On electric fields in hot QCD: perturbation theory

We investigate the response of a hot gas of quarks to external electric fields via leading-order perturbation theory. In particular, we discuss how equilibrium is maintained in the presence of the electric field and calculate the electric susceptibility, providing its high-temperature expansion for arbitrary quark mass. Furthermore, we point out that there is a mismatch between this, direct determination of the susceptibility at zero field and the weak-field expansion of the effective action at nonzero electric fields, as obtained using Schwinger's exact propagator. We discuss the origin of this mismatch and elaborate on the generalization of our results to full QCD in electric fields.Comment: 16 pages, 4 figure

Loss of solution in the symmetry improved Phi-derivable expansion scheme

We consider the two-loop Phi-derivable approximation for the O(2)-symmetric scalar model, augmented by the symmetry improvement introduced in [A. Pilaftsis and D. Teresi, Nucl. Phys. B874, 594 (2013)], which enforces Goldstone's theorem in the broken phase. Although the corresponding equations admit a solution in the presence of a large enough infrared (IR) regulating scale, we argue that, for smooth ultraviolet (UV) regulators, the solution is lost when the IR scale becomes small enough. Infrared regular solutions exist for certain non-analytic UV regulators, but we argue that these solutions are artifacts which should disappear when the sensitivity to the UV regulator is removed by a renormalization procedure. The loss of solution is observed both at zero and at finite temperature, although it is simpler to identify in the latter case. We also comment on possible ways to cure this problem.Comment: 20 pages, 7 figures, uses elsarticle, published versio

Pad\'e approximants and analytic continuation of Euclidean Phi-derivable approximations

We investigate the Pad\'e approximation method for the analytic continuation of numerical data and its ability to access, from the Euclidean propagator, both the spectral function and part of the physical information hidden in the second Riemann sheet. We test this method using various benchmarks at zero temperature: a simple perturbative approximation as well as the two-loop Phi-derivable approximation. The analytic continuation method is then applied to Euclidean data previously obtained in the O(4) symmetric model (within a given renormalization scheme) to assess the difference between zero-momentum and pole masses, which is in general a difficult question to answer within nonperturbative approaches such as the Phi-derivable expansion scheme.Comment: 20 pages, 8 figures, uses RevTeX 4-

The O(N)-model within the Phi-derivable expansion to order lambda^2: on the existence, UV and IR sensitivity of the solutions to self-consistent equations

We discuss various aspects of the O(N)-model in the vacuum and at finite temperature within the Phi-derivable expansion scheme to order lambda^2. In continuation to an earlier work, we look for a physical parametrization in the N=4 case that allows to accommodate the lightest mesons. Using zero-momentum curvature masses to approximate the physical masses, we find that, in the parameter range where a relatively large sigma mass is obtained, the scale of the Landau pole is lower compared to that obtained in the two-loop truncation. This jeopardizes the insensitivity of the observables to the ultraviolet regulator and could hinder the predictivity of the model. Both in the N=1 and N=4 cases, we also find that, when approaching the chiral limit, the (iterative) solution to the Phi-derivable equations is lost in an interval around the would-be transition temperature. In particular, it is not possible to conclude at this order of truncation on the order of the transition in the chiral limit. Because the same issue could be present in other approaches, we investigate it thoroughly by considering a localized version of the Phi-derivable equations, whose solution displays the same qualitative features, but allows for a more analytical understanding of the problem. In particular, our analysis reveals the existence of unphysical branches of solutions which can coalesce with the physical one at some temperatures, with the effect of opening up a gap in the admissible values for the condensate. Depending on its rate of growth with the temperature, this gap can eventually engulf the physical solution.Comment: 26 pages, 15 figures, uses RevTeX4-1, published versio

Thermodynamics and phase transition of the O(N) model from the two-loop Phi-derivable approximation

We discuss the thermodynamics of the O(N) model across the corresponding phase transition using the two-loop Phi-derivable approximation of the effective potential and compare our results to those obtained in the literature within the Hartree-Fock approximation. In particular, we find that in the chiral limit the transition is of the second order, whereas it was found to be of the first order in the Hartree-Fock case. These features are manifest at the level of the thermodynamical observables. We also compute the thermal sigma and pion masses from the curvature of the effective potential. In the chiral limit, this guarantees that the Goldstone's theorem is obeyed in the broken phase. A realistic parametrization of the model in the N=4 case, based on the vacuum values of the curvature masses, shows that a sigma mass of around 450 MeV can be obtained. The equations are renormalized after extending our previous results for the N=1 case by means of the general procedure described in [J. Berges et al., Annals Phys. 320, 344-398 (2005)]. When restricted to the Hartree-Fock approximation, our approach reveals that certain problems raised in the literature concerning the renormalization are completely lifted. Finally, we introduce a new type of Phi-derivable approximation in which the gap equation is not solved at the same level of accuracy as the accuracy at which the potential is computed. We discuss the consistency and applicability of these types of "hybrid" approximations and illustrate them in the two-loop case by showing that the corresponding effective potential is renormalizable and that the transition remains of the second order.Comment: 26 pages, 9 figures, uses RevTeX4-1, published versio

O(4) ϕ^4 model as an effective light meson theory: A lattice-continuum comparison

We investigate the possibility of using the 4 dimensional $O(4)$ symmetric $\phi^4$ model as an effective theory for the sigma-pion system. We carry out lattice Monte Carlo simulations to establish the triviality bound in the case of explicitly broken symmetry and to compare it with results from continuum functional methods. In case of a physical parametrization we find that triviality restricts the possible lattice spacings to a narrow range, therefore cutoff independence in the effective theory sense is practically impossible for thermal quantities. We match the critical line in the space of bare couplings in the different approaches and compare vacuum physical quantities along the line of constant physics (LCP).Comment: 9 pages, 8 figures, published versio

Bose-Einstein condensation and Silver Blaze property from the two-loop Φ\Phi-derivable approximation

We extend our previous investigation of the two-loop $\Phi$-derivable approximation to finite chemical potential $\mu$ and discuss Bose-Einstein condensation (BEC) in the case of a charged scalar field with $O(2)$ symmetry. We show that the approximation is renormalizable by means of counterterms which are independent of both the temperature and the chemical potential. We point out the presence of an additional skew contribution to the propagator as compared to the $\mu=0$ case, which comes with its own gap equation (except at Hartree level). We solve this equation together with the field equation, and the usual longitudinal and transversal gap equations to find that the transition is second order, in agreement with recent lattice results to which we compare. We also discuss a general criterion an approximation should obey for the so-called Silver Blaze property to hold, and we show that any $\Phi$-derivable approximation at finite temperature and density obeys this criterion if one chooses a UV regularization that does not cut off the Matsubara sums.Comment: 22 pages, 6 figures, uses RevTeX 4-

Erdészeti utak szubjektív állapotfelvétele és értékelése

Az erdészeti utak megépítésük után fenntartásra szorulnak. A jó járhatóság megőrzése érdekében a fenntartási munkákat a teljes úthálózat állapotának és a nehéz forgalom nagyságának ismeretében a megfelelő időben és módon kell végrehajtani. Az informatika és a digitális technika felhasználásával létrehozható egy olyan hatékony eszközrendszer és mérési módszer, amelynek segítségével az erdészeti utak állapotáról kis időráfordítással tájékozódhatunk. Az Intézetünkben kifejlesztett digitális szubjektív állapotfelvételi és állapotértékelési rendszer naponta 20-25 km erdészeti út állapotának rögzítését és kiértékelését teszi lehetővé. Ha az erdőgazdaság digitális útnyilvántartással rendelkezik, akkor az erdészeti utak állapota a geoinformatikai rendszerben megjeleníthető. Ennek felhasználásával a várható forgalom ismeretében a szükséges útfenntartási beavatkozások és azok becsült költsége megtervezhető. Az általunk létrehozott rendszert több mint 1000 km erdészeti úton teszteltük. Erre az adatbázisra támaszkodva a közel 3000 km-es burkolt erdészeti úthálózat állapotára is következtethetünk