Critical behavior of dissipative two-dimensional spin lattices

We explore critical properties of two-dimensional lattices of spins interacting via an anisotropic Heisenberg Hamiltonian and subject to incoherent spin flips. We determine the steady-state solution of the master equation for the density matrix via the corner-space renormalization method. We investigate the finite-size scaling and critical exponent of the magnetic linear susceptibility associated to a dissipative ferromagnetic transition. We show that the Von Neumann entropy increases across the critical point, revealing a strongly mixed character of the ferromagnetic phase. Entanglement is witnessed by the quantum Fisher information which exhibits a critical behavior at the transition point, showing that quantum correlations play a crucial role in the transition even though the system is in a mixed state.Comment: Accepted for publication on Phys. Rev. B (6 pages, 5 figures

The Maximal Amount of Gravitational Waves in the Curvaton Scenario

The curvaton scenario for the generation of the cosmological curvature perturbation on large scales represents an alternative to the standard slow-roll scenario of inflation in which the observed density perturbations are due to fluctuations of the inflaton field itself. Its basic assumption is that the initial curvature perturbation due to the inflaton field is negligible. This is attained by lowering the energy scale of inflation, thereby highly suppressing the amount of gravitational waves produced during inflation. We compute the power-spectrum of the gravitational waves generated at second order in perturbation theory by the curvaton (isocurvature) perturbations between the end of inflation and the curvaton decay. An interesting property of this contribution to the tensor perturbations is that it is directly proportional to the amount of non-Gaussianity predicted within the curvaton scenario. We show that the spectrum of gravitational waves may be in the range of future gravitational wave detectors.Comment: 4 pages, laTeX; added a clarifying comment in the conclusions, version matches publication in PRD, Rapid Communication

CMB Anisotropies at Second Order I

We present the computation of the full system of Boltzmann equations at second-order describing the evolution of the photon, baryon and cold dark matter fluids. These equations allow to follow the time evolution of the Cosmic Microwave Background (CMB) anisotropies at second-order at all angular scales from the early epoch, when the cosmological perturbations were generated, to the present through the recombination era. This paper sets the stage for the computation of the full second-order radiation transfer function at all scales and for a a generic set of initial conditions specifying the level of primordial non-Gaussianity. In a companion paper, we will present the computation of the three-point correlation function at recombination which is so relevant for the issue of non-Gaussianity in the CMB anisotropies.Comment: 26 pages, LaTeX file, typos correcte

On the non-Gaussianity from Recombination

The non-linear effects operating at the recombination epoch generate a non-Gaussian signal in the CMB anisotropies. Such a contribution is relevant because it represents a major part of the second-order radiation transfer function which must be determined in order to have a complete control of both the primordial and non-primordial part of non-Gaussianity in the CMB anisotropies. We provide an estimate of the level of non-Gaussianity in the CMB arising from the recombination epoch which shows up mainly in the equilateral configuration. We find that it causes a contamination to the possible measurement of the equilateral primordial bispectrum shifting the minimum detectable value of the non-Gaussian parameter f^equil_NL by Delta f^equil_NL= O(10) for an experiment like Planck.Comment: LaTeX file; 11 pages. v2: Typos corrected; references added; comments about the effective non-linearity parameter added in Sec. IV; comments added in the conclusions of Sec. IV. v3: References added; some clarifications added as footnotes 4 and 6, and in Sec. 3. Matches version accepted for publication in JCA

Non-Gaussianity in the Cosmic Microwave Background Anisotropies at Recombination in the Squeezed limit

We estimate analytically the second-order cosmic microwave background temperature anisotropies at the recombination epoch in the squeezed limit and we deduce the contamination to the primordial local non-Gaussianity. We find that the level of contamination corresponds to f_NL^{con}=O(1) which is below the sensitivity of present experiments and smaller than the value O(5) recently claimed in the literature.Comment: LaTeX file; 15 pages. Slightly revised version. Main result unchange

High order correlation functions for self interacting scalar field in de Sitter space

We present the expressions of the three- and four-point correlation functions of a self interacting light scalar field in a de Sitter spacetime at tree order respectively for a cubic and a quartic potential. Exact expressions are derived and their limiting behaviour on super-horizon scales are presented. Their essential features are shown to be similar to those obtained in a classical approach.Comment: 8 pages, 4 figure

Infinitesimal and local convexity of a hypersurface in a semi-Riemannian manifold

Given a Riemannian manifold M and a hypersurface H in M, it is well known that infinitesimal convexity on a neighborhood of a point in H implies local convexity. We show in this note that the same result holds in a semi-Riemannian manifold. We make some remarks for the case when only timelike, null or spacelike geodesics are involved. The notion of geometric convexity is also reviewed and some applications to geodesic connectedness of an open subset of a Lorentzian manifold are given.Comment: 14 pages, AMSLaTex, 2 figures. v2: typos fixed, added one reference and several comments, statement of last proposition correcte

Bouncing or sticky droplets: impalement transitions on superhydrophobic micropatterned surfaces

When a liquid drops impinges a hydrophobic rough surface it can either bounce off the surface (fakir droplets) or be impaled and strongly stuck on it (Wenzel droplets). The analysis of drop impact and quasi static ''loading'' experiments on model microfabricated surfaces allows to clearly identify the forces hindering the impalement transitions. A simple semi-quantitative model is proposed to account for the observed relation between the surface topography and the robustness of fakir non-wetting states. Motivated by potential applications in microfluidics and in the fabrication of self cleaning surfaces, we finally propose some guidelines to design robust superhydrophobic surfaces.Comment: 7 pages, 5 figure

A new approach to cosmological perturbations in f(R) models

We propose an analytic procedure that allows to determine quantitatively the deviation in the behavior of cosmological perturbations between a given f(R) modified gravity model and a LCDM reference model. Our method allows to study structure formation in these models from the largest scales, of the order of the Hubble horizon, down to scales deeply inside the Hubble radius, without employing the so-called "quasi-static" approximation. Although we restrict our analysis here to linear perturbations, our technique is completely general and can be extended to any perturbative order.Comment: 21 pages, 2 figures; Revised version according to reviewer's suggestions; Typos corrected; Added Reference