36263241
New optimization methods for converging perturbative series with a field cutoff
We take advantage of the fact that in lambda phi ^4 problems a large field cutoff phi_max makes perturbative series converge toward values exponentially close to the exact values, to make optimal choices of phi_max. For perturbative series terminated at even order, it is in principle possible to adjust phi_max in order to obtain the exact result. For perturbative series terminated at odd order, the error can only be minimized. It is however possible to introduce a mass shift in order to obtain the exact result. We discuss weak and strong coupling methods to determine the unknown parameters. The numerical calculations in this article have been performed with a simple integral with one variable. We give arguments indicating that the qualitative features observed should extend to quantum mechanics and quantum field theory. We found that optimization at even order is more efficient that at odd order. We compare our methods with the linear delta-expansion (LDE) (combined with the principle of minimal sensitivity) which provides an upper envelope of for the accuracy curves of various Pade and Pade-Borel approximants. Our optimization method performs better than the LDE at strong and intermediate coupling, but not at weak coupling where it appears less robust and subject to further improvements. We also show that it is possible to fix the arbitrary parameter appearing in the LDE using the strong coupling expansion, in order to get accuracies comparable to ours.
16150971
The Third Catalog of Active Galactic Nuclei Detected by the Fermi Large Area Telescope
The third catalog of active galactic nuclei (AGNs) detected by the Fermi-LAT (3LAC) is presented. It is based on the third Fermi-LAT catalog (3FGL) of sources detected between 100 MeV and 300 GeV with a Test Statistic (TS) greater than 25, between 2008 August 4 and 2012 July 31. The 3LAC includes 1591 AGNs located at high Galactic latitudes (|b|>10{\deg}), a 71% increase over the second catalog based on 2 years of data. There are 28 duplicate associations, thus 1563 of the 2192 high-latitude gamma-ray sources of the 3FGL catalog are AGNs. Most of them (98%) are blazars. About half of the newly detected blazars are of unknown type, i.e., they lack spectroscopic information of sufficient quality to determine the strength of their emission lines. Based on their gamma-ray spectral properties, these sources are evenly split between flat-spectrum radio quasars (FSRQs) and BL~Lacs. The most abundant detected BL~Lacs are of the high-synchrotron-peaked (HSP) type. About 50% of the BL~Lacs have no measured redshifts. A few new rare outliers (HSP-FSRQs and high-luminosity HSP BL~Lacs) are reported. The general properties of the 3LAC sample confirm previous findings from earlier catalogs. The fraction of 3LAC blazars in the total population of blazars listed in BZCAT remains non-negligible even at the faint ends of the BZCAT-blazar radio, optical and X-ray flux distributions, which is a clue that even the faintest known blazars could eventually shine in gamma rays at LAT-detection levels. The energy-flux distributions of the different blazar populations are in good agreement with extrapolation from earlier catalogs.
119420110
High-accuracy critical exponents for O(N) hierarchical 3D sigma models
The critical exponent γ and its subleading exponent Δ in the 3D O(N) Dyson’s hierarchical model for N up to 20 are calculated with high accuracy. We calculate the critical temperatures for the measure δ(φ.φ − 1). We extract the first coefficients of the 1/N expansion from our numerical data. We show that the leading and subleading exponents agree with Polchinski equation and the equivalent Litim equation, in the local potential approximation, with at least 4 significant digits.
15702909
The continuum limit of perturbative coefficients calculated with a large field cutoff
Abstract We report MC calculations of perturbative coefficients for lattice scalar field theory in dimensions l, 2 and 3, where the large field contributions are cutoff. This produces converging (instead of asymptotic) perturbative series. We discuss the statistical errors and the lattice effects and sho-kv that accurate calculations are possible even in a crossover region where no approximation works. We show that the field cutoff is also a UV regulator. We point out the relevance for QCD questions discussed by Tomboulis ad Trottier at this conference.
10496964
Asymptotically universal crossover in perturbation theory with a field cutoff
We discuss the crossover between the small and large field cutoff (denoted as x max ) limits of the perturbative coefficients for a simple integral and anharmonic oscillators. We show that in the limit where the order k of the perturbative coefficient a k (x max ) becomes large and for x max in the crossover region, a k (x max ) ∝ ∫ xmax -∞ e -A(x-x 0 (k))2 dx. The order-independent constant A and the function x 0 (k) are determined empirically and compared with exact (for the integral) and approximate (for the anharmonic oscillator) calculations. Numerically, our best estimates are A ≃ 1.5, 1.3 and 1.2 for a λx 4 , λx 6 and λx 8 perturbation respectively.
122632442
In-medium kaon-nucleon vector interaction based on chiral effective Lagrangian
We investigate the implications of the four-nucleon terms in the chiral effective Lagrangian for the s-wave K-nucleon effective interaction. We nd that such terms play a nontrivial role in the description of symmetric nuclear matter. Our results for the kaon effective energy and in-medium K+- nucleon scattering are in agreement with the previous prediction obtained by in-medium scaling qualitatively.
119496386
Inflation in Kaluza-Klein theory: Relation between the fine structure constant and the cosmological constant
In this paper we investigate a model of an inflationary universe in Kaluza-Klein theory, which is a four-dimensional de Sitter space plus a one-dimensional compactified internal space. We find that the energy scale for inflation can be predicted from the fine-structure constant in a self-consistent solution of the semi-classical Einstein equations including the Casimir effect. From the observed value of the fine-structure constant, we obtain an energy scale for inflation of $\epsilon=1.84\times 10^{16}g_*^{1/4}$ Gev, where $g_*$ is a dimensionless number depending on the spin and number of matter fields existing in the universe. This value is consistent with the values often discussed for inflation and grand unification. The wave function for this model predicts a high probability for forming such universes, independent of the value of the cosmological constant. The tunneling probability favors the creation of inflationary universes with a compactified dimension, over those with all macroscopic dimensions.
55133202
Entanglement entropy in a holographic p-wave superconductor model
In a recent paper, arXiv:1309.4877, a holographic p-wave model has been proposed in an Einstein– Maxwell-complex vector field theory with a negative cosmological constant. The model exhibits rich phase structure depending on the mass and the charge of the vector field. We investigate the behavior of the entanglement entropy of dual field theory in this model. When the above two model parameters change, we observe the second order, first order and zeroth order phase transitions from the behavior of the entanglement entropy at some intermediate temperatures. These imply that the entanglement entropy can indicate not only the occurrence of the phase transition, but also the order of the phase transition. The entanglement entropy is indeed a good probe to phase transition. Furthermore, the “retrograde condensation” which is a sub-dominated phase is also reflected on the entanglement entropy. © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP 3 .
14227222
Two-Dimensional Stellar Evolution Code Including Arbitrary Magnetic Fields. II. Precision Improvement and Inclusion of Turbulence and Rotation
In the second paper of this series we pursue two objectives. First, in order to make the code more sensitive to small effects, we remove many approximations made in Paper I. Second, we include turbulence and rotation in the two-dimensional framework. The stellar equilibrium is described by means of a set of five differential equations, with the introduction of a new dependent variable, namely the perturbation to the radial gravity, that is found when the nonradial effects are considered in the solution of the Poisson equation. Following the scheme of the first paper, we write the equations in such a way that the two-dimensional effects can be easily disentangled. The key concept introduced in this series is the equipotential surface. We use the underlying cause-effect relation to develop a recurrence relation to calculate the equipotential surface functions for uniform rotation, differential rotation, rotation-like toroidal magnetic fields, and turbulence. We also develop a more precise code to numerically solve the two-dimensional stellar structure and evolution equations based on the equipotential surface calculations. We have shown that with this formulation we can achieve the precision required by observations by appropriately selecting the convergence criterion. Several examples are presented to show that the method works well. Since we are interested in modeling the effects of a dynamo-type field on the detailed envelope structure and global properties of the Sun, the code has been optimized for short timescales phenomena (down to 1 yr). The time dependence of the code has so far been tested exclusively to address such problems.
14075406
Quasi-periodic Oscillations from Rayleigh-Taylor and Kelvin-Helmholtz Instability at a Disk-Magnetosphere Interface
We consider the interface between an accretion disk and a magnetosphere surrounding the accreting mass. We argue that such an interface can occur not only with a magnetized neutron star but also sometimes with an unmagnetized neutron star or a black hole. The gas at the magnetospheric interface is generally Rayleigh-Taylor unstable and may also be Kelvin-Helmholtz unstable. Because of these instabilities, modes with low azimuthal wavenumbers m are expected to grow to large amplitude. It is proposed that the resulting nonaxisymmetric structures contribute to the high-frequency quasi-periodic oscillations that have been seen in neutron star and black hole X-ray binaries. The mode oscillation frequencies are calculated to be approximately equal to mΩm, where Ωm is the angular velocity of the accreting gas at the magnetospheric radius. Thus, mode frequencies should often be in the approximate ratio 1 : 2 : 3, etc. If the pressure of the gas in the disk is not large, then the m = 1 mode will be stable. In this case, the mode frequencies should be in the approximate ratio 2 : 3, etc. There is some observational evidence for such simple frequency ratios.