Explanation of the RHIC HBT Puzzle by a Granular Source of Quark-Gluon Plasma Droplets

We present a review on the explanation of the RHIC HBT puzzle by a granular pion-emitting source of quark-gluon plasma droplets. The evolution of the droplet is described by relativistic hydrodynamics with an equation of state suggested by lattice gauge results. The granular source evolution is obtained by superposing all of the evolutions of individual droplets. Pions are assumed to be emitted thermally from the droplets at the freeze-out configuration characterized by a freeze-out temperature $T_f$. We find that the average particle emission time scales with the initial radius of the droplet. Pions will be emitted earlier if the droplet radius is smaller. An earlier emission time will lead to a smaller extracted HBT radius $R_{\rm out}$, while the extracted HBT radius $R_{\rm side}$ is determined by the scale of the distribution of the droplet centers. However, a collective expansion of the droplets can further decrease $R_{\rm out}$. As a result, the value of $R_{\rm out}/R_{\rm side}$ can be close to, or even less than 1 for theComment: 8 pages, 4 figures, invited talk presented at the XI International Workshop on Correlation and Fluctuation in Multiparticle Production, Nov. 21-24, 2006, Hangzhou, Chin

Analysis of pion elliptic flows and HBT interferometry in a granular quark-gluon plasma droplet model

In many simulations of high-energy heavy-ion collisions on an event-by-event analysis, it is known that the initial energy density distribution in the transverse plane is highly fluctuating. Subsequent longitudinal expansion will lead to many longitudinal tubes of quark-gluon plasma which have tendencies to break up into many spherical droplets because of sausage instabilities. We are therefore motivated to use a model of quark-gluon plasma granular droplets that evolve hydrodynamically to investigate pion elliptic flows and Hanbury-Brown-Twiss interferometry. We find that the data of pion transverse momentum spectra, elliptic flows, and HBT radii in \sqrt{s_{NN}}=200 GeV Au + Au collisions at RHIC can be described well by an expanding source of granular droplets with an anisotropic velocity distribution.Comment: 9 pages, 6 figures, in Late

Ground States for Exponential Random Graphs

We propose a perturbative method to estimate the normalization constant in exponential random graph models as the weighting parameters approach infinity. As an application, we give evidence of discontinuity in natural parametrization along the critical directions of the edge-triangle model.Comment: 12 pages, 3 figures, 1 tabl

Quarkonia and Quark Drip Lines in Quark-Gluon Plasma

We extract the $Q$-$\bar Q$ potential by using the thermodynamic quantities obtained in lattice gauge calculations. The potential is tested and found to give dissociation temperatures that agree well with those from lattice gauge spectral function analysis. Using such a $Q$-$\bar Q$ potential, we examine the quarkonium states in a quark-gluon plasma and determine the `quark drip lines' which separate the region of bound color-singlet $Q\bar Q$ states from the unbound region. The characteristics of the quark drip lines severely limit the region of possible bound $Q\bar Q$ states with light quarks to temperatures close to the phase transition temperature. Bound quarkonia with light quarks may exist very near the phase transition temperature if their effective quark mass is of the order of 300-400 MeV and higher.Comment: 24 pages, 13 figures, in LaTe

Flavor-twisted boundary condition for simulations of quantum many-body systems

We present an approximative simulation method for quantum many-body systems based on coarse graining the space of the momentum transferred between interacting particles, which leads to effective Hamiltonians of reduced size with the flavor-twisted boundary condition. A rapid, accurate, and fast convergent computation of the ground-state energy is demonstrated on the spin-1/2 quantum antiferromagnet of any dimension by employing only two sites. The method is expected to be useful for future simulations and quick estimates on other strongly correlated systems.Comment: 6 pages, 2 figure