Analytical properties of horizontal visibility graphs in the Feigenbaum scenario

Time series are proficiently converted into graphs via the horizontal visibility (HV) algorithm, which prompts interest in its capability for capturing the nature of different classes of series in a network context. We have recently shown [B. Luque et al., PLoS ONE 6, 9 (2011)] that dynamical systems can be studied from a novel perspective via the use of this method. Specifically, the period-doubling and band-splitting attractor cascades that characterize unimodal maps transform into families of graphs that turn out to be independent of map nonlinearity or other particulars. Here, we provide an in depth description of the HV treatment of the Feigenbaum scenario, together with analytical derivations that relate to the degree distributions, mean distances, clustering coefficients, etc., associated to the bifurcation cascades and their accumulation points. We describe how the resultant families of graphs can be framed into a renormalization group scheme in which fixed-point graphs reveal their scaling properties. These fixed points are then re-derived from an entropy optimization process defined for the graph sets, confirming a suggested connection between renormalization group and entropy optimization. Finally, we provide analytical and numerical results for the graph entropy and show that it emulates the Lyapunov exponent of the map independently of its sign.

Horizontal visibility graphs generated by type-I intermittency

The type-I intermittency route to (or out of) chaos is investigated within the horizontal visibility (HV) graph theory. For that purpose, we address the trajectories generated by unimodal maps close to an inverse tangent bifurcation and construct their associatedHVgraphs.We showhowthe alternation of laminar episodes and chaotic bursts imprints a fingerprint in the resulting graph structure. Accordingly, we derive a phenomenological theory that predicts quantitative values for several network parameters. In particular, we predict that the characteristic power-law scaling of the mean length of laminar trend sizes is fully inherited by the variance of the graph degree distribution, in good agreement with the numerics. We also report numerical evidence on how the characteristic power-law scaling of the Lyapunov exponent as a function of the distance to the tangent bifurcation is inherited in the graph by an analogous scaling of block entropy functionals defined on the graph. Furthermore, we are able to recast the full set of HV graphs generated by intermittent dynamics into a renormalization-group framework, where the fixed points of its graph-theoretical renormalization-group flow account for the different types of dynamics.We also establish that the nontrivial fixed point of this flow coincides with the tangency condition and that the corresponding invariant graph exhibits extremal entropic properties.

Quasiperiodic Graphs: Structural Design, Scaling and Entropic Properties

A novel class of graphs, here named quasiperiodic, are const ructed via application of the Horizontal Visibility algorithm to the time series generated along the quasiperiodic route to chaos. We show how the hierarchy of mode-locked regions represented by the Far ey tree is inherited by their associated graphs. We are able to establish, via Renormalization Group (RG) theory, the architecture of the quasiperiodic graphs produced by irrational winding numbers with pure periodic continued fraction. And finally, we demonstrate that the RG fixed-point degree distributions are recovered via optimization of a suitably defined graph entropy

Phase Transitions in Disordered Systems: The Example of the Random-Field Ising Model in Four Dimensions

By performing a high-statistics simulation of the D = 4 random-field Ising model at zero temperature for different shapes of the random-field distribution, we show that the model is ruled by a single universality class. We compute to a high accuracy the complete set of critical exponents for this class, including the correction-to-scaling exponent. Our results indicate that in four dimensions (i) dimensional reduction as predicted by the perturbative renormalization group does not hold and (ii) three independent critical exponents are needed to describe the transition.

Phase diagram of the three-band half-filled Cu-O two-leg ladder

We determine the phase diagram of the half-filled two-leg ladder both at weak and strong coupling, taking into account the Cu d(x)(2)-y(2) and the O p(x) and p(y) orbitals. At weak coupling, renormalization group flows are interpreted with the use of bosonization. Two different models with and without outer oxygen orbitals are examined. For physical parameters, and in the absence of the outer oxygen orbitals, the D-Mott phase arises; a dimerized phase appears when the outer oxygen atoms are included. We show that the circulating current phase that preserves translational symmetry does not appear at weak coupling. In the opposite strong-coupling atomic limit the model is purely electrostatic and the ground states may be found by simple energy minimization. The phase diagram so obtained is compared to the weak-coupling one.

Classical simulation of quantum many-body systems with a tree tensor network

We show how to efficiently simulate a quantum many-body system with tree structure when its entanglement (Schmidt number) is small for any bipartite split along an edge of the tree. As an application, we show that any one-way quantum computation on a tree graph can be efficiently simulated with a classical computer.

Impurity scattering in a Luttinger liquid with electron-phonon coupling

We study the influence of electron-phonon coupling on electron transport through a Luttinger liquid with an embedded weak scatterer or weak link. We derive the renormalization group (RG) equations, which indicate that the directions of RG flows can change upon varying either the relative strength of the electron-electron and electron-phonon coupling or the ratio of Fermi to sound velocities. This results in a rich phase diagram with up to three fixed points: an unstable one with a finite value of conductance and two stable ones, corresponding to an ideal metal or insulator.

Quantum wire hybridized with a single-level impurity

We have studied low-temperature properties of interacting electrons in a one-dimensional quantum wire (Luttinger liquid) side-hybridized with a single-level impurity. The hybridization induces a backscattering of electrons in the wire which strongly affects its low-energy properties. Using a one-loop renormalization group approach valid for a weak electron-electron interaction, we have calculated a transmission coefficient through the wire, T(epsilon), and a local density of states, nu(epsilon) at low energies epsilon. In particular, we have found that the antiresonance in T(epsilon) has a generalized Breit-Wigner shape with the effective width Gamma(epsilon) which diverges at the Fermi level.

Impurity scattering in Luttinger liquid with electron-phonon coupling

We study the influence of electron-phonon coupling on electron transport through a Luttinger liquid with an embedded weak scatterer or weak link. We derive the renormalization group (RG) equations which indicate that the directions of RG flows can change upon varying either the relative strength of the electron-electron and electron-phonon coupling or the ratio of Fermi to sound velocities. This results in the rich phase diagram with up to three fixed points: an unstable one with a finite value of conductance and two stable ones, corresponding to an ideal metal or insulator.

Universal duality in a Luttinger liquid coupled to a generic environment

We study a Luttinger liquid (LL) coupled to a generic environment consisting of bosonic modes with arbitrary density-density and current-current interactions. The LL can be either in the conducting phase and perturbed by a weak scatterer or in the insulating phase and perturbed by a weak link. The environment modes can also be scattered by the imperfection in the system with arbitrary transmission and reflection amplitudes. We present a general method of calculating correlation functions under the presence of the environment and prove the duality of exponents describing the scaling of the weak scatterer and of the weak link. This duality holds true for a broad class of models and is sensitive to neither interaction nor environmental modes details, thus it shows up as the universal property. It ensures that the environment cannot generate new stable fixed points of the renormalization group flow. Thus, the LL always flows toward either conducting or insulating phase. Phases are separated by a sharp boundary which is shifted by the influence of the environment. Our results are relevant, for example, for low-energy transport in (i) an interacting quantum wire or a carbon nanotube where the electrons are coupled to the acoustic phonons scattered by the lattice defect; (ii) a mixture of interacting fermionic and bosonic cold atoms where the bosonic modes are scattered due to an abrupt local change of the interaction; (iii) mesoscopic electric circuits.

Dynamics of cholesteric liquid crystals in the presence of a random magnetic field:stochastic dynamics of cholesteric liquid crystal

Based on dynamic renormalization group techniques, this letter analyzes the effects of external stochastic perturbations on the dynamical properties of cholesteric liquid crystals, studied in presence of a random magnetic field. Our analysis quantifies the nature of the temperature dependence of the dynamics; the results also highlight a hitherto unexplored regime in cholesteric liquid crystal dynamics. We show that stochastic fluctuations drive the system to a second-ordered Kosterlitz-Thouless phase transition point, eventually leading to a Kardar-Parisi-Zhang (KPZ) universality class. The results go beyond quasi-first order mean-field theories, and provides the first theoretical understanding of a KPZ phase in distorted nematic liquid crystal dynamics.

Leading birds by their beaks : the response of flocks to external perturbations

Peer reviewed

Bosonization and entanglement spectrum for one-dimensional polar bosons on disordered lattices

Ultra cold polar bosons in a disordered lattice potential, described by the extended Bose-Hubbard model, display a rich phase diagram. In the case of uniform random disorder one finds two insulating quantum phases-the Mott-insulator and the Haldane insulator-in addition to a superfluid and a Bose glass phase. In the case of a quasiperiodic potential, further phases are found, e.g. the incommensurate density wave, adiabatically connected to the Haldane insulator. For the case of weak random disorder we determine the phase boundaries using a perturbative bosonization approach. We then calculate the entanglement spectrum for both types of disorder, showing that it provides a good indication of the various phases.

Accidental SUSY: Enhanced bulk supersymmetry from brane back-reaction

We compute how bulk loops renormalize both bulk and brane effective interactions for codimension-two branes in 6D gauged chiral supergravity, as functions of the brane tension and brane-localized flux. We do so by explicitly integrating out hyper- and gauge-multiplets in 6D gauged chiral supergravity compactified to 4D on a flux-stabilized 2D rugby-ball geometry, specializing the results of a companion paper, arXiv:1210.3753 , to the supersymmetric case. While the brane back-reaction generically breaks supersymmetry, we show that the bulk supersymmetry can be preserved if the amount of brane- localized flux is related in a specific BPS-like way to the brane tension, and verify that the loop corrections to the brane curvature vanish in this special case. In these systems it is the brane-bulk couplings that fix the size of the extra dimensions, and we show that in some circumstances the bulk geometry dynamically adjusts to ensure the supersymmetric BPS-like condition is automatically satisfied. We investigate the robustness of this residual supersymmetry to loops of non-supersymmetric matter on the branes, and show that supersymmetry- breaking effects can enter only through effective brane-bulk interactions involving at least two derivatives. We comment on the relevance of this calculation to proposed applications of codimension-two 6D models to solutions of the hierarchy and cosmological constant problems. © 2013 SISSA.

Análisis de posicionamiento en el sector de servicios de hosterías en el Valle de Yunguilla y propuesta de diseño de un plan estratégico de marketing para la hostería “Los Cisnes” en el periodo 2015-2018

El proyecto está enfocado al desarrollo de un Plan Estratégico aplicado a Hostería “Los Cisnes”. Tiene como objetivo contribuir con el desarrollo organizacional de la empresa, hacer frente a la competencia con la finalidad de prestar un servicio de calidad.Para la consecución de lo mencionado anteriormente se realizó un esquema que contempla lo siguiente: Se Expone conceptos y definiciones básicos de marketing que se necesitarán a lo largo del desarrollo del proyecto para el entendimiento del mismo.Se realizó el estudio del sector mediante encuestas y entrevistas aplicadas a personas que hacen uso del servicio de hostería y a los administradores de estos establecimientos. Para la obtención de resultados se utilizó el programa SPSS donde se emplearon variables e indicadores. Se estableció un ranking de acuerdo al catastro de establecimientos otorgado por el Ministerio de Turismo, encontrándose Hostería Los Cisnes en el tercer lugar, esto de acuerdo a la encuesta aplicada por las autoras del trabajo de titulación. Se desarrolló la situación actual de la empresa mediante herramientas como: análisis del micro-entrono y macro-entorno, análisis FODA, matriz EFI, matriz EFE, matriz BCG. Se desarrolló el Plan Estratégico de Marketing que contempla: misión, visión, objetivos, implementación de estrategias, planes de acción y presupuestos, es decir, está formado por todos los recursos necesarios para posicionamiento de la empresa.Finalmente se presenta las conclusiones y recomendaciones que fortalezcan la realización de las estrategias planteadas y que a la vez determinen resultados óptimos para la hostería.