Primordial Bispectrum Information from CMB Polarization

After the precise observations of the Cosmic Microwave Background (CMB) anisotropy power spectrum, attention is now being focused on the higher order statistics of the CMB anisotropies. Since linear evolution preserves the statistical properties of the initial conditions, observed non-Gaussianity of the CMB will mirror primordial non-Gaussianity. Single field slow-roll inflation robustly predicts negligible non-Gaussianity so an indication of non-Gaussianity will suggest alternative scenarios need to be considered. In this paper we calculate the information on primordial non-Gaussianity encoded in the polarization of the CMB. After deriving the optimal weights for a cubic estimator we evaluate the Signal-to-Noise ratio of the estimator for WMAP, Planck and an ideal cosmic variance limited experiment. We find that when the experiment can observe CMB polarization with good sensitivity, the sensitivity to primordial non-Gaussianity increases by roughly a factor of two. We also test the weakly non-Gaussian assumption used to derive the optimal weight factor by calculating the degradation factor produced by the gravitational lensing induced connected four-point function. The physical scales in the radiative transfer functions are largely irrelevant for the constraints on the primordial non-Gaussianity. We show that the total (S/N)^2 is simply proportional to the number of observed pixels on the sky.Comment: To be submitted to PRD, 25 pages, 6 figure

Phase transition in the Countdown problem

Here we present a combinatorial decision problem, inspired by the celebrated quiz show called the countdown, that involves the computation of a given target number T from a set of k randomly chosen integers along with a set of arithmetic operations. We find that the probability of winning the game evidences a threshold phenomenon that can be understood in the terms of an algorithmic phase transition as a function of the set size k. Numerical simulations show that such probability sharply transitions from zero to one at some critical value of the control parameter, hence separating the algorithm's parameter space in different phases. We also find that the system is maximally efficient close to the critical point. We then derive analytical expressions that match the numerical results for finite size and permit us to extrapolate the behavior in the thermodynamic limit.Comment: Submitted for publicatio

Traffic jams and intermittent flows in microfluidic networks

We investigate both experimentally and theoretically the traffic of particles flowing in microfluidic obstacle networks. We show that the traffic dynamics is a non-linear process: the particle current does not scale with the particle density even in the dilute limit where no particle collision occurs. We demonstrate that this non-linear behavior stems from long range hydrodynamic interactions. Importantly, we also establish that there exists a maximal current above which no stationary particle flow can be sustained. For higher current values, intermittent traffic jams form thereby inducing the ejection of the particles from the initial path and the subsequent invasion of the network. Eventually, we put our findings in the broader context of the transport proccesses of driven particles in low dimension

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

Gauge invariant Boltzmann equation and the fluid limit

This article investigates the collisionless Boltzmann equation up to second order in the cosmological perturbations. It describes the gauge dependence of the distribution function and the construction of a gauge invariant distribution function and brightness, and then derives the gauge invariant fluid limit.Comment: 36 page

CMB 3-point functions generated by non-linearities at recombination

We study the 3-point functions generated at recombination in the squeezed triangle limit, when one mode has a wavelength much larger than the other two and is outside the horizon. The presence of the long wavelength mode cannot change the physics inside the horizon but modifies how a late time observer sees the anisotropies. The effect of the long wavelength mode can be divided into a redefinition of time and spatial scales, a Shapiro time delay and gravitational lensing. The separation is gauge dependent but helps develop intuition. We show that the resulting 3-point function corresponds to an f_NL < 1 and that its shape is different from that created by the f_NL (or local) model.Comment: 16 pages, 4 figures. Expanded introduction of sec.2. Published versio

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

Electronic structure of crystalline binary and ternary Cd-Te-O compounds

The electronic structure of crystalline CdTe, CdO, $\alpha$-TeO$_2$, CdTeO$_3$ and Cd$_3$TeO$_6$ is studied by means of first principles calculations. The band structure, total and partial density of states, and charge densities are presented. For $\alpha$-TeO$_2$ and CdTeO$_3$, Density Functional Theory within the Local Density Approximation (LDA) correctly describes the insulating character of these compounds. In the first four compounds, LDA underestimates the optical bandgap by roughly 1 eV. Based on this trend, we predict an optical bandgap of 1.7 eV for Cd$_3$TeO$_6$. This material shows an isolated conduction band with a low effective mass, thus explaining its semiconducting character observed recently. In all these oxides, the top valence bands are formed mainly from the O 2p electrons. On the other hand, the binding energy of the Cd 4d band, relative to the valence band maximum, in the ternary compounds is smaller than in CdTe and CdO.Comment: 13 pages, 15 figures, 2 tables. Accepted in Phys Rev

Long-range Casimir interactions between impurities in nematic liquid crystals and the collapse of polymer chains in such solvents

The elastic interactions between objects embedded in a nematic liquid crystal are usually caused by the average distorsion-rather than by the fluctuations-of the nematic orientational field. We argue that for sufficiently small particles, the nematic-mediated interaction originates purely from the fluctuations of the nematic director. This Casimir interaction decays as d^(-6), d being the distance between the particles, and it dominates van der Waals interactions close to the isotropic-to-nematic transition. Considering the nematic as a polymer solvent, we show that the onset of this Casimir interaction at the isotropic-to-nematic transition can discontinuously induce the collapse of a flexible polymer chain from the swollen state to the globular state, without crossing the Theta-point.Comment: 6 pages, 1 figur

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