Early thermalization at RHIC

It is shown that recent RHIC data on hadron spectra and elliptic flow can be excellently reproduced within a hydrodynamic description of the collision dynamics, and that this provides strong evidence for rapid thermalization while the system is still in the quark-gluon plasma phase. But even though the hydrodynamic approach provides an impressive description of the single-particle momentum distributions, it fails to describe the two-particle momentum correlation (HBT) data for central Au+Au collisions at RHIC. We suggest that this is not likely to be repaired by further improvements in our understanding of the early collision stages, but probably requires a better modelling of the freeze-out process. We close with a prediction of the phases of the azimuthal oscillations of the HBT radii in noncentral collisions at RHIC.Comment: 12 pages, including 6 figures. Invited talk at the International Conference on "Statistical QCD", Bielefeld, August 26-30, 2001, to appear in the proceedings (F. Karsch and H. Satz, eds.) in Nucl. Phys.

Tail asymptotics for the maximum of perturbed random walk

Consider a random walk $S=(S_n:n\geq 0)$ that is ``perturbed'' by a stationary sequence $(\xi_n:n\geq 0)$ to produce the process $(S_n+\xi_n:n\geq0)$. This paper is concerned with computing the distribution of the all-time maximum $M_{\infty}=\max \{S_k+\xi_k:k\geq0\}$ of perturbed random walk with a negative drift. Such a maximum arises in several different applications settings, including production systems, communications networks and insurance risk. Our main results describe asymptotics for $\mathbb{P}(M_{\infty}>x)$ as $x\to\infty$. The tail asymptotics depend greatly on whether the $\xi_n$'s are light-tailed or heavy-tailed. In the light-tailed setting, the tail asymptotic is closely related to the Cram\'{e}r--Lundberg asymptotic for standard random walk.Comment: Published at http://dx.doi.org/10.1214/105051606000000268 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Selling Solar: Financing Household Solar Energy in the Developing World

Based on value chain analyses of case studies, outlines the issues and challenges for developing a solar energy industry, with a focus on the need for a financing infrastructure that serves purchasers, manufacturers, distributors, and investors

Thermal history of the early Miocene Waitemata Basin and adjacent Waipapa Group, North Island, New Zealand

Apatite fission track (AFT) and vitrinite reflectance (VR) data for early Miocene outcrops from the Waitemata Basin reveal that the basin sequence was subjected to shallow burial before denudation. AFT results suggest that the total sediment thickness within the basin was <=1 km and maximum paleotemperatures during burial never exceeded c. 60deg.C. Statistical analyses of the detrital AFT ages distinguish four dominant sources of sediment supply: contemporaneous volcanism; metagreywacke rocks of the Waipapa Group; the Northland Allochthon; and an unidentified source south of the basin. The apatite and zircon fission track results from the Waipapa Group rocks (Gondwana Terrane) adjacent to the basin suggest two discrete phases of accelerated cooling: the first during the early Cretaceous (c. 117 Ma) and the second during the mid Cretaceous (c. 84 Ma). These events probably reflect key stages in the tectonic development of the New Zealand microcontinent during the Cretaceous period, the earlier event being related to the climax of compressional deformation (Rangitata Orogeny) and the latter to extensional tectonism associated with the opening of the Tasman Sea. Waipapa Group rocks now exposed at the surface cooled from maximum paleotemperatures of c. 250deg.C at an estimated rate of c. 180-36deg.C/m.y., involving substantial denudation

Indirect Signals from Dark Matter in Split Supersymmetry

We study the possibilities for the indirect detection of dark matter in Split Supersymmetry from gamma-rays, positrons, and antiprotons. The most promising signal is the gamma-ray line, which may be observable at the next generation of detectors. For certain halo profiles and a high mass neutralino, the line can even be visible in current experiments. The continuous gamma-ray signal may be observable, if there is a central spike in the galactic halo density. The signals are found to be similar to those in MSSM models. These indirect signals complement other experiments, being most easily observable for regions of parameter space, such as heavy wino and higgsino dominated neutralinos, which are least accessible for direct detection and accelerator searches.Comment: 10 pages, 5 figures; experimental sensitivities added to figure 2, revised version to appear in Phys. Rev.

An electric-field representation of the harmonic XY model

The two-dimensional harmonic XY (HXY) model is a spin model in which the classical spins interact via a piecewise parabolic potential. We argue that the HXY model should be regarded as the canonical classical lattice spin model of phase fluctuations in two-dimensional condensates, as it is the simplest model that guarantees the modular symmetry of the experimental systems. Here we formulate a lattice electric-field representation of the HXY model and contrast this with an analogous representation of the Villain model and the two-dimensional Coulomb gas with a purely rotational auxiliary field. We find that the HXY model is a spin-model analogue of a lattice electric-field model of the Coulomb gas with an auxiliary field, but with a temperature-dependent vacuum (electric) permittivity that encodes the coupling of the spin vortices to their background spin-wave medium. The spin vortices map to the Coulomb charges, while the spin-wave fluctuations correspond to auxiliary-field fluctuations. The coupling explains the striking differences in the high-temperature asymptotes of the specific heats of the HXY model and the Coulomb gas with an auxiliary field. Our results elucidate the propagation of effective long-range interactions throughout the HXY model (whose interactions are purely local) by the lattice electric fields. They also imply that global spin-twist excitations (topological-sector fluctuations) generated by local spin dynamics are ergodically excluded in the low-temperature phase. We discuss the relevance of these results to condensate physics.Comment: 13 pages, 10 figure

Topological-sector fluctuations and ergodicity breaking at the Berezinskii-Kosterlitz-Thouless transition

The Berezinskii-Kosterlitz-Thouless (BKT) phase transition drives the unbinding of topological defects in many two-dimensional systems. In the two-dimensional Coulomb gas, it corresponds to an insulator-conductor transition driven by charge deconfinement. We investigate the global topological properties of this transition, both analytically and by numerical simulation, using a lattice-field description of the two-dimensional Coulomb gas on a torus. The BKT transition is shown to be an ergodicity breaking between the topological sectors of the electric field, which implies a definition of topological order in terms of broken ergodicity. The breakdown of local topological order at the BKT transition leads to the excitation of global topological defects in the electric field, corresponding to different topological sectors. The quantized nature of these classical excitations, and their strict suppression by ergodicity breaking in the low-temperature phase, afford striking global signatures of topological-sector fluctuations at the BKT transition. We discuss how these signatures could be detected in experiments on, for example, magnetic films and cold-atom systems.Comment: 11 pages, 6 figure

Chiral Rings, Vacua and Gaugino Condensation of Supersymmetric Gauge Theories

We find the complete chiral ring relations of the supersymmetric U(N) gauge theories with matter in adjoint representation. We demonstrate exact correspondence between the solutions of the chiral ring and the supersymmetric vacua of the gauge theory. The chiral ring determines the expectation values of chiral operators and the low energy gauge group. All the vacua have nonzero gaugino condensation. We study the chiral ring relations obeyed by the gaugino condensate. These relations are generalizations of the formula $S^N=\Lambda^{3N}$ of the pure ${\cal N} =1$ gauge theory.Comment: 38 page