fifth required upscaled starlight to fit, hence comparable mass of unobserved baryons and/or DM distributed similarly across the SAMI aperture that came to dominate motions as the starlight CSC declined rapidly. The rest had mass distributed differently from starlight. Subtracting fits of S\'ersic profiles to 13 VIKING Z-band images revealed residual weak bars. Near the bar PA, we assessed m = 2 streaming velocities, and found deviations usually <30 km/s from the CSC; three showed no deviation. Thus, asymmetries rarely influenced our CSCs despite co-located shock-indicating, emission-line flux ratios in more than 2/3.Comment: 21 pages, 15 figures. Accepted to MNRA

Performance of HPGe Detectors in High Magnetic Fields

A new generation of high-resolution hypernuclear gamma$-spectroscopy experiments with high-purity germanium detectors (HPGe) are presently designed at the FINUDA spectrometer at DAPhiNE, the Frascati phi-factory, and at PANDA, the antiproton proton hadron spectrometer at the future FAIR facility. Both, the FINUDA and PANDA spectrometers are built around the target region covering a large solid angle. To maximise the detection efficiency the HPGe detectors have to be located near the target, and therefore they have to be operated in strong magnetic fields B ~ 1 T. The performance of HPGe detectors in such an environment has not been well investigated so far. In the present work VEGA and EUROBALL Cluster HPGe detectors were tested in the field provided by the ALADiN magnet at GSI. No significant degradation of the energy resolution was found, and a change in the rise time distribution of the pulses from preamplifiers was observed. A correlation between rise time and pulse height was observed and is used to correct the measured energy, recovering the energy resolution almost completely. Moreover, no problems in the electronics due to the magnetic field were observed.Comment: submitted to Nucl. Instrum. Meth. Phys. Res. A, LaTeX, 19 pages, 9 figure

Vibron-assisted spin excitation in a magnetically anisotropic nickelocene complex

The ability to electrically-drive spin excitations in molecules with magnetic anisotropy is key for high-density storage and quantum-information technology. Electrons, however, also tunnel via the vibrational excitations unique to a molecule. The interplay of spin and vibrational excitations offers novel routes to study and, ultimately, electrically manipulate molecular magnetism. Here we use a scanning tunneling microscope to electrically induce spin and vibrational excitations in a single molecule consisting of a nickelocene magnetically coupled to a Ni atom. We evidence a vibron-assisted spin excitation at an energy one order of magnitude higher compared to the usual spin excitations of nickelocene and explain it using first-principles calculations that include electron correlations. Furthermore, we observe that spin excitations can be quenched by modifying the Ni-nickelocene coupling. Our study suggests that nickelocene-based complexes constitute a model playground for exploring the interaction of spin and vibrations in the electron transport through single magnetic molecules

FeCoCp3 Molecular Magnets as Spin Filters

Metallorganic molecules have been proposed as excellent spin filters in molecular spintronics because of the large spin-polarization of their electronic structure. However, most of the studies involving spin transport, have disregarded fundamental aspects such as the magnetic anisotropy of the molecule and the excitation of spin-flip processes during electron transport. Here, we study a molecule containing a Co and an Fe atoms stacked between three cyclopentadienyl rings that presents a large magnetic anisotropy and a S=1. These figures are superior to other molecules with the same transition metal, and improves the spin-filtering capacities of the molecule. Non-equilibrium Green's functions calculations based on density functional theory predict excellent spin-filtering properties both in tunnel and contact transport regimes. However, exciting the first magnetic state drastically reduces the current's spin polarization. Furthermore, a difference of temperature between electrodes leads to strong thermoelectric effects that also suppress spin polarization. Our study shows that in-principle good molecular candidates for spintronics need to be confronted with inelastic and thermoelectric effects

Electron transport via local polarons at interface atoms

Electronic transport is profoundly modified in the presence of strong electron-vibration coupling. We show that in certain situations, the electron flow takes place only when vibrations are excited. By controlling the segregation of boron in semiconducting Si(111)-3√×3√R30° surfaces, we create a type of adatom with a dangling-bond state that is electronically decoupled from any other electronic state. However, probing this state with scanning tunnelling microscopy at 5 K yields high currents. These findings are rationalized by ab-initio calculations that show the formation of a local polaron in the transport process