Quark number susceptibilities of hot QCD up to g^6ln(g)

The pressure of hot QCD has recently been determined to the last perturbatively computable order g^6 ln(g) by Kajantie et al. using three-dimensional effective theories. A similar method is applied here to the pressure in the presence of small but non-vanishing quark chemical potentials, and the result is used to derive the quark number susceptibilities in the limit mu = 0. The diagonal quark number susceptibility of QCD with n_f flavours of massless quarks is evaluated to order g^6ln(g) and compared with recent lattice simulations. It is observed that the results qualitatively resemble the lattice ones, and that when combined with the fully perturbative but yet undetermined g^6 term they may well explain the behaviour of the lattice data for a wide range of temperatures.Comment: 11 pages, 3 figures Typos corrected, references added, figures modifie

Jacobi Fields on Statistical Manifolds of Negative Curvature

Two entropic dynamical models are considered. The geometric structure of the statistical manifolds underlying these models is studied. It is found that in both cases, the resulting metric manifolds are negatively curved. Moreover, the geodesics on each manifold are described by hyperbolic trajectories. A detailed analysis based on the Jacobi equation for geodesic spread is used to show that the hyperbolicity of the manifolds leads to chaotic exponential instability. A comparison between the two models leads to a relation among statistical curvature, stability of geodesics and relative entropy-like quantities. Finally, the Jacobi vector field intensity and the entropy-like quantity are suggested as possible indicators of chaoticity in the ED models due to their similarity to the conventional chaos indicators based on the Riemannian geometric approach and the Zurek-Paz criterion of linear entropy growth, respectively.Comment: 22 page

Emission of thermal photons and the equilibration time in Heavy-Ion collisions

The emission of hard real photons from thermalized expanding hadronic matter is dominated by the initial high-temperature expansion phase. Therefore, a measurement of photon emission in ultrarelativistic heavy-ion collisions provides valuable insights into the early conditions realized in such a collision. In particular, the initial temperature of the expanding fireball or equivalently the equilibration time of the strongly interacting matter are of great interest. An accurate determination of these quantities could help to answer the question whether or not partonic matter (the quark gluon plasma) is created in such collisions. In this work, we investigate the emission of real photons using a model which is based on the thermodynamics of QCD matter and which has been shown to reproduce a large variety of other observables. With the fireball evolution fixed beforehand, we are able to extract limits for the equilibration time by a comparison with photon emission data measured by WA98.Comment: 12 pages, 5 figures, accepted for publication at Phys. Rev.

Level spacing statistics of classically integrable systems -Investigation along the line of the Berry-Robnik approach-

By extending the approach of Berry and Robnik, the limiting level spacing distribution of a system consisting of infinitely many independent components is investigated. The limiting level spacing distribution is characterized by a single monotonically increasing function $\bar{\mu}(S)$ of the level spacing $S$. Three cases are distinguished: (i) Poissonian if $\bar{\mu}(+\infty)=0$, (ii) Poissonian for large $S$, but possibly not for small $S$ if $0<\bar{\mu}(+\infty)< 1$, and (iii) sub-Poissonian if $\bar{\mu}(+\infty)=1$. This implies that, even when energy-level distributions of individual components are statistically independent, non-Poissonian level spacing distributions are possible.Comment: 19 pages, 4 figures. Accepted for publication in Phys. Rev.

Parton rescattering and screening in Au+Au collisions at RHIC

We study the microscopic dynamics of quarks and gluons in relativistic heavy ion collisions in the framework of the Parton Cascade Model. We use lowest order perturbative QCD cross sections with fixed lower momentum cutoff p_0. We calculate the time-evolution of the Debye-screening mass for Au+Au collisions at sqrt(s)=200 GeV per nucleon pair. The screening mass is used to determine a lower limit for the allowed range of p_0. We also determine the energy density reached through hard and semi-hard processes at RHIC, obtain a lower bound for the rapidity density of charged hadrons produced by semihard interactions, and analyze the extent of perturbative rescattering among partons.Comment: 6 pages, 4 figures, uses RevTeX 4.0; revised version with minor corrections and one updated figur

Duality properties of Gorringe-Leach equations

In the category of motions preserving the angular momentum's direction, Gorringe and Leach exhibited two classes of differential equations having elliptical orbits. After enlarging slightly these classes, we show that they are related by a duality correspondence of the Arnold-Vassiliev type. The specific associated conserved quantities (Laplace-Runge-Lenz vector and Fradkin-Jauch-Hill tensor) are then dual reflections one of the othe

Wavepacket Dynamics in Yang-Mills Theory

We discuss the results of numerical simulations of colliding wavepackets in $SU(2)$ Yang--Mills theory. We investigate their behavior as a function of amplitude and momentum distribution. We find regions in our parameter space in which initial wave packets scatter into final configurations with dramatically different momentum distributions. These results constitute new classical trajectories with multiparticle boundary conditions. We explain their relevance for the calculation of scattering amplitudes in the semiclassical approximation. Finally, we give directions for future work.Comment: 11 pgs. text, 11 optional figs using PiCTeX and epsf, new version contains improved discussion of scaling properties of results and one additional figure

Quark-Gluon Plasma Fireball

Lattice-QCD results provide an opportunity to model, and extrapolate to finite baryon density, the properties of the quark-gluon plasma (QGP). Upon fixing the scale of the thermal coupling constant and vacuum energy to the lattice data, the properties of resulting QGP equations of state (EoS) are developed. We show that the physical properties of the dense matter fireball formed in heavy ion collision experiments at CERN-SPS are well described by the QGP-EoS we presented. We also estimate the properties of the fireball formed in early stages of nuclear collision, and argue that QGP formation must be expected down to 40A GeV in central Pb--Pb interactions.Comment: 10 pages, 9 postscript figures, 1 table, uses revtex, V3: introduced difference between n_f and n_s; fireball restframe energy corrected, references added. Publisched version in press Phys. Rev.

Perturbations of anti-de Sitter black holes

I review perturbations of black holes in asymptotically anti-de Sitter space. I show how the quasi-normal modes governing these perturbations can be calculated analytically and discuss the implications on the hydrodynamics of gauge theory fluids per the AdS/CFT correspondence. I also discuss phase transitions of hairy black holes with hyperbolic horizons and the dual superconductors emphasizing the analytical calculation of their properties.Comment: 25 pages, 4 figures, prepared for the proceedings of the 5th Aegean Summer School "From Gravity to Thermal Gauge Theories: the AdS/CFT Correspondence," Milos, Greece, September 2009

The pressure of hot QCD up to g^6 ln(1/g)

The free energy density, or pressure, of QCD has at high temperatures an expansion in the coupling constant g, known so far up to order g^5. We compute here the last contribution which can be determined perturbatively, g^6 ln(1/g), by summing together results for the 4-loop vacuum energy densities of two different three-dimensional effective field theories. We also demonstrate that the inclusion of the new perturbative g^6 ln(1/g) terms, once they are summed together with the so far unknown perturbative and non-perturbative g^6 terms, could potentially extend the applicability of the coupling constant series down to surprisingly low temperatures.Comment: 18 pages. Small clarifications added. To appear in Phys.Rev.