Note On Certain Inequalities for Neuman Means

In this paper, we give the explicit formulas for the Neuman means $N_{AH}$, $N_{HA}$, $N_{AC}$ and $N_{CA}$, and present the best possible upper and lower bounds for theses means in terms of the combinations of harmonic mean $H$, arithmetic mean $A$ and contraharmonic mean $C$.Comment: 9 page

Power-Law Decay of Standing Waves on the Surface of Topological Insulators

We propose a general theory on the standing waves (quasiparticle interference pattern) caused by the scattering of surface states off step edges in topological insulators, in which the extremal points on the constant energy contour of surface band play the dominant role. Experimentally we image the interference patterns on both Bi$_2$Te$_3$ and Bi$_2$Se$_3$ films by measuring the local density of states using a scanning tunneling microscope. The observed decay indices of the standing waves agree excellently with the theoretical prediction: In Bi$_2$Se$_3$, only a single decay index of -3/2 exists; while in Bi$_2$Te$_3$ with strongly warped surface band, it varies from -3/2 to -1/2 and finally to -1 as the energy increases. The -1/2 decay indicates that the suppression of backscattering due to time-reversal symmetry does not necessarily lead to a spatial decay rate faster than that in the conventional two-dimensional electron system. Our formalism can also explain the characteristic scattering wave vectors of the standing wave caused by non-magnetic impurities on Bi$_2$Te$_3$.Comment: 4 pages, 3 figure

Spin Manipulation by Creation of Single-Molecule Radical Cations

All-trans-retinoic acid (ReA), a closed-shell organic molecule comprising only C, H, and O atoms, is investigated on a Au(111) substrate using scanning tunneling microscopy and spectroscopy. In dense arrays single ReA molecules are switched to a number of states, three of which carry a localized spin as evidenced by conductance spectroscopy in high magnetic fields. The spin of a single molecule may be reversibly switched on and off without affecting its neighbors. We suggest that ReA on Au is readily converted to a radical by the abstraction of an electron.Comment: 5 pages, 3 figures, accepted for publication in Phys. Rev. Let

Geometry and optics calibration of WFCTA prototype telescopes using star light

The Large High Altitude Air Shower Observatory project is proposed to study high energy gamma ray astronomy ( 40 GeV-1 PeV ) and cosmic ray physics ( 20 TeV-1 EeV ). The wide field of view Cherenkov telescope array, as a component of the LHAASO project, will be used to study energy spectrum and compositions of cosmic ray by measuring the total Cherenkov light generated by air showers and shower maximum depth. Two prototype telescopes have been in operation since 2008. The pointing accuracy of each telescope is crucial to the direction reconstruction of the primary particles. On the other hand the primary energy reconstruction relies on the shape of the Cherenkov image on the camera and the unrecorded photons due to the imperfect connections between photomultiplier tubes. UV bright stars are used as point-like objects to calibrate the pointing and to study the optical properties of the camera, the spot size and the fractions of unrecorded photons in the insensitive areas of the camera.Comment: 5 pages, 6 figures, submitted to Chinese Physics