Shear viscosity in ϕ4\phi^4 theory from an extended ladder resummation

We study shear viscosity in weakly coupled hot $\phi^4$ theory using the CTP formalism . We show that the viscosity can be obtained as the integral of a three-point function. Non-perturbative corrections to the bare one-loop result can be obtained by solving a decoupled Schwinger-Dyson type integral equation for this vertex. This integral equation represents the resummation of an infinite series of ladder diagrams which contribute to the leading order result. It can be shown that this integral equation has exactly the same form as the Boltzmann equation. We show that the integral equation for the viscosity can be reexpressed by writing the vertex as a combination of polarization tensors. An expression for this polarization tensor can be obtained by solving another Schwinger-Dyson type integral equation. This procedure results in an expression for the viscosity that represents a non-perturbative resummation of contributions to the viscosity which includes certain non-ladder graphs, as well as the usual ladders. We discuss the motivation for this resummation. We show that these resummations can also be obtained by writing the viscosity as an integral equation involving a single four-point function. Finally, we show that when the viscosity is expressed in terms of a four-point function, it is possible to further extend the set of graphs included in the resummation by treating vertex and propagator corrections self-consistently. We discuss the significance of such a self-consistent resummation and show that the integral equation contains cancellations between vertex and propagator corrections.Comment: Revtex 40 pages with 29 figures, version to appear in Phys. Rev.

Geometrical entanglement of highly symmetric multipartite states and the Schmidt decomposition

In a previous paper we examined a geometric measure of entanglement based on the minimum distance between the entangled target state of interest and the space of unnormalized product states. Here we present a detailed study of this entanglement measure for target states with a large degree of symmetry. We obtain analytic solutions for the extrema of the distance function and solve for the Hessian to show that, up to the action of trivial symmetries, the solutions correspond to local minima of the distance function. In addition, we show that the conditions that determine the extremal solutions for general target states can be obtained directly by parametrizing the product states via their Schmidt decomposition.Comment: 16 pages, references added and discussion expande

Dynamical renormalization group approach to transport in ultrarelativistic plasmas: the electrical conductivity in high temperature QED

The DC electrical conductivity of an ultrarelativistic QED plasma is studied in real time by implementing the dynamical renormalization group. The conductivity is obtained from the realtime dependence of a dissipative kernel related to the retarded photon polarization. Pinch singularities in the imaginary part of the polarization are manifest as growing secular terms that in the perturbative expansion of this kernel. The leading secular terms are studied explicitly and it is shown that they are insensitive to the anomalous damping of hard fermions as a result of a cancellation between self-energy and vertex corrections. The resummation of the secular terms via the dynamical renormalization group leads directly to a renormalization group equation in real time, which is the Boltzmann equation for the (gauge invariant) fermion distribution function. A direct correspondence between the perturbative expansion and the linearized Boltzmann equation is established, allowing a direct identification of the self energy and vertex contributions to the collision term.We obtain a Fokker-Planck equation in momentum space that describes the dynamics of the departure from equilibrium to leading logarithmic order in the coupling.This determines that the transport time scale is given by t_{tr}=(24 pi)/[e^4 T \ln(1/e)}]. The solution of the Fokker-Planck equation approaches asymptotically the steady- state solution as sim e^{-t/(4.038 t_{tr})}.The steady-state solution leads to the conductivity sigma = 15.698 T/[e^2 ln(1/e)] to leading logarithmic order. We discuss the contributions beyond leading logarithms as well as beyond the Boltzmann equation. The dynamical renormalization group provides a link between linear response in quantum field theory and kinetic theory.Comment: LaTex, 48 pages, 14 .ps figures, final version to appear in Phys. Rev.

Landau-Pomeranchuk-Migdal effect in thermal field theory

In recent studies, the production rate of photons or lepton pairs by a quark gluon plasma has been found to be enhanced due to collinear singularities. This enhancement pattern is very dependent on rather strict collinearity conditions between the photon and the quark momenta. It was estimated by neglecting the collisional width of quasi-particles. In this paper, we study the modifications of this collinear enhancement when we take into account the possibility for the quarks to have a finite mean free path. Assuming a mean free path of order $(g^2T\ln(1/g))^{-1}$, we find that only low invariant mass photons are affected. The region where collision effects are important can be interpreted as the region where the Landau-Pomeranchuk-Migdal effect plays a role in thermal photon production by bremsstrahlung. It is found that this effect modifies the spectrum of very energetic photons as well. Based on these results and on a previous work on infrared singularities, we end this paper by a reasonable physical picture for photon production by a quark gluon plasma, that should be useful to set directions for future technical developments.Comment: 28 pages Latex document, 9 postscript figures, typos corrected, semantics cleanup, final version to appear in Phys. Rev.

Formal Specification and Testing of a Management Architecture

The importance of network and distributed systems management to supply and maintain services required by users has led to a demand for management facilities. Open network management is assisted by representing the system resources to be managed as objects, and providing standard services and protocols for interrogating and manipulating these objects. This paper examines the application of formal description techniques to the specification of managed objects by presenting a case study in the specification and testing of a management architecture. We describe a formal specification of a management architecture suitable for scheduling and distributing services across nodes in a distributed system. In addition, we show how formal specifications can be used to generate conformance tests for the management architecture

Shubnikov-de Haas oscillations in YBa_2Cu_4O_8

We report the observation of Shubnikov-de Haas oscillations in the underdoped cuprate superconductor YBa$_2$Cu$_4$O$_8$ (Y124). For field aligned along the c-axis, the frequency of the oscillations is $660\pm 30$ T, which corresponds to $\sim 2.4$ % of the total area of the first Brillouin zone. The effective mass of the quasiparticles on this orbit is measured to be $2.7\pm0.3$ times the free electron mass. Both the frequency and mass are comparable to those recently observed for ortho-II YBa$_2$Cu$_3$O$_{6.5}$ (Y123-II). We show that although small Fermi surface pockets may be expected from band structure calculations in Y123-II, no such pockets are predicted for Y124. Our results therefore imply that these small pockets are a generic feature of the copper oxide plane in underdoped cuprates.Comment: v2: Version of paper accepted for publication in Physical Review Letters. Only minor changes to the text and reference

Electroweak bubbles and sphalerons

We consider non-perturbative solutions of the Weinberg-Salam model at finite temperature. We employ an effective temperature-dependent potential yielding a first order phase transition. In the region of the phase transition, there exist two kinds of static, spherically symmetric solutions: sphalerons and bubbles. We analyze these solutions as functions of temperature. We consider the most general spherically symmetric fluctuations about the two solutions and construct the discrete modes in the region of the phase transition. Sphalerons and bubbles both possess a single unstable mode. We present simple approximation formulae for these levels.Comment: 14 pages, plain tex, 9 figures appended as postscript files at the end of the paper. THU-93/0

Effective Lorentz Force due to Small-angle Impurity Scattering: Magnetotransport in High-Tc Superconductors

We show that a scattering rate which varies with angle around the Fermi surface has the same effect as a periodic Lorentz force on magnetotransport coefficients. This effect, together with the marginal Fermi liquid inelastic scattering rate gives a quantitative explanation of the temperature dependence and the magnitude of the observed Hall effect and magnetoresistance with just the measured zero-field resistivity as input.Comment: 4 pages, latex, one epsf figure included in text. Several revisions and corrections are included. Major conclusions are the sam

Resummation Methods at Finite Temperature: The Tadpole Way

We examine several resummation methods for computing higher order corrections to the finite temperature effective potential, in the context of a scalar $\phi^4$ theory. We show by explicit calculation to four loops that dressing the propagator, not the vertex, of the one-loop tadpole correctly counts ``daisy'' and ``super-daisy'' diagrams.Comment: 18 pages, LaTeX, CALT-68-1858, HUTP-93-A011, EFI-93-2