Results from the 4PI Effective Action in 2- and 3-dimensions

We consider a symmetric scalar theory with quartic coupling and solve the equations of motion from the 4PI effective action in 2- and 3-dimensions using an iterative numerical lattice method. For coupling less than 10 (in dimensionless units) good convergence is obtained in less than 10 iterations. We use lattice size up to 16 in 2-dimensions and 10 in 3-dimensions and demonstrate the convergence of the results with increasing lattice size. The self-consistent solutions for the 2-point and 4-point functions agree well with the perturbative ones when the coupling is small and deviate when the coupling is large.Comment: 14 pages, 11 figures; v5: added numerical calculations in 3D; version accepted for publication in EPJ

Perturbative and Nonperturbative Kolmogorov Turbulence in a Gluon Plasma

In numerical simulations of nonabelian plasma instabilities in the hard-loop approximation, a turbulent spectrum has been observed that is characterized by a phase-space density of particles $n(p)\sim p^{-\nu}$ with exponent $\nu\simeq 2$, which is larger than expected from relativistic $2\leftrightarrow 2$ scatterings. Using the approach of Zakharov, L'vov and Falkovich, we analyse possible Kolmogorov coefficients for relativistic $(m \ge 4)$-particle processes, which give at most $\nu=5/3$ perturbatively for an energy cascade. We discuss nonperturbative scenarios which lead to larger values. As an extreme limit we find the result $\nu=5$ generically in an inherently nonperturbative effective field theory situation, which coincides with results obtained by Berges et al.\ in large-$N$ scalar field theory. If we instead assume that scaling behavior is determined by Schwinger-Dyson resummations such that the different scaling of bare and dressed vertices matters, we find that intermediate values are possible. We present one simple scenario which would single out $\nu=2$.Comment: published versio

Spontaneous Symmetry Breaking for Scalar QED with Non-minimal Chern-Simons Coupling

We investigate the two-loop effective potential for both minimally and non-minimally coupled Maxwell-Chern-Simons theories. The non-minimal gauge interaction represents the magnetic moment interaction between a charged scalar and the electromagnetic field. In a previous paper we have shown that the two loop effective potential for this model is renormalizable with an appropriate choice of the non-minimal coupling constant. We carry out a detailed analysis of the spontaneous symmetry breaking induced by radiative corrections. As long as the renormalization point for all couplings is chosen to be the true minimum of the effective potential, both models predict the presence of spontaneous symmetry breaking. Two loop corrections are small compared to the one loop result, and thus the symmetry breaking is perturbatively stable.Comment: Revtex 25 pages, 9 figure

Tool support for statistical testing of software components

We describe the "STSC" prototype tool that supports the statistical testing of software components. The tool supports a wide range of operational profiles and test oracles for test case generation and output evaluation. The tool also generates appropriate values for different types of input parameters of operations. STSC automatically generates a test driver from an operational profile. This test driver invokes a test oracle that is implemented as a behaviour-checking version of the implementation. To evaluate the flexibility and usability of the tool, it has been applied to several case studies using different types of operational profiles and test oracles

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

Measurements of the absolute value of the penetration depth in high-Tc T_c superconductors using a tunnel diode resonator

A method is presented to measure the absolute value of the London penetration depth, $\lambda$, from the frequency shift of a resonator. The technique involves coating a high-$T_c$ superconductor (HTSC) with film of low - Tc material of known thickness and penetration depth. The method is applied to measure London penetration depth in YBa2Cu3O{7-\delta} (YBCO) Bi2Sr2CaCu2O{8+\delta} (BSCCO) and Pr{1.85}Ce{0.15}CuO{4-\delta}$(PCCO). For YBCO and BSCCO, the values of$\lambda (0)$are in agreement with the literature values. For PCCO$\lambda \approx 2790$ \AA, reported for the first time.Comment: RevTex 4 (beta 4). 4 pages, 4 EPS figures. Submitted to Appl. Phys. Let

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

de Haas-van Alphen effect investigation of the electronic structure of Al substituted MgB_2

We report a de Haas-van Alphen (dHvA) study of the electronic structure of Al doped crystals of MgB$_2$. We have measured crystals with $\sim 7.5$% Al which have a $T_c$ of 33.6 K, ($\sim 14$% lower than pure MgB$_2$). dHvA frequencies for the $\sigma$ tube orbits in the doped samples are lower than in pure MgB$_2$, implying a $16\pm2$ reduction in the number of holes in this sheet of Fermi surface. The mass of the quasiparticles on the larger $\sigma$ orbit is lighter than the pure case indicating a reduction in electron-phonon coupling constant $\lambda$. These observations are compared with band structure calculations, and found to be in excellent agreement.Comment: 4 pages with figure