We study an ultrarelativistic QED plasma in thermal equilibrium. Plasmons---photon collective excitations---are postulated to correspond not to poles of the retarded photon propagator but to poles of the propagator multiplied by the fine-structure constant. This product is an invariant of the renormalization group that is independent of an arbitrarily chosen renormalization scale. In addition, our proposal is physically motivated since one needs to scatter a charged particle off a plasma system to probe its spectrum of collective excitations. We present a detailed calculation of the QED running coupling constant at finite temperature using the Keldysh-Schwinger representation of the real-time formalism. We discuss the issue of how to choose the renormalization scale and show that the temperature is a natural choice which prevents the breakdown of perturbation theory through the generation of potentially large logarithmic terms. Our method could be applied to anisotropic systems where the choice of the renormalization scale is less clear, and could have important consequences for the study of collective modes.
In this proceedings contribution, we review recent calculations of the dynamics of the chromo-Weibel instability in the quark-gluon plasma.This instability is present in gauge theories which possess a one-particle distribution function which, in the local rest frame, is momentum-space anisotropic.The conditions necessary for triggering this instability can be present already in the color-glass-condensate initial state or dynamically generated by the rapid longitudinal expansion of the matter created in a heavyion collision.Using the hard-loop framework, we study the case that the one-particle distribution function possesses an arbitrary initial momentum anisotropy that increases in time due to longitudinal free streaming.The resulting three-dimensional dynamical equations for the chromofield evolution are solved numerically.We find that there is regeneration of the longitudinal pressure due to unstable plasma modes; nevertheless, the system seems to maintain a high-degree of momentum-space anisotropy.Despite this anisotropy, we find that there is rapid longitudinal thermalization of the plasma due to the non-linear mode couplings inherent in the unstable evolution.
We examine the approach to equilibrium of the micromaser. Analytic methods are first used to show that for large times (i.e., many atoms) the convergence is governed by the next-to-leading eigenvalue of the corresponding discrete evolution matrix. The model is then studied numerically. The numerical results confirm the phase structure expected from analytic approximation methods and agree for large times with the analysis of Elmfors et al. in terms of the ``continuous master equation.'' For short times, however, we see evidence for interesting new structure not previously reported in the literature. PACS No.: 42.55Sa
We calculate the leading and next-to-leading corrections to the real-time QCD static potential in a high-temperature medium in the region where bound states transit from narrow resonances to wide ones. We find sizable contributions to both the real and the imaginary part of the potential. The calculation involves both loop diagrams calculated in the hard thermal loop effective theory and power corrections to the hard thermal loop Lagrangian calculated in QCD. We compare our results with recent lattice data and check the consistency of different methods used in lattice calculations. We also discuss the usefulness of our results to guide lattice inputs.
We study next-to-leading-order contributions to the soft static fermion dispersion relation in hot QED. We derive an expression for the complete next-to-leading-order contribution to the retarded fermion self-energy. The real and imaginary parts of this expression give the next-to-leading-order contributions to the mass and damping rate of the fermionic quasiparticle. Many of the terms that are expected to contribute according to the traditional power counting argument are actually subleading. We explain why the power counting method over estimates the contribution from these terms. For the electron damping rate in QED we obtain: ${\ensuremath{\gamma}}_{\mathrm{QED}}=\frac{{e}^{2}T}{4\ensuremath{\pi}}(2.70)$. We check our method by calculating the next-to-leading-order contribution to the damping rate for the case of QCD with two flavors and three colors. Our result agrees with the result obtained previously in the literature. The numerical evaluation of the nlo contribution to the mass is left to a future publication.
We discuss the transverse momentum broadening of hard probes traversing an evolving glasma, which is the earliest phase of the matter produced in relativistic heavy-ion collisions. The coefficient qˆ is calculated using the Fokker-Planck equation, and an expansion in the proper time τ which is applied to describe the temporal evolution of the glasma. The correlators of the chromodynamic fields that determine the Fokker-Planck collision terms, which in turn provide qˆ, are computed to fifth order in τ. The momentum broadening is shown to rapidly grow in time and reach a magnitude of several GeV2/fm. We show that the transient pre-equilibrium phase provides a contribution to the energy loss of hard probes which is comparable to that of the long lasting, hydrodynamically evolving, equilibrium phase.
We use a quasi-particle picture and the hard-loop approximation to study collective modes in anisotropic plasmas. We study a general class of anisotropic distribution functions and derive and solve the dispersion equations. We focus on imaginary modes because of their potential influence on plasma dynamics, and we study their dependence on the parameters that characterize the anisotropy of the system. We show that the strength of the imaginary modes is related to the oblateness of the distribution, and the size of the azimuthal Fourier coefficients.
We present numerical simulations for the evolution of an expanding system of massless scalar fields with quartic coupling. By setting a rotating, non-isotropic initial configuration, we compute the energy density, the transverse and longitudinal pressures and the angular momentum of the system. We compare the time scales associated with the isotropization and the decay of the initial angular momentum due to the expansion, and show that even for fairly large initial angular momentum, it decays significantly faster than the pressure anisotropy.
