The static potential in {\cal N}=4 supersymmetric Yang-Mills at weak coupling

We compute the static potential associated to the locally 1/2 BPS Wilson loop in ${\cal N}$=4 supersymmetric Yang-Mills theory with ${\cal O}(\lambda^2/r)$ accuracy. We also resum the leading logarithms, of ${\cal O}(\lambda^{n+1}\ln^n\lambda/r)$, and show the structure of the renormalization group equation at next-to-leading order in the multipole expansion. In order to obtain these results it is crucial the use of an effective theory for the ultrasoft degrees of freedom. We develop this theory up to next-to-leading order in the multipole expansion. Using the same formalism we also compute the leading logarithms, of ${\cal O}(\lambda^{n+3}\ln^n\lambda/r)$, of the static potential associated to an ordinary Wilson loop in the same theory.Comment: 6 pages, 1 figure. Two references added, misprints corrected. Computation of the static potential associated to the ordinary static Wilson loop incorporate

Preparing the bound instance of quantum entanglement

Among the possibly most intriguing aspects of quantum entanglement is that it comes in "free" and "bound" instances. Bound entangled states require entangled states in preparation but, once realized, no free entanglement and therefore no pure maximally entangled pairs can be regained. Their existence hence certifies an intrinsic irreversibility of entanglement in nature and suggests a connection with thermodynamics. In this work, we present a first experimental unconditional preparation and detection of a bound entangled state of light. We consider continuous-variable entanglement, use convex optimization to identify regimes rendering its bound character well certifiable, and realize an experiment that continuously produced a distributed bound entangled state with an extraordinary and unprecedented significance of more than ten standard deviations away from both separability and distillability. Our results show that the approach chosen allows for the efficient and precise preparation of multimode entangled states of light with various applications in quantum information, quantum state engineering and high precision metrology.Comment: The final version accounts for a recent comment in Nature Physics [24] clarifying that a previous claim of having generated bound entanglement [23] was not supported by the authors' data. We also extended our introduction and discussion and also added reference

A Herschel [C II] Galactic plane survey II: CO-dark H2 in clouds

ABRIDGED: Context: HI and CO large scale surveys of the Milky Way trace the diffuse atomic clouds and the dense shielded regions of molecular hydrogen clouds. However, until recently, we have not had spectrally resolved C+ surveys to characterize the photon dominated interstellar medium, including, the H2 gas without C, the CO-dark H2, in a large sample of clouds. Aims: To use a sparse Galactic plane survey of the 1.9 THz [C II] spectral line from the Herschel Open Time Key Programme, Galactic Observations of Terahertz C+ (GOT C+), to characterize the H2 gas without CO in a statistically significant sample of clouds. Methods: We identify individual clouds in the inner Galaxy by fitting [CII] and CO isotopologue spectra along each line of sight. We combine these with HI spectra, along with excitation models and cloud models of C+, to determine the column densities and fractional mass of CO-dark H2 clouds. Results: We identify 1804 narrow velocity [CII] interstellar cloud components in different categories. About 840 are diffuse molecular clouds with no CO, 510 are transition clouds containing [CII] and 12CO, but no 13CO, and the remainder are dense molecular clouds containing 13CO emission. The CO-dark H2 clouds are concentrated between Galactic radii 3.5 to 7.5 kpc and the column density of the CO-dark H2 layer varies significantly from cloud-to-cloud with an average 9X10^(20) cm-2. These clouds contain a significant fraction of CO-dark H2 mass, varying from ~75% for diffuse molecular clouds to ~20% for dense molecular clouds. Conclusions: We find a significant fraction of the warm molecular ISM gas is invisible in HI and CO, but is detected in [CII]. The fraction of CO-dark H2 is greatest in the diffuse clouds and decreases with increasing total column density, and is lowest in the massive clouds.Comment: 21 pages, 19 figures, accepted for publication in A&A (2014

The role of noise and initial conditions in the asymptotic solution of a bounded confidence, continuous-opinion model

We study a model for continuous-opinion dynamics under bounded confidence. In particular, we analyze the importance of the initial distribution of opinions in determining the asymptotic configuration. Thus, we sketch the structure of attractors of the dynamical system, by means of the numerical computation of the time evolution of the agents density. We show that, for a given bound of confidence, a consensus can be encouraged or prevented by certain initial conditions. Furthermore, a noisy perturbation is added to the system with the purpose of modeling the free will of the agents. As a consequence, the importance of the initial condition is partially replaced by that of the statistical distribution of the noise. Nevertheless, we still find evidence of the influence of the initial state upon the final configuration for a short range of the bound of confidence parameter