Microscale application of column theory for high resolution force and displacement sensing

We present the design, fabrication and experimental validation of a novel device that exploits the amplification of displacement and attenuation of structural stiffness in the post-buckling deformation of slender columns to obtain pico-Newton force and nanometer displacement resolution even under an optical microscope. The extremely small size, purely mechanical sensing scheme and vacuum compatibility of the instrument makes it compatible with existing visualization tools of nanotechnology. The instrument has a wide variety of potential applications ranging from electro-mechanical characterization of one dimensional solids to single biological cells

Geometric phases and Wannier functions of Bloch electrons in 1-dimension

We present a formal expression for Wannier functions of composite bands of 1-D Bloch electrons in terms of parallel-transported Bloch functions and their non-Abelian geometric phases. Spatial decay properties of these Wannier functions are studied in the case of simple bands of 1-D model insulator and metal. Within first-principles density functional theory, we illustrate the formalism through the construction of Wannier functions of polyethylene and polyacetylene.Comment: 4 pages, 4 figure

The Geometric Phase and Ray Space Isometries

We study the behaviour of the geometric phase under isometries of the ray space. This leads to a better understanding of a theorem first proved by Wigner: isometries of the ray space can always be realised as projections of unitary or anti-unitary transformations on the Hilbert space. We suggest that the construction involved in Wigner's proof is best viewed as an use of the Pancharatnam connection to ``lift'' a ray space isometry to the Hilbert space.Comment: 17 pages, Latex file, no figures, To appear in Pramana J. Phy

Electron Microprobe Chemical Dating of Uraninite as a Reconnaissance Tool for Leucogranite Geochronology

We suggest that electron microprobe techniques may be employed to date Tertiary samples of uraninite (UO~2~), which can contain very high concentrations of radiogenic Pb after only a few million of years of U and Th decay. Although uraninite is regarded as a rare accessory mineral, it is relatively abundant in leucogranitic rocks such as those found in the Himalayan orogen. We apply the U-Th-total Pb electron microprobe chemical dating method to a uraninite crystal from a ca. 18.3 Ma dike of the Mugu granite from the Upper Mustang region of central Nepal. With this technique, we calculate a mean chemical date that is consistent with isotope-dilution thermal ionization mass spectrometry (ID-TIMS) U-Pb dates obtained from seven other uraninite grains and a monazite crystal from the same sample. Electron microprobe chemical dating yields results that typically will be an order of magnitude less precise than conventional dates: in the specific case of the Mugu granite, single point chemical dates each have ca. 1.5 Ma 2[sigma] (95%) confidence level uncertainties. However, the mean chemical date of 15 point analyses of the crystal we study has a 2SE (2 standard error) uncertainty of ca. 400 ka, comparable to uncertainties obtained with ID-TIMS. These results show that electron microprobe chemical dating of uraninite has substantial promise as a reconnaissance tool for the geochronology of young granitic rocks. The electron microprobe work also reveals substantial chemical complexity within uraninite that must be taken into account. The analyzed crystal displays a texturally and chemically distinctive core and rim that suggests episodic growth. Concentration gradients in U, Th, and Y across the boundary imply diffusive modification. We estimate the diffusivity of U, Th, and Y in uraninite at ca. 700 °C to be > 10-7 cm2 s-1. In contrast, Pb shows no distinctive concentration gradient across the core-rim boundary, implying that Pb has a much higher diffusivity in uraninite than U, Th, or Y. We estimate that Pb loss of as much as ca. 8.9% has occurred in the uraninite grains we analyzed by ID-TIMS

Renormalization-Scale Invariance, Minimal Sensitivity, and the Inclusive Hadronic Decays of a 115 GeV Higgs Particle

Known perturbative expressions for the decay rates of 115 GeV Higgs particle into either two gluons or a $b\bar{b}$ pair are shown to exhibit renormalization-scale-($\mu$)-dependence that is largely removed via renormalization-group/Pade-approximant estimates of these rates' next order contributions. The extrema in $\mu$ characterizing both rates, as determined from fully-known orders of perturbation theory, are very nearly equal to corresponding $\mu$-insensitive rates obtained via estimation of their next order contributions, consistent with "minimal-sensitivity" expectations.Comment: 12 pages, 3 figures, LaTe

Multi-Dimensional Hermite Polynomials in Quantum Optics

We study a class of optical circuits with vacuum input states consisting of Gaussian sources without coherent displacements such as down-converters and squeezers, together with detectors and passive interferometry (beam-splitters, polarisation rotations, phase-shifters etc.). We show that the outgoing state leaving the optical circuit can be expressed in terms of so-called multi-dimensional Hermite polynomials and give their recursion and orthogonality relations. We show how quantum teleportation of photon polarisation can be modelled using this description.Comment: 10 pages, submitted to J. Phys. A, removed spurious fil