Non-equilibrium behavior at a liquid-gas critical point

Second-order phase transitions in a non-equilibrium liquid-gas model with reversible mode couplings, i.e., model H for binary-fluid critical dynamics, are studied using dynamic field theory and the renormalization group. The system is driven out of equilibrium either by considering different values for the noise strengths in the Langevin equations describing the evolution of the dynamic variables (effectively placing these at different temperatures), or more generally by allowing for anisotropic noise strengths, i.e., by constraining the dynamics to be at different temperatures in d_par- and d_perp-dimensional subspaces, respectively. In the first, case, we find one infrared-stable and one unstable renormalization group fixed point. At the stable fixed point, detailed balance is dynamically restored, with the two noise strengths becoming asymptotically equal. The ensuing critical behavior is that of the standard equilibrium model H. At the novel unstable fixed point, the temperature ratio for the dynamic variables is renormalized to infinity, resulting in an effective decoupling between the two modes. We compute the critical exponents at this new fixed point to one-loop order. For model H with spatially anisotropic noise, we observe a critical softening only in the d_perp-dimensional sector in wave vector space with lower noise temperature. The ensuing effective two-temperature model H does not have any stable fixed point in any physical dimension, at least to one-loop order. We obtain formal expressions for the novel critical exponents in a double expansion about the upper critical dimension d_c = 4 - d_par and with respect to d_par, i.e., about the equilibrium theory.Comment: 17 pages, revtex, one figure and EPJB style files include

Boundary Conditions for Kerr-AdS Perturbations

The Teukolsky master equation and its associated spin-weighted spheroidal harmonic decomposition simplify considerably the study of linear gravitational perturbations of the Kerr(-AdS) black hole. However, the formulation of the problem is not complete before we assign the physically relevant boundary conditions. We find a set of two Robin boundary conditions (BCs) that must be imposed on the Teukolsky master variables to get perturbations that are asymptotically global AdS, i.e. that asymptotes to the Einstein Static Universe. In the context of the AdS/CFT correspondence, these BCs allow a non-zero expectation value for the CFT stress-energy tensor while keeping fixed the boundary metric. When the rotation vanishes, we also find the gauge invariant differential map between the Teukolsky and the Kodama-Ishisbashi (Regge-Wheeler-Zerilli) formalisms. One of our Robin BCs maps to the scalar sector and the other to the vector sector of the Kodama-Ishisbashi decomposition. The Robin BCs on the Teukolsky variables will allow for a quantitative study of instability timescales and quasinormal mode spectrum of the Kerr-AdS black hole. As a warm-up for this programme, we use the Teukolsky formalism to recover the quasinormal mode spectrum of global AdS-Schwarzschild, complementing previous analysis in the literature.Comment: 33 pages, 6 figure

AdS nonlinear instability: moving beyond spherical symmetry

Anti-de Sitter (AdS) is conjectured to be nonlinear unstable to a weakly turbulent mechanism that develops a cascade towards high frequencies, leading to black hole formation [1,2]. We give evidence that the gravitational sector of perturbations behaves differently from the scalar one studied in [2]. In contrast with [2], we find that not all gravitational normal modes of AdS can be nonlinearly extended into periodic horizonless smooth solutions of the Einstein equation. In particular, we show that even seeds with a single normal mode can develop secular resonances, unlike the spherically symmetric scalar field collapse studied in [2]. Moreover, if the seed has two normal modes, more than one resonance can be generated at third order, unlike the spherical collapse of [2]. We also show that weak turbulent perturbative theory predicts the existence of direct and inverse cascades, with the former dominating the latter for equal energy two-mode seeds.Comment: 7 pages, no figures, 2 table

Klein-Gordon oscillator in a topologically nontrivial space-time

In this study, we analyze solutions of the wave equation for scalar particles in a space-time with nontrivial topology. Solutions for the Klein--Gordon oscillator are found considering two configurations of this space-time. In the first one, it is assumed the $S^{1}\times R^{3}$ space where the metric is written in the usual inertial frame of reference. In the second case, we consider a rotating reference frame adapted to the circle S1. We obtained compact expressions for the energy spectrum and for the particles wave functions in both configurations. Additionally, we show that the energy spectrum of the solution associated to the rotating system has an additional term that breaks the symmetry around $E = 0$

Ages and metallicities of star clusters: new calibrations and diagnostic diagrams from visible integrated spectra

We present homogeneous scales of ages and metallicities for star clusters from very young objects, through intermediate-age ones up to the oldest known clusters. All the selected clusters have integrated spectra in the visible range, as well as reliable determinations of their ages and metallicities. From these spectra equivalent widths (EWs) of KCaII, Gband(CH) and MgI metallic, and Hdelta, Hgamma and Hbeta Balmer lines have been measured homogeneously. The analysis of these EWs shows that the EW sums of the metallic and Balmer H lines, separately, are good indicators of cluster age for objects younger than 10 Gyr, and that the former is also sensitive to cluster metallicity for ages greater than 10 Gyr. We propose an iterative procedure for estimating cluster ages by employing two new diagnostic diagrams and age calibrations based on the above EW sums. For clusters older than 10 Gyr, we also provide a calibration to derive their overall metal contents.Comment: 9 pages, 4 figures, accepted by A&

On the P-representable subset of all bipartite Gaussian separable states

P-representability is a necessary and sufficient condition for separability of bipartite Gaussian states only for the special subset of states whose covariance matrix are $Sp(2,R)\otimes Sp(2,R)$ locally invariant. Although this special class of states can be reached by a convenient $Sp(2,R)\otimes Sp(2,R)$ transformation over an arbitrary covariance matrix, it represents a loss of generality, avoiding inference of many general aspects of separability of bipartite Gaussian states.Comment: Final version with new results added. Slightly more detailed than the accepted manuscript (to appear in Phys. Rev. A

A model for the time uncertainty measurements in the Auger surface detector array

The precise determination of the arrival direction of cosmic rays is a fundamental prerequisite for the search for sources or the study of their anisotropies on the sky. One of the most important aspects to achieve an optimal measurement of these directions is to properly take into account the measurement uncertainties in the estimation procedure. In this article we present a model for the uncertainties associated with the time measurements in the Auger surface detector array. We show that this model represents well the measurement uncertainties and therefore provides the basis for an optimal determination of the arrival direction. With this model and a description of the shower front geometry it is possible to estimate, on an event by event basis, the uncertainty associated with the determination of the arrival directions of the cosmic rays