All-electron GW calculation for molecules: Ionization energy and electron affinity of conjugated molecules

An efficient all-electron G$^0$W$^0$ method and a quasiparticle selfconsistent GW (QSGW) method for molecules are proposed in the molecular orbital space with the full random phase approximation. The convergence with basis set is examined. As an application, the ionization energy ($I$) and electron affinity ($A$) of a series of conjugated molecules (up to 32 atoms) are calculated and compared to experiment. The QSGW result improves the G$^0$W$^0$ result and both of them are in significantly better agreement with experimental data than those from Hartree-Fock (HF) and hybrid density functional calculations, especially for $A$. The nearly correct energy gap and suppressed self-interaction error by the HF exchange make our method a good candidate for investigating electronic and transport properties of molecular systems.Comment: 4 pages, 2 figures, 1 tabl

The Algebraic Structure of the gl(n∣m)gl(n|m) Color Calogero-Sutherland Models

We extend the study on the algebraic structure of the $su(n)$ color Calogero-Sutherland models to the case of $gl(n|m)$ color CS model and show that the generators of the super-Yangian $Y(gl(n|m))$ can be obtained from two $gl(n|m)$ loop algebras. Also, a super $W_{\infty}$ algebra for the SUSY CS model is constructed.Comment: LaTeX, 13 page

Quadratic distances on probabilities: A unified foundation

This work builds a unified framework for the study of quadratic form distance measures as they are used in assessing the goodness of fit of models. Many important procedures have this structure, but the theory for these methods is dispersed and incomplete. Central to the statistical analysis of these distances is the spectral decomposition of the kernel that generates the distance. We show how this determines the limiting distribution of natural goodness-of-fit tests. Additionally, we develop a new notion, the spectral degrees of freedom of the test, based on this decomposition. The degrees of freedom are easy to compute and estimate, and can be used as a guide in the construction of useful procedures in this class.Comment: Published in at http://dx.doi.org/10.1214/009053607000000956 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Multidimensional optical fractionation with holographic verification

The trajectories of colloidal particles driven through a periodic potential energy landscape can become kinetically locked in to directions dictated by the landscape's symmetries. When the landscape is realized with forces exerted by a structured light field, the path a given particle follows has been predicted to depend exquisitely sensitively on such properties as the particle's size and refractive index These predictions, however, have not been tested experimentally. Here, we describe measurements of colloidal silica spheres' transport through arrays of holographic optical traps that use holographic video microscopy to track individual spheres' motions in three dimensions and simultaneously to measure each sphere's radius and refractive index with part-per-thousand resolution. These measurements confirm previously untested predictions for the threshold of kinetically locked-in transport, and demonstrate the ability of optical fractionation to sort colloidal spheres with part-per-thousand resolution on multiple characteristics simultaneously.Comment: 4 pages, 2 figures. Accepted for publication in Physical Review Letter

Tau function and Hirota bilinear equations for the Extended bigraded Toda Hierarchy

In this paper we generalize the Sato theory to the extended bigraded Toda hierarchy (EBTH). We revise the definition of the Lax equations,give the Sato equations, wave operators, Hirota bilinear identities (HBI) and show the existence of $tau$ function $\tau(t)$. Meanwhile we prove the validity of its Fay-like identities and Hirota bilinear equations (HBEs) in terms of vertex operators whose coefficients take values in the algebra of differential operators. In contrast with HBEs of the usual integrable system, the current HBEs are equations of product of operators involving $e^{\partial_x}$ and $\tau(t)$.Comment: 29 pages, to appear Journal of Mathematical Physics(2010

Sensitivity of Ag/Al Interface Specific Resistances to Interfacial Intermixing

We have measured an Ag/Al interface specific resistance, 2AR(Ag/Al)(111) = 1.4 fOhm-m^2, that is twice that predicted for a perfect interface, 50% larger than for a 2 ML 50%-50% alloy, and even larger than our newly predicted 1.3 fOhmm^2 for a 4 ML 50%-50% alloy. Such a large value of 2ARAg/Al(111) confirms a predicted sensitivity to interfacial disorder and suggests an interface greater than or equal to 4 ML thick. From our calculations, a predicted anisotropy ratio, 2AR(Ag/Al)(001)/2AR(Ag/Al)(111), of more then 4 for a perfect interface, should be reduced to less than 2 for a 4 ML interface, making it harder to detect any such anisotropy.Comment: 3 pages, 2 figures, 1 table. In Press: Journal of Applied Physic