The Hamiltonian Analysis for Yang-Mills Theory on R×S2R\times S^2

Pure Yang-Mills theory on ${\mathbb R} \times S^2$ is analyzed in a gauge-invariant Hamiltonian formalism. Using a suitable coordinatization for the sphere and a gauge-invariant matrix parametrization for the gauge potentials, we develop the Hamiltonian formalism in a manner that closely parallels previous analysis on ${\mathbb R}^3$. The volume measure on the physical configuration space of the gauge theory, the nonperturbative mass-gap and the leading term of the vacuum wave functional are discussed using a point-splitting regularization. All the results carry over smoothly to known results on ${\mathbb R}^3$ in the limit in which the sphere is de-compactified to a plane

Mutual Dependence: A Novel Method for Computing Dependencies Between Random Variables

In data science, it is often required to estimate dependencies between different data sources. These dependencies are typically calculated using Pearson's correlation, distance correlation, and/or mutual information. However, none of these measures satisfy all the Granger's axioms for an "ideal measure". One such ideal measure, proposed by Granger himself, calculates the Bhattacharyya distance between the joint probability density function (pdf) and the product of marginal pdfs. We call this measure the mutual dependence. However, to date this measure has not been directly computable from data. In this paper, we use our recently introduced maximum likelihood non-parametric estimator for band-limited pdfs, to compute the mutual dependence directly from the data. We construct the estimator of mutual dependence and compare its performance to standard measures (Pearson's and distance correlation) for different known pdfs by computing convergence rates, computational complexity, and the ability to capture nonlinear dependencies. Our mutual dependence estimator requires fewer samples to converge to theoretical values, is faster to compute, and captures more complex dependencies than standard measures

Tailoring the photonic bandgap of porous silicon dielectric mirror

A systematic method to fabricate porous silicon one dimensional photonic crystals has been engineered to have a photonic bandwidth up to 2000nm. The observation of the tailorability of the photonic bandgap (PBG) underscores the requirement of the large refractive index contrast for making broad PBG structures. In this letter, we present the fabrication and characteristics of such structures that may be promising structures for a large variety of applications.Comment: Published in Appl. Phys. Let

W+W−W^+W^- production in Large extra dimension model at next-to-leading order in QCD at the LHC

We present next-to-leading order QCD corrections to production of two $W$ bosons in hadronic collisions in the extra dimension ADD model. Various kinematical distributions are obtained to order $\alpha_s$ in QCD by taking into account all the parton level subprocesses. We estimate the impact of the QCD corrections on various observables and find that they are significant. We also show the reduction in factorization scale uncertainty when ${\cal O}(\alpha_s)$ effects are included.Comment: Journal versio

Method of measuring cross-flow vortices by use of an array of hot-film sensors

The invention is a method for measuring the wavelength of cross-flow vortices of air flow having streamlines of flow traveling across a swept airfoil. The method comprises providing a plurality of hot-film sensors. Each hot-film sensor provides a signal which can be processed, and each hot-film sensor is spaced in a straight-line array such that the distance between successive hot-film sensors is less than the wavelength of the cross-flow vortices being measured. The method further comprises determining the direction of travel of the streamlines across the airfoil and positioning the straight-line array of hot film sensors perpendicular to the direction of travel of the streamlines, such that each sensor has a spanwise location. The method further comprises processing the signals provided by the sensors to provide root-mean-square values for each signal, plotting each root-mean-square value as a function of its spanwise location, and determining the wavelength of the cross-flow vortices by noting the distance between two maxima or two minima of root-mean-square values

Analysis of folding of bladder structures

Analysis of folding bladder structure

Enhancing laser sideband cooling in one-dimensional optical lattices via the dipole interaction

We study resolved sideband laser cooling of a one-dimensional optical lattice with one atom per site, and in particular the effect of the dipole interaction between radiating atoms. For simplicity, we consider the case where only a single cooling laser is applied. We derive a master equation, and solve it in the limit of a deep lattice and weak laser driving. We find that the dipole interaction significantly changes the final temperature of the particles, increasing it for some phonon wavevectors and decreasing it for others. The total phonon energy over all modes is typically higher than in the non-interacting case, but can be made lower by the right choice of parameters

Supersymmetry and Mass Gap in 2+1 Dimensions: A Gauge Invariant Hamiltonian Analysis

A Hamiltonian formulation of Yang-Mills-Chern-Simons theories with $0\leq N\leq 4$ supersymmetry in terms of gauge-invariant variables is presented, generalizing earlier work on nonsupersymmetric gauge theories. Special attention is paid to the volume measure of integration (over the gauge orbit space of the fields) which occurs in the inner product for the wave functions and arguments relating it to the renormalization of the Chern-Simons level number and to mass-gaps in the spectrum of the Hamiltonians are presented. The expression for the integration measure is consistent with the absence of mass gap for theories with extended supersymmetry (in the absence of additional matter hypermultiplets and/or Chern-Simons couplings), while for the minimally supersymmetric case, there is a mass-gap, the scale of which is set by a renormalized level number, in agreement with indications from existing literature. The realization of the supersymmetry algebra and the Hamiltonian in terms of the gauge invariant variables is also presented.Comment: 31 pages, References added, typos correcte