Real space mapping of topological invariants using artificial neural networks

Topological invariants allow to characterize Hamiltonians, predicting the existence of topologically protected in-gap modes. Those invariants can be computed by tracing the evolution of the occupied wavefunctions under twisted boundary conditions. However, those procedures do not allow to calculate a topological invariant by evaluating the system locally, and thus require information about the wavefunctions in the whole system. Here we show that artificial neural networks can be trained to identify the topological order by evaluating a local projection of the density matrix. We demonstrate this for two different models, a 1-D topological superconductor and a 2-D quantum anomalous Hall state, both with spatially modulated parameters. Our neural network correctly identifies the different topological domains in real space, predicting the location of in-gap states. By combining a neural network with a calculation of the electronic states that uses the Kernel Polynomial Method, we show that the local evaluation of the invariant can be carried out by evaluating a local quantity, in particular for systems without translational symmetry consisting of tens of thousands of atoms. Our results show that supervised learning is an efficient methodology to characterize the local topology of a system.Comment: 9 pages, 6 figure

Dynamical generation of wormholes with charged fluids in quadratic Palatini gravity

The dynamical generation of wormholes within an extension of General Relativity (GR) containing (Planck's scale-suppressed) Ricci-squared terms is considered. The theory is formulated assuming the metric and connection to be independent (Palatini formalism) and is probed using a charged null fluid as a matter source. This has the following effect: starting from Minkowski space, when the flux is active the metric becomes a charged Vaidya-type one, and once the flux is switched off the metric settles down into a static configuration such that far from the Planck scale the geometry is virtually indistinguishable from that of the standard Reissner-Nordstr\"om solution of GR. However, the innermost region undergoes significant changes, as the GR singularity is generically replaced by a wormhole structure. Such a structure becomes completely regular for a certain charge-to-mass ratio. Moreover, the nontrivial topology of the wormhole allows to define a charge in terms of lines of force trapped in the topology such that the density of lines flowing across the wormhole throat becomes a universal constant. To the light of our results we comment on the physical significance of curvature divergences in this theory and the topology change issue, which support the view that space-time could have a foam-like microstructure pervaded by wormholes generated by quantum gravitational effects.Comment: 14 pages, 3 figures, revtex4-1 style. New content added on section VI. Other minor corrections introduced. Final version to appear in Phys. Rev.

Frictions, cracks and micro-resistances: physical activity and sport as strategies to dignify imprisoned women

Discipline and control are key concepts within industrial and capitalist societies. In this context, prisons are a warning tool about the consequences of non-conformity [Foucault, M., 1995. Discipline and Punish: The birth of Prison. NY: Vintage Books]. As a result, punitive power is used as a corrective technique to transform prisoners into docile and useful citizen. However, power in prison is no static and inmates can create various strategies of resistance. The aim of this research is to understand how physical activity and sport are used by incarcerated women to confront social control and negotiate power relations. Underpinned within a critical feminist epistemology, we interviewed 16 women about their prison sports experience. According to the interviewees, physical activity and sport helped them to cope with the sentence while it was a useful tool confronting and negotiating the patriarchal punitive power. The women pointed out that the prison did not fully subdue them. Also, they highlighted their abilities to minimally destabilize the prison order. This enabled them to regain some autonomy and identity, while opposing to the total institution. Engaging in physical practices enabled incarcerated women to create small spaces of freedom and frictions within a limiting a prohibitive prison environmen

Black hole mass estimates in quasars - A comparative analysis of high- and low-ionization lines

The inter-line comparison between high- and low-ionization emission lines has yielded a wealth of information on the quasar broad line region (BLR) structure and dynamics, including perhaps the earliest unambiguous evidence in favor of a disk + wind structure in radio-quiet quasars. We carried out an analysis of the CIV 1549 and Hbeta line profiles of 28 Hamburg-ESO high luminosity quasars and of 48 low-z, low luminosity sources in order to test whether the high-ionization line CIV 1549 width could be correlated with Hbeta and be used as a virial broadening estimator. We analyze intermediate- to high-S/N, moderate resolution optical and NIR spectra covering the redshifted CIV and H$\beta$ over a broad range of luminosity log L ~ 44 - 48.5 [erg/s] and redshift (0 - 3), following an approach based on the quasar main sequence. The present analysis indicates that the line width of CIV 1549 is not immediately offering a virial broadening estimator equivalent to H$\beta$. At the same time a virialized part of the BLR appears to be preserved even at the highest luminosities. We suggest a correction to FWHM(CIV) for Eddington ratio (using the CIV blueshift as a proxy) and luminosity effects that can be applied over more than four dex in luminosity. Great care should be used in estimating high-L black hole masses from CIV 1549 line width. However, once corrected FWHM(CIV) values are used, a CIV-based scaling law can yield unbiased MBH values with respect to the ones based on H$\beta$ with sample standard deviation ~ 0.3 dex.Comment: 43 pages, 15 Figures, submitted to A&

Detection of the ISW effect and corresponding dark energy constraints made with directional spherical wavelets

Using a directional spherical wavelet analysis we detect the integrated Sachs-Wolfe (ISW) effect, indicated by a positive correlation between the first-year Wilkinson Microwave Anisotropy Probe (WMAP) and NRAO VLA Sky Survey (NVSS) data. Detections are made using both a directional extension of the spherical Mexican hat wavelet and the spherical butterfly wavelet. We examine the possibility of foreground contamination and systematics in the WMAP data and conclude that these factors are not responsible for the signal that we detect. The wavelet analysis inherently enables us to localise on the sky those regions that contribute most strongly to the correlation. On removing these localised regions the correlation that we detect is reduced in significance, as expected, but it is not eliminated, suggesting that these regions are not the sole source of correlation between the data. This finding is consistent with predictions made using the ISW effect, where one would expect weak correlations over the entire sky. In a flat universe the detection of the ISW effect provides direct and independent evidence for dark energy. We use our detection to constrain dark energy parameters by deriving a theoretical prediction for the directional wavelet covariance statistic for a given cosmological model. Comparing these predictions with the data we place constraints on the equation-of-state parameter $w$ and the vacuum energy density $\Omega_\Lambda$. We also consider the case of a pure cosmological constant, i.e. $w=-1$. For this case we rule out a zero cosmological constant at greater than the 99.9% significance level. All parameter estimates that we obtain are consistent with the standand cosmological concordance model values.Comment: 16 pages, 13 figures; replaced to match version accepted by MNRA

Graphite from the viewpoint of Landau level spectroscopy: An effective graphene bilayer and monolayer

We describe an infrared transmission study of a thin layer of bulk graphite in magnetic fields up to B = 34 T. Two series of absorption lines whose energy scales as sqrtB and B are present in the spectra and identified as contributions of massless holes at the H point and massive electrons in the vicinity of the K point, respectively. We find that the optical response of the K point electrons corresponds, over a wide range of energy and magnetic field, to a graphene bilayer with an effective inter-layer coupling 2\gamma_1, twice the value for a real graphene bilayer, which reflects the crystal ordering of bulk graphite along the c-axis. The K point electrons thus behave as massive Dirac fermions with a mass enhanced twice in comparison to a true graphene bilayer.Comment: 4 pages, 2 figure

Spectral Measures of Bipartivity in Complex Networks

We introduce a quantitative measure of network bipartivity as a proportion of even to total number of closed walks in the network. Spectral graph theory is used to quantify how close to bipartite a network is and the extent to which individual nodes and edges contribute to the global network bipartivity. It is shown that the bipartivity characterizes the network structure and can be related to the efficiency of semantic or communication networks, trophic interactions in food webs, construction principles in metabolic networks, or communities in social networks.Comment: 16 pages, 1 figure, 1 tabl