Charmonium properties in hot quenched lattice QCD

We study the properties of charmonium states at finite temperature in quenched QCD on large and fine isotropic lattices. We perform a detailed analysis of charmonium correlation and spectral functions both below and above $T_c$. Our analysis suggests that both S wave states ($J/\psi$ and $\eta_c$) and P wave states ($\chi_{c0}$ and $\chi_{c1}$) disappear already at about $1.5 T_c$. The charm diffusion coefficient is estimated through the Kubo formula and found to be compatible with zero below $T_c$ and approximately $1/\pi T$ at $1.5 T_c\lesssim T\lesssim 3 T_c$.Comment: 32 pages, 19 figures, typo corrected, discussions on isotropic vs anisotropic lattices expanded, published versio

Heavy Quark diffusion from lattice QCD spectral functions

We analyze the low frequency part of charmonium spectral functions on large lattices close to the continuum limit in the temperature region $1.5\lesssim T/T_c\lesssim 3$ as well as for $T \simeq 0.75T_c$. We present evidence for the existence of a transport peak above $T_c$ and its absence below $T_c$. The heavy quark diffusion constant is then estimated using the Kubo formula. As part of the calculation we also determine the temperature dependence of the signature for the charmonium bound state in the spectral function and discuss the fate of charmonium states in the hot medium.Comment: 4 pages, Proceedings for Quark Matter 2011 Conference, May 23-28, 2011, Annecy, Franc

The evolution of the cover time

The cover time of a graph is a celebrated example of a parameter that is easy to approximate using a randomized algorithm, but for which no constant factor deterministic polynomial time approximation is known. A breakthrough due to Kahn, Kim, Lovasz and Vu yielded a (log log n)^2 polynomial time approximation. We refine this upper bound, and show that the resulting bound is sharp and explicitly computable in random graphs. Cooper and Frieze showed that the cover time of the largest component of the Erdos-Renyi random graph G(n,c/n) in the supercritical regime with c>1 fixed, is asymptotic to f(c) n \log^2 n, where f(c) tends to 1 as c tends to 1. However, our new bound implies that the cover time for the critical Erdos-Renyi random graph G(n,1/n) has order n, and shows how the cover time evolves from the critical window to the supercritical phase. Our general estimate also yields the order of the cover time for a variety of other concrete graphs, including critical percolation clusters on the Hamming hypercube {0,1}^n, on high-girth expanders, and on tori Z_n^d for fixed large d. For the graphs we consider, our results show that the blanket time, introduced by Winkler and Zuckerman, is within a constant factor of the cover time. Finally, we prove that for any connected graph, adding an edge can increase the cover time by at most a factor of 4.Comment: 14 pages, to appear in CP

Evolution of the Fermi surface with carrier concentration in Bi_2Sr_2CaCu_2O_{8+\delta}

We show, by use of angle-resolved photoemission spectroscopy, that underdoped Bi_2Sr_2CaCu_2O_{8+\delta} appears to have a large Fermi surface centered at (\pi,\pi), even for samples with a T_c as low as 15 K. No clear evidence of a Fermi surface pocket around (\pi/2,\pi/2) has been found. These conclusions are based on a determination of the minimum gap locus in the pseudogap regime T_c < T < T^*, which is found to coincide with the locus of gapless excitations in momentum space (Fermi surface) determined above T^*. These results suggest that the pseudogap is more likely of precursor pairing rather than magnetic origin.Comment: 4 pages, revtex, 4 postscript color figure

Direct observation of particle-hole mixing in the superconducting state by angle-resolved photoemission

Particle-hole (p-h) mixing is a fundamental consequence of the existence of a pair condensate. We present direct experimental evidence for p-h mixing in the angle-resolved photoemission (ARPES) spectra in the superconducting state of Bi_2Sr_2CaCu_2O_{8+\delta}. In addition to its pedagogical importance, this establishes unambiguously that the gap observed in ARPES is associated with superconductivity.Comment: 3 pages, revtex, 4 postscript figure