Real photons produced from photoproduction in pppp collisions

We calculate the production of real photons originating from the photoproduction in relativistic $pp$ collisions. The Weizs$\ddot{\mathrm{a}}$cker-Williams approximation in the photoproduction is considered. Numerical results agree with the experimental data from Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC). We find that the modification of the photoproduction is more prominent in large transverse momentum region.Comment: 2 figure

Renormalization Group Study of the Electron-phonon Interaction in the High Tc Cuprates

We generalize the numerical renormalization group scheme to study the phonon-mediated retarded interactions in the high Tc cuprates. We find that three sets of phonon-mediated retarded quasiparticle scatterings grow under RG flow. These scatterings share the following common features: 1) the initial and final quasiparticle momenta are in the antinodal regions, and 2) the scattering amplitudes have a $x^2-y^2$ symmetry. All three sets of retarded interaction are driven to strong coupling by the magnetic fluctuations around $(\pi,\pi)$. After growing strong, these retarded interaction will trigger density wave orders with d-wave symmetry. However, due to the d-wave form factor they will leave the nodal quasiparticle unaffected. We conclude that the main effect of electron-phonon coupling in the cuprates is to promote these density wave orders.Comment: 4 pages, 3 figures, references added, added more details about others' previous studie

On Convergence of Epanechnikov Mean Shift

Epanechnikov Mean Shift is a simple yet empirically very effective algorithm for clustering. It localizes the centroids of data clusters via estimating modes of the probability distribution that generates the data points, using the `optimal' Epanechnikov kernel density estimator. However, since the procedure involves non-smooth kernel density functions, the convergence behavior of Epanechnikov mean shift lacks theoretical support as of this writing---most of the existing analyses are based on smooth functions and thus cannot be applied to Epanechnikov Mean Shift. In this work, we first show that the original Epanechnikov Mean Shift may indeed terminate at a non-critical point, due to the non-smoothness nature. Based on our analysis, we propose a simple remedy to fix it. The modified Epanechnikov Mean Shift is guaranteed to terminate at a local maximum of the estimated density, which corresponds to a cluster centroid, within a finite number of iterations. We also propose a way to avoid running the Mean Shift iterates from every data point, while maintaining good clustering accuracies under non-overlapping spherical Gaussian mixture models. This further pushes Epanechnikov Mean Shift to handle very large and high-dimensional data sets. Experiments show surprisingly good performance compared to the Lloyd's K-means algorithm and the EM algorithm.Comment: AAAI 201

Numerical Study of Quantum Hall Bilayers at Total Filling νT=1\nu_T=1: A New Phase at Intermediate Layer Distances

We study the phase diagram of quantum Hall bilayer systems with total filing $\nu_T=1/2+1/2$ of the lowest Landau level as a function of layer distances $d$. Based on numerical exact diagonalization calculations, we obtain three distinct phases, including an exciton superfluid phase with spontaneous interlayer coherence at small $d$, a composite Fermi liquid at large $d$, and an intermediate phase for $1.1<d/l_B<1.8$ ($l_B$ is the magnetic length). The transition from the exciton superfluid to the intermediate phase is identified by (i) a dramatic change in the Berry curvature of the ground state under twisted boundary conditions on the two layers; (ii) an energy level crossing of the first excited state. The transition from the intermediate phase to the composite Fermi liquid is identified by the vanishing of the exciton superfluid stiffness. Furthermore, from our finite-size study, the energy cost of transferring one electron between the layers shows an even-odd effect and possibly extrapolates to a finite value in the thermodynamic limit, indicating the enhanced intralayer correlation. Our identification of an intermediate phase and its distinctive features shed new light on the theoretical understanding of the quantum Hall bilayer system at total filling $\nu_T=1$.Comment: 5 pages, 3 figures (main text); 5 pages, 4 figures (supplementary material); to be published in PR