Dynamics near the critical point: the hot renormalization group in quantum field theory

The perturbative approach to the description of long wavelength excitations at high temperature breaks down near the critical point of a second order phase transition. We study the \emph{dynamics} of these excitations in a relativistic scalar field theory at and near the critical point via a renormalization group approach at high temperature and an $\epsilon$ expansion in $d=5-\epsilon$ space-time dimensions. The long wavelength physics is determined by a non-trivial fixed point of the renormalization group. At the critical point we find that the dispersion relation and width of quasiparticles of momentum $p$ is $\omega_p \sim p^{z}$ and $\Gamma_p \sim (z-1) \omega_p$ respectively, the group velocity of quasiparticles $v_g \sim p^{z-1}$ vanishes in the long wavelength limit at the critical point. Away from the critical point for $T\gtrsim T_c$ we find $\omega_p \sim \xi^{-z}[1+(p \xi)^{2z}]^{{1/2}}$ and $\Gamma_p \sim (z-1) \omega_p \frac{(p \xi)^{2z}}{1+(p \xi)^{2z}}$ with $\xi$ the finite temperature correlation length $\xi \propto |T-T_c|^{-\nu}$. The new \emph{dynamical} exponent $z$ results from anisotropic renormalization in the spatial and time directions. For a theory with O(N) symmetry we find $z=1+ \epsilon \frac{N+2}{(N+8)^2}+\mathcal{O}(\epsilon^2)$. Critical slowing down, i.e, a vanishing width in the long-wavelength limit, and the validity of the quasiparticle picture emerge naturally from this analysis.Comment: Discussion on new dynamical universality class. To appear in Phys. Rev.

Investigation into O(N) Invariant Scalar Model Using Auxiliary-Mass Method at Finite Temperature

Using auxiliary-mass method, O(N) invariant scalar model is investigated at finite temperature. This mass and an evolution equation allow us to calculate an effective potential without an infrared divergence. Second order phase transition is indicated by the effective potential. The critical exponents are determined numerically.Comment: LaTex 8 pages with 3 eps figure

Cantor Spectrum for Schr\"odinger Operators with Potentials arising from Generalized Skew-shifts

We consider continuous $SL(2,\mathbb{R})$-cocycles over a strictly ergodic homeomorphism which fibers over an almost periodic dynamical system (generalized skew-shifts). We prove that any cocycle which is not uniformly hyperbolic can be approximated by one which is conjugate to an $SO(2,\mathbb{R})$-cocycle. Using this, we show that if a cocycle's homotopy class does not display a certain obstruction to uniform hyperbolicity, then it can be $C^0$-perturbed to become uniformly hyperbolic. For cocycles arising from Schr\"odinger operators, the obstruction vanishes and we conclude that uniform hyperbolicity is dense, which implies that for a generic continuous potential, the spectrum of the corresponding Schr\"odinger operator is a Cantor set.Comment: Final version. To appear in Duke Mathematical Journa

Infrared Behavior of High-Temperature QCD

The damping rate \gamma_t(p) of on-shell transverse gluons with ultrasoft momentum p is calculated in the context of next-to-leading-order hard-thermal-loop-summed perturbation of high-temperature QCD. It is obtained in an expansion to second order in p. The first coefficient is recovered but that of order p^2 is found divergent in the infrared. Divergences from light-like momenta do also occur but are circumvented. Our result and method are critically discussed, particularly regarding a Ward identity obtained in the literature. When enforcing the equality between \gamma_t(0) and \gamma_l(0), a rough estimate of the magnetic mass is obtained. Carrying a similar calculation in the context of scalar quantum electrodynamics shows that the early ultrasoft-momentum expansion we make has little to do with the infrared sensitivity of the result.Comment: REVTEX4, 55 page

Shear Viscosity to Entropy Density Ratio of QCD below the Deconfinement Temperature

Using chiral perturbation theory we investigate the QCD shear viscosity to entropy density ratio below the deconfinement temperature (~170 MeV) with zero baryon number density. It is found that the viscosity to entropy density ratio of QCD is monotonically decreasing in temperature (T) and reaches 0.6 with estimated ~50% uncertainty at T=120 MeV. A naive extrapolation of the leading order result shows that the ratio reaches the 1/(4 pi) minimum bound proposed by Kovtun, Son, and Starinets using string theory methods at T~200 MeV. This suggests a phase transition or cross over might occur at T less than 200 MeV in order for the bound to remain valid. Also, it is natural for the ratio to stay close to the minimum bound around the phase transition temperature as was recently found in heavy ion collisions.Comment: 12 pages and 2 figure

Heparan sulfates and heparan sulfate binding proteins in sepsis

Heparan sulfates (HSs) are the main components in the glycocalyx which covers endothelial cells and modulates vascular homeostasis through interactions with multiple Heparan sulfate binding proteins (HSBPs). During sepsis, heparanase increases and induces HS shedding. The process causes glycocalyx degradation, exacerbating inflammation and coagulation in sepsis. The circulating heparan sulfate fragments may serve as a host defense system by neutralizing dysregulated Heparan sulfate binding proteins or pro-inflammatory molecules in certain circumstances. Understanding heparan sulfates and heparan sulfate binding proteins in health and sepsis is critical to decipher the dysregulated host response in sepsis and advance drug development. In this review, we will overview the current understanding of HS in glycocalyx under septic condition and the dysfunctional heparan sulfate binding proteins as potential drug targets, particularly, high mobility group box 1 (HMGB1) and histones. Moreover, several drug candidates based on heparan sulfates or related to heparan sulfates, such as heparanase inhibitors or heparin-binding protein (HBP), will be discussed regarding their recent advances. By applying chemical or chemoenzymatic approaches, the structure-function relationship between heparan sulfates and heparan sulfate binding proteins is recently revealed with structurally defined heparan sulfates. Such homogenous heparan sulfates may further facilitate the investigation of the role of heparan sulfates in sepsis and the development of carbohydrate-based therapy

Perturbation theory and non-perturbative renormalization flow in scalar field theory at finite temperature

We use the non-perturbative renormalization group to clarify some features of perturbation theory in thermal field theory. For the specific case of the scalar field theory with O(N) symmetry, we solve the flow equations within the local potential approximation. This approximation reproduces the perturbative results for the screening mass and the pressure up to order g^3, and starts to differ at order g^4. The method allows a smooth extrapolation to the regime where the coupling is not small, very similar to that obtained from a simple self-consistent approximation.Comment: 42 pages, 19 figures; v2: typos corrected and references added, version accepted for publication in Nucl. Phys.

Bose--Einstein Condensation and Thermalization of the Quark Gluon Plasma

In ultra-relativistic heavy ion collisions, the matter formed shortly after the collision is a dense, out of equilibrium, system of gluons characterized by a semi-hard momentum scale $Q_{\rm s}$. Simple power counting arguments indicate that this system is over-occupied: the gluon occupation number is parametrically large when compared to a system in thermal equilibrium with the same energy density. On short time scales, soft elastic scatterings tend to drive the system towards the formation of a Bose--Einstein condensate that contains a large fraction of the gluons while contributing little to the energy density. The lifetime and existence of this condensate depends on whether inelastic processes, that occur on the same time scale as the elastic ones, preferably increase or decrease the number of gluons. During this overpopulated stage, and all the way to thermalization, the system behaves as a strongly interacting fluid, even though the elementary coupling constant is small. We argue that while complete isotropization may never be reached, the system may yet evolve for a long time with a fixed anisotropy between average longitudinal and transverse momenta.Comment: 19 pages, 1 figure, v2 is a substantial re-write aimed at clarifying the presentation. Major arguments essentially unchanged, except in the discussion of inelastic processe

Sensitivity of Azimuthal Jet Tomography to Early Time Energy-Loss at RHIC and LHC

We compute the jet path-length dependence of energy-loss for higher azimuthal harmonics of jet-fragments in a generalized model of energy-loss that can interpolate between pQCD and AdS/CFT limits and compare results with Glauber and CGC/KLN initial conditions. We find, however, that even the high-pT second moment is most sensitive to the poorly known early-time evolution during the first fm/c. Moreover, we demonstrate that quite generally the energy and density-dependence leads to an overquenching jet fragments relative to the first LHC $R_{AA}$-data, once the parameters of the energy-loss model are fixed from $R_{AA}$-data at RHIC.Comment: 4 pages, 2 figures, version accepted for publication in J. Phys. G: Nucl. Part. Phys. as conference proceedings for Quark Matter 2011, May 23 - May 28, Annecy, Franc