Unitariedad y unicidad en la cuantización de perturbaciones cosmológicas (Unitarity and uniqueness in the quantization of cosmological perturbations)

En este trabajo se estudia la cuantización de Fock de las perturbaciones escalares al modelo de Friedmann-Lemaître-Robertson-Walker con un campo escalar masivo como contenido material. Se considera el caso en el que las secciones espaciales son compactas, con la topología de una 3-esfera, como caso prototípico en el que no surgen divergencias infrarrojas en la cuantización, ya que los modos perturbativos, obtenidos a partir de los autoestados del operador de Laplace-Beltrami, forman una serie infinita pero discreta. Tras expandir las perturbaciones en estos modos, se obtiene el hamiltoniano del sistema hasta orden cuadrático en los mismos. Se introduce entonces una fijación casi completa del gauge y se realiza una transformación canónica para obtener una formulación manejable y conveniente del sistema. En el modelo así obtenido, en particular, se derivan las ecuaciones dinámicas. El resto del trabajo está dedicado al análisis de las ambigüedades intrínsecas a la elección de representación para la cuantización de Fock de la perturbación del campo escalar en el fondo cósmico dado por las variables homogéneas, descritas clásicamente. Se consideran tan sólo cuantizaciones determinadas por estructuras complejas que compartan la simetría bajo rotaciones SO(4) de las secciones espaciales. Se selecciona una elección particular de una tal estructura compleja y se prueba que, en la representación asociada, la dinámica de las perturbaciones es unitariamente implementable. Cualquier otra representación en la que el vacío sea invariante bajo el grupo SO(4) y cuya dinámica sea unitaria debe ser unitariamente equivalente a la seleccionada, y por lo tanto, no diferirá de ella en sus predicciones físicas, que pueden considerarse así robustas. [ABSTRACT] In this work, we study the Fock quantization of the scalar perturbations about the Friedmann-Lemaître-Robertson-Walker model with a scalar massive field as matter content. We consider the case in which the spatial sections are compact, with the topology of a 3-sphere, as the prototypical case in which no infrared divergences appear in the quantization, since the perturbative modes, obtained from the eigenstates of the Laplace-Beltrami operator, form an infinite but discrete series. After expanding the pertubations in these modes, the Hamiltonian of the system is obtained up to terms quadratic in them. An almost complete gauge fixing is then introduced and a canonical transformation performed in order to reach a manageable and convenient formulation of the system. In the model so attained, in particular, the dynamical equations are derived. The rest of the work is devoted to the analysis of the ambiguities inherent to the choice of representation for the Fock quantization of the perturbations of the scalar field on the cosmological background provided by the homogeneous variables, described classically. We only consider quantizations determined by complex structures which share the SO(4) rotation symmetry of the spatial sections. A particular choice of such a complex structure is selected and it is shown that the perturbations dynamics are unitarily implementable in the associated representation. Any other representation with an SO(4) invariant vacuum and whose dynamics be unitary is proven unitarily equivalent to the aforementioned one and, therefore, they will both yield the same physical predictions, which can hence be considered robust

Parque y fitodepuradora del Barrio de la Estación : recuperación de las capas metabólica, social y natural como conseduencia de la explotación minera

Recuperación de las capas metabólica, social y natural como consecuencia de la explotación minera, mediante la instalación de un sistema de fitodepuración, el cual se adapta a las necesidades de accesibilidad, paisajísitca y biológicas, en el Barrio de la Estación, Sallent del Llobregat

Effective dynamics of scalar perturbations in a flat Friedmann-Robertson-Walker spacetime in Loop Quantum Cosmology

We study the evolution of a homogeneous and isotropic spacetime whose spatial sections have three-torus topology, coupled to a massless scalar field with small scalar perturbations within loop quantum cosmology. We consider a proposal for the effective dynamics based on a previous hybrid quantization completed by us. Consequently, we introduce a convenient gauge fixing and adopt reduced canonical variables adapted to that hybrid quantum description. Besides, we keep backreaction contributions on the background coming from terms quadratic in the perturbations in the action of the system. We carry out a numerical analysis assuming that the inhomogeneities were in a massless vacuum state at distant past (where the initial data are set). At distant future, we observe a statistical amplification of the modes amplitude in the infrared region, as well as a phase synchronization arising from quantum gravity phenomena. A description of the perturbations in terms of the Mukhanov-Sasaki gauge invariants provides the same qualitative results. Finally, we analyze some consequences of the backreaction in our effective description.Comment: 15 pages, 9 figures. Accepted for publication in Phys. Rev.

Hybrid quantization of an inflationary model: The flat case

We present a complete quantization of an approximately homogeneous and isotropic universe with small scalar perturbations. We consider the case in which the matter content is a minimally coupled scalar field and the spatial sections are flat and compact, with the topology of a three-torus. The quantization is carried out along the lines that were put forward by the authors in a previous work for spherical topology. The action of the system is truncated at second order in perturbations. The local gauge freedom is fixed at the classical level, although different gauges are discussed and shown to lead to equivalent conclusions. Moreover, descriptions in terms of gauge-invariant quantities are considered. The reduced system is proven to admit a symplectic structure, and its dynamical evolution is dictated by a Hamiltonian constraint. Then, the background geometry is polymerically quantized, while a Fock representation is adopted for the inhomogeneities. The latter is selected by uniqueness criteria adapted from quantum field theory in curved spacetimes, which determine a specific scaling of the perturbations. In our hybrid quantization, we promote the Hamiltonian constraint to an operator on the kinematical Hilbert space. If the zero mode of the scalar field is interpreted as a relational time, a suitable ansatz for the dependence of the physical states on the polymeric degrees of freedom leads to a quantum wave equation for the evolution of the perturbations. Alternatively, the solutions to the quantum constraint can be characterized by their initial data on the minimum-volume section of each superselection sector. The physical implications of this model will be addressed in a future work, in order to check whether they are compatible with observations.Comment: 20 pages, no figures. v2: minor changes, in particular, abstract shortened, final discussion improve

Do you want to become (or be) a principal? No, thank you. The difficulties of forming an administrative team in the basque public schools

Los equipos directivos de los centros escolares tienen una importancia relevante tanto en el desarrollo de un liderazgo pedagógico acorde con las necesidades de la sociedad actual, como en la organización eficiente de los centros. Sin embargo en la Comunidad Autónoma Vasca (CAV) hay serias dificultades para que miembros del claustro del profesorado accedan a ocupar cargos de dirección. El objetivo de esta investigación ha sido investigar las dificultades para asignar canditatos/as para estos puestos de vital importancia para las comunidades educativas y entender las razones que tiene el profesorado para no presentarse al citado puesto de trabajo. Desde una perspectiva cualitativa se ha llevado a cabo un estudio de caso centrado en la escuela pública de Elgoibar (Gipuzkoa)School administrations not only have the important responsibility to develop the school’s pedagogical leadership in accordance with the needs of today's society, but they are also responsible for the efficient organization of the school itself. However, in the Basque Country (CAV), there are serious difficulties for teachers to transition into the leadership positions of the school’s administration. The objective of this research has been to investigate the difficulties in finding candidates for these positions of vital importance to the educational communities; and to understand the reasons why teachers aren’t presenting themselves for these administrative positions. From a qualitative perspective, a case study has been carried out focusing on the public school of Elgoibar (Gipuzkoa

A complete hybrid quantization in inhomogeneous cosmology

A complete quantization of a homogeneous and isotropic spacetime with closed spatial sections coupled to a massive scalar field is provided, within the framework of Loop Quantum Cosmology. We identify solutions with their initial data on the minimum volume section, and from this we construct the physical Hilbert space. Moreover, a perturbative study allows us to introduce small inhomogeneities. After gauge fixing, the inhomogeneous part of the system is reduced to a linear field theory. We then adopt a standard Fock representation to quantize these degrees of freedom. For the considered case of compact spatial topology, the requirements of: i) invariance under the spatial isometries, and ii) unitary implementation of the quantum dynamics, pick up a unique Fock representation and a particular set of canonical fields (up to unitary equivalence).Comment: 6 page

Spoken dialogue systems: architectures and applications

171 p.Technology and technological devices have become habitual and omnipresent. Humans need to learn tocommunicate with all kind of devices. Until recently humans needed to learn how the devices expressthemselves to communicate with them. But in recent times the tendency has become to makecommunication with these devices in more intuitive ways. The ideal way to communicate with deviceswould be the natural way of communication between humans, the speech. Humans have long beeninvestigating and designing systems that use this type of communication, giving rise to the so-calledSpoken Dialogue Systems.In this context, the primary goal of the thesis is to show how these systems can be implemented.Additionally, the thesis serves as a review of the state-of-the-art regarding architectures and toolkits.Finally, the thesis is intended to serve future system developers as a guide for their construction. For that

Using nodal coordinates as variables for the dimensional synthesis of mechanisms

The method of the lower deformation energy has been successfully used for the synthesis of mechanisms for quite a while. It has shown to be a versatile, yet powerful method for assisting in the design of mechanisms. Until now, most of the implementations of this method used the dimensions of the mechanism as the synthesis variables, which has some advantages and some drawbacks. For example, the assembly configuration is not taken into account in the optimization process, and this means that the same initial configuration is used when computing the deformed positions in each synthesis point. This translates into a reduction of the total search space. A possible solution to this problem is the use of a set of initial coordinates as variables for the synthesis, which has been successfully applied to other methods. This also has some additional advantages, such as the fact that any generated mechanism can be assembled. Another advantage is that the fixed joint locations are also included in the optimization at no additional cost. But the change from dimensions to initial coordinates means a reformulation of the optimization problem when using derivatives if one wants them to be analytically derived. This paper tackles this reformulation, along with a proper comparison of the use of both alternatives using sequential quadratic programming methods. In order to do so, some examples are developed and studied.The authors wish to thank the Spanish Ministry of Economy and Competitiveness for its support through Grant DPI2013-46329-P and DPI2016-80372-R. Additionally the authors wish to thank the Education Department of the Basque Government for ist support through grant IT947-16

Improving early design stage timing modeling in multicore based real-time systems

This paper presents a modelling approach for the timing behavior of real-time embedded systems (RTES) in early design phases. The model focuses on multicore processors - accepted as the next computing platform for RTES - and in particular it predicts the contention tasks suffer in the access to multicore on-chip shared resources. The model presents the key properties of not requiring the application's source code or binary and having high-accuracy and low overhead. The former is of paramount importance in those common scenarios in which several software suppliers work in parallel implementing different applications for a system integrator, subject to different intellectual property (IP) constraints. Our model helps reducing the risk of exceeding the assigned budgets for each application in late design stages and its associated costs.This work has received funding from the European Space Agency under Project Reference AO=17722=13=NL=LvH, and has also been supported by the Spanish Ministry of Science and Innovation grant TIN2015-65316-P. Jaume Abella has been partially supported by the MINECO under Ramon y Cajal postdoctoral fellowship number RYC-2013-14717.Peer ReviewedPostprint (author's final draft