Geometry and observables in (2+1)-gravity

We review the geometrical properties of vacuum spacetimes in (2+1)-gravity with vanishing cosmological constant. We explain how these spacetimes are characterised as quotients of their universal cover by holonomies. We explain how this description can be used to clarify the geometrical interpretation of the fundamental physical variables of the theory, holonomies and Wilson loops. In particular, we discuss the role of Wilson loop observables as the generators of the two fundamental transformations that change the geometry of (2+1)-spacetimes, grafting and earthquake. We explain how these variables can be determined from realistic measurements by an observer in the spacetime.Comment: Talk given at 2nd School and Workshop on Quantum Gravity and Quantum Geometry (Corfu, September 13-20 2009); 10 pages, 13 eps figure

Control of unstable macroscopic oscillations in the dynamics of three coupled Bose condensates

We study the dynamical stability of the macroscopic quantum oscillations characterizing a system of three coupled Bose-Einstein condensates arranged into an open-chain geometry. The boson interaction, the hopping amplitude and the central-well relative depth are regarded as adjustable parameters. After deriving the stability diagrams of the system, we identify three mechanisms to realize the transition from an unstable to stable behavior and analyze specific configurations that, by suitably tuning the model parameters, give rise to macroscopic effects which are expected to be accessible to experimental observation. Also, we pinpoint a system regime that realizes a Josephson-junction-like effect. In this regime the system configuration do not depend on the model interaction parameters, and the population oscillation amplitude is related to the condensate-phase difference. This fact makes possible estimating the latter quantity, since the measure of the oscillating amplitudes is experimentally accessible.Comment: 25 pages, 12 figure

Topology and phase transitions: a paradigmatic evidence

We report upon the numerical computation of the Euler characteristic \chi (a topologic invariant) of the equipotential hypersurfaces \Sigma_v of the configuration space of the two-dimensional lattice $\phi^4$ model. The pattern \chi(\Sigma_v) vs. v (potential energy) reveals that a major topology change in the family {\Sigma_v}_{v\in R} is at the origin of the phase transition in the model considered. The direct evidence given here - of the relevance of topology for phase transitions - is obtained through a general method that can be applied to any other model.Comment: 4 pages, 4 figure

Spectral Properties of Coupled Bose-Einstein Condensates

We investigate the energy spectrum structure of a system of two (identical) interacting bosonic wells occupied by N bosons within the Schwinger realization of the angular momentum. This picture enables us to recognize the symmetry properties of the system Hamiltonian H and to use them for characterizing the energy eigenstates. Also, it allows for the derivation of the single-boson picture which is shown to be the background picture naturally involved by the secular equation for H. After deriving the corresponding eigenvalue equation, we recast it in a recursive N-dependent form which suggests a way to generate the level doublets (characterizing the H spectrum) via suitable inner parameters. Finally, we show how the presence of doublets in the spectrum allows to recover, in the classical limit, the symmetry breaking effect that characterizes the system classically.Comment: 8 pages, 3 figures; submitted to Phys. Rev. A. The present extended form replaces the first version in the letter forma

Relationship between food industries maturity and quality certification

Purpose: The purpose of this paper is to analyze the PDP (Product Development Process) maturity level in the food industry to identify the compatibility status of their quality certification and their maturity level.Design/methodology/approach: A bibliographical review was conducted about product development, maturity process, and Capability Maturity Model Integration (CMMI). An adapted method from CMMI was used, which allows evaluating the level of maturity, through a semi-structured questionnaire. The questionnaires were applied in five companies of this industry and then, an analysis of the information obtained in each company was carried out and compared, aiming to understand the sector maturity.Findings: After conducting the interviews in each company, the median of each group of questions was calculated, according to the methodology described. Data collected from this sector show consistency between certification time and maturity level. Research limitations/implications: Due to the low number of respondents, this data cannot be generalized to this sector, being considered only an indication of the situation of the food industry located in Curitiba region. Practical implications: This study shows the relationship between the maturity level of food industry and ISO 9001 quality certification. The study shows that for the company to obtain an ISO certification, it must have been at least maturity level 2, highlighting, as well, the main deficiencies of this sector. Originality/value: The original value is to show the relationship between the maturity level of food industry and ISO 9001 quality certification

Phase transitions as topology changes in configuration space: an exact result

The phase transition in the mean-field XY model is shown analytically to be related to a topological change in its configuration space. Such a topology change is completely described by means of Morse theory allowing a computation of the Euler characteristic--of suitable submanifolds of configuration space--which shows a sharp discontinuity at the phase transition point, also at finite N. The present analytic result provides, with previous work, a new key to a possible connection of topological changes in configuration space as the origin of phase transitions in a variety of systems.Comment: REVTeX file, 5 pages, 1 PostScript figur

Nonadiabatic effects in the dynamics of atoms confined in a cylindric time-orbiting-potential magnetic trap

In a time-orbiting-potential magnetic trap the neutral atoms are confined by means of an inhomogeneous magnetic field superimposed to an uniform rotating one. We perform an analytic study of the atomic motion by taking into account the nonadiabatic effects arising from the spin dynamics about the local magnetic field. Geometric-like magnetic-fields determined by the Berry's phase appear within the quantum description. The application of a variational procedure on the original quantum equation leads to a set of dynamical evolution equations for the quantum average value of the position operator and of the spin variables. Within this approximation we derive the quantum-mechanical ground state configuration matching the classical adiabatic solution and perform some numerical simulations.Comment: 12 pages, 4 figure

Hamiltonian Hopf bifurcations in the discrete nonlinear Schr\"odinger trimer: oscillatory instabilities, quasiperiodic solutions and a 'new' type of self-trapping transition

Oscillatory instabilities in Hamiltonian anharmonic lattices are known to appear through Hamiltonian Hopf bifurcations of certain time-periodic solutions of multibreather type. Here, we analyze the basic mechanisms for this scenario by considering the simplest possible model system of this kind where they appear: the three-site discrete nonlinear Schr\"odinger model with periodic boundary conditions. The stationary solution having equal amplitude and opposite phases on two sites and zero amplitude on the third is known to be unstable for an interval of intermediate amplitudes. We numerically analyze the nature of the two bifurcations leading to this instability and find them to be of two different types. Close to the lower-amplitude threshold stable two-frequency quasiperiodic solutions exist surrounding the unstable stationary solution, and the dynamics remains trapped around the latter so that in particular the amplitude of the originally unexcited site remains small. By contrast, close to the higher-amplitude threshold all two-frequency quasiperiodic solutions are detached from the unstable stationary solution, and the resulting dynamics is of 'population-inversion' type involving also the originally unexcited site.Comment: 25 pages, 11 figures, to be published in J. Phys. A: Math. Gen. Revised and shortened version with few clarifying remarks adde

The Origins of Phase Transitions in Small Systems

The identification and classification of phases in small systems, e.g. nuclei, social and financial networks, clusters, and biological systems, where the traditional definitions of phase transitions are not applicable, is important to obtain a deeper understanding of the phenomena observed in such systems. Within a simple statistical model we investigate the validity and applicability of different classification schemes for phase transtions in small systems. We show that the whole complex temperature plane contains necessary information in order to give a distinct classification.Comment: 3 pages, 4 figures, revtex 4 beta 5, for further information see http://www.smallsystems.d

Density and distribution of euphausiid larvae in the Scotia Sea in the 2011 summer

Monitoring of early euphausiid larvae provides valuable information on the mechanisms involved in recruitment to the adult populations. As the Antarctic is undergoing rapid environmental change, these mechanisms are key to ecosystem-based management of the krill fishery. We analyzed the distribution and abundance of early euphausiid larvae (calyptopes I to late furciliae) from 76 plankton samples from surface to 300 m depth in the Atlantic sector in January 2011 in relation with a previous survey and published information. Thysanoessa macrura (mean density: 209 ind m−2) dominated the sampling while Euphausia superba (mean density: 13.63 ind m−2) and Euphausia frigida (mean density: 10.05 ind m−2) were also present. T. macrura density increased while E. superba experienced a high decrease respect to historical data. Clustering of stations and correspondence analysis showed that the associations of larvae and water masses are in agreement with literature reports, so the differences on the abundance of early larvae are within the observed variability and cannot be attributed to any single factor, suggesting that it is due to more subtle changes such as the stability of the water column and/or vorticity in the fronts.Fil: Rombola, Emilce Florencia. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Ministerio de Relaciones Exteriores, Comercio Interno y Culto. Dirección Nacional del Antártico. Instituto Antártico Argentino; ArgentinaFil: Franzosi, C.. Ministerio de Relaciones Exteriores, Comercio Interno y Culto. Dirección Nacional del Antártico. Instituto Antártico Argentino; ArgentinaFil: Tosonotto, G.. Ministerio de Relaciones Exteriores, Comercio Interno y Culto. Dirección Nacional del Antártico. Instituto Antártico Argentino; ArgentinaFil: Vivequin, Sandra Maria. Ministerio de Relaciones Exteriores, Comercio Interno y Culto. Dirección Nacional del Antártico. Instituto Antártico Argentino; ArgentinaFil: Alder, Viviana Andrea. Ministerio de Relaciones Exteriores, Comercio Interno y Culto. Dirección Nacional del Antártico. Instituto Antártico Argentino; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Ecología, Genética y Evolución de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Ecología, Genética y Evolución de Buenos Aires; ArgentinaFil: Marschoff, Enrique Ricardo. Ministerio de Relaciones Exteriores, Comercio Interno y Culto. Dirección Nacional del Antártico. Instituto Antártico Argentino; Argentin