Quantum gas mixtures in different correlation regimes

We present a many-body description for two-component ultracold bosonic gases when one of the species is in the weakly interacting regime and the other is either weakly or strongly interacting. In the one-dimensional limit the latter case system is a hybrid in which a Tonks-Girardeau gas is immersed in a Bose-Einstein condensate, which is an example of a new class of quantum system involving a tunable, superfluid environment. We describe the process of phase separation microscopically and semiclassically in both situations and show that the quantum correlations are maintained in the separated phase.Comment: 4 pages, 3 figure

On the Localization of the Personalized PageRank of Complex Networks

In this paper new results on personalized PageRank are shown. We consider directed graphs that may contain dangling nodes. The main result presented gives an analytical characterization of all the possible values of the personalized PageRank for any node.We use this result to give a theoretical justification of a recent model that uses the personalized PageRank to classify users of Social Networks Sites. We introduce new concepts concerning competitivity and leadership in complex networks. We also present some theoretical techniques to locate leaders and competitors which are valid for any personalization vector and by using only information related to the adjacency matrix of the graph and the distribution of its dangling nodes

Testing microscopic discretization

What can we say about the spectra of a collection of microscopic variables when only their coarse-grained sums are experimentally accessible? In this paper, using the tools and methodology from the study of quantum nonlocality, we develop a mathematical theory of the macroscopic fluctuations generated by ensembles of independent microscopic discrete systems. We provide algorithms to decide which multivariate gaussian distributions can be approximated by sums of finitely-valued random vectors. We study non-trivial cases where the microscopic variables have an unbounded range, as well as asymptotic scenarios with infinitely many macroscopic variables. From a foundational point of view, our results imply that bipartite gaussian states of light cannot be understood as beams of independent d-dimensional particle pairs. It is also shown that the classical description of certain macroscopic optical experiments, as opposed to the quantum one, requires variables with infinite cardinality spectra.Comment: Proof of strong NP-hardness. Connection with random walks. New asymptotic results. Numerous typos correcte

Effects of gabergic phenols on the dynamic and structure of lipid bilayers: A molecular dynamic simulation approach

γ-Aminobutyric acid (GABA) is the major inhibitory neurotransmitter in the vertebrate and invertebrate nervous system. GABAA receptors are activated by GABA and their agonists, and modulated by a wide variety of recognized drugs, including barbiturates, anesthetics, and benzodiazepines. The phenols propofol, thymol, chlorothymol, carvacrol and eugenol act as positive allosteric modulators on GABAA-R receptor. These GABAergic phenols interact with the lipid membrane, therefore, their anesthetic activity could be the combined result of their specific activity (with receptor proteins) as well as nonspecific interactions (with surrounding lipid molecules) modulating the supramolecular organization of the receptor environment. Therefore, we aimed to contribute to a description of the molecular events that occur at the membrane level as part of the mechanism of general anesthesia, using a molecular dynamic simulation approach. Equilibrium molecular dynamics simulations indicate that the presence of GABAergic phenols in a DPPC bilayer orders lipid acyl chains for carbons near the interface and their effect is not significant at the bilayer center. Phenols interacts with the polar interface of phospholipid bilayer, particularly forming hydrogen bonds with the glycerol and phosphate group. Also, potential of mean force calculations using umbrella sampling show that propofol partition is mainly enthalpic driven at the polar region and entropic driven at the hydrocarbon chains. Finally, potential of mean force indicates that propofol partition into a gel DPPC phase is not favorable. Our in silico results were positively contrasted with previous experimental data.Fil: Miguel, Virginia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Investigaciones Biológicas y Tecnológicas. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas, Físicas y Naturales. Instituto de Investigaciones Biológicas y Tecnológicas; ArgentinaFil: Villarreal, Marcos Ariel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Investigaciones en Físico-química de Córdoba. Universidad Nacional de Córdoba. Facultad de Ciencias Químicas. Instituto de Investigaciones en Físico-química de Córdoba; ArgentinaFil: Garcia, Daniel Asmed. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Investigaciones Biológicas y Tecnológicas. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas, Físicas y Naturales. Instituto de Investigaciones Biológicas y Tecnológicas; Argentin

Numerical Study of a Lyapunov Functional for the Complex Ginzburg-Landau Equation

We numerically study in the one-dimensional case the validity of the functional calculated by Graham and coworkers as a Lyapunov potential for the Complex Ginzburg-Landau equation. In non-chaotic regions of parameter space the functional decreases monotonically in time towards the plane wave attractors, as expected for a Lyapunov functional, provided that no phase singularities are encountered. In the phase turbulence region the potential relaxes towards a value characteristic of the phase turbulent attractor, and the dynamics there approximately preserves a constant value. There are however very small but systematic deviations from the theoretical predictions, that increase when going deeper in the phase turbulence region. In more disordered chaotic regimes characterized by the presence of phase singularities the functional is ill-defined and then not a correct Lyapunov potential.Comment: 20 pages,LaTeX, Postcript version with figures included available at http://formentor.uib.es/~montagne/textos/nep