DEVELOPMENT AND APPLICATIONS OF TIME-DEPENDENT DENSITY MATRIX FUNCTIONAL THEORY

En esta tesis estudiamos las teorías sobre la Matriz Densidad Reducida (MDR) como un marco prometedor. Nos enfocamos sobre esta teorías desde dos aspectos: Primero, usamos algunos modelos sencillos hechos con dos partículas las cuales estan armónicamente confinadas como una base para ilustrar la utilidad de la matriz densidad. Para tales sistemas, usamos la MDR de un cuerpo para calcular algunas cantidades de interés tales como densidad de momentum. Posteriormente obtenemos los orbitales naturales y su número de ocupación para algunos de los modelos, y en uno de los casos expresamos la MDR de dos cuerpos de manera exacta en términos de la MDR de un cuerpo. También usamos el teorema diferencial del virial para establecer una descripción unificada de la familia entera de estos sistemas modelo en términos de la densidad. En la seguna parte cambiamos a casos fuera del equilibrio y analizamos la así llamada jerarquía BBGKY de ecuaciones para describir la evolución temporal de un sistema de muchos cuerpos en términos de sus MDRs (a todos los órdenes). Proveemos un exhaustivo estudio de los desafíos y problemas abiertos ligados a la truncación de tales jerarquías de ecuaciones para hacerlas aplicables. Restringimos nuestro análisis a la evolución acoplada de la MDR de uno y dos cuerpos, donde los efectos de correlación de alto orden estan embebidos dentro de la aproximación usada para cerrar las ecuaciones. Probamos que dentro de esta aproximación, el número de electrones y la energía total se conservan, sin importar la aproximación usada. Luego, demostramos que aplicando los esquemas de truncación de estado base para llevar los electrones a comportamientos indeseables y no físicos, tales como la violación e incluso la divergencia en la densidad electrónica local, tanto en regímenes correlacionados débiles y fuertes.

The propagation of nerve pulses: From the Hodgkin-Huxley model to the soliton theory

The present project aims to describe and study the nature and transmission of nerve pulses. First we review a classical model by Hodgkin-Huxley which describes the nerve pulse as a pure electric signal which propagates due to the opening of some time- and voltage-dependent ion channels. Although this model was quite successful when introduced, it fails to provide a satisfactory explanation to other phenomena that occur in the transmission of nerve pulses, therefore a new theory seems to be necessary. The soliton theory is one such theory, which we explain after introducing two topics that are important for its understanding: (i) the lipid melting of membranes, which are found to display nonlinearity and dispersion during the melting transition, and (ii) the discovery and the conditions required for the existence of solitons. In the soliton theory, the pulse is presented as an electromechanical soliton which forces the membrane through the transition while propagating. The action of anesthesia is also explained in the new framework by the melting point depression caused by anesthetics. Finally, we present a comparison between the two models.

Treewidth: theory and applications to computer science

This report is an introduction to the concept of treewidth, a property of graphs that has important implications in algorithms. Some basic concepts of graph theory are presented in the first chapter for those readers that are not familiar with the notation. In Chapter 2, the definition of treewidth and some different ways of characterizing it are explained. The last two chapters focus on the algorithmic implications of treewidth, which are very relevant in Computer Science. An algorithm to compute the treewidth of a graph is presented and its result can be later applied to many other problems in graph theory, like those introduced in the last chapter.

Learning to perceive in the sensor motor approach: Piaget's theory of equilibration interpreted dynamically

Learning to perceive is faced with a classical paradox: if understanding is required for perception, how can we learn to perceive something new, something we do not yet understand? According to the sensorimotor approach, perception involves mastery of regular sensorimotor co-variations that depend on the agent and the environment, also known as the "laws" of sensorimotor contingencies (SMCs). In this sense, perception involves enacting relevant sensorimotor skills in each situation. It is important for this proposal that such skills can be learned and refined with experience and yet up to this date, the sensorimotor approach has had no explicit theory of perceptual learning. The situation is made more complex if we acknowledge the open-ended nature of human learning. In this paper we propose Piaget's theory of equilibration as a potential candidate to fulfill this role. This theory highlights the importance of intrinsic sensorimotor norms, in terms of the closure of sensorimotor schemes. It also explains how the equilibration of a sensorimotor organization faced with novelty or breakdowns proceeds by re-shaping pre-existing structures in coupling with dynamical regularities of the world. This way learning to perceive is guided by the equilibration of emerging forms of skillful coping with the world. We demonstrate the compatibility between Piaget's theory and the sensorimotor approach by providing a dynamical formalization of equilibration to give an explicit micro-genetic account of sensorimotor learning and, by extension, of how we learn to perceive. This allows us to draw important lessons in the form of general principles for open-ended sensorimotor learning, including the need for an intrinsic normative evaluation by the agent itself. We also explore implications of our micro-genetic account at the personal level.

Spectroscopic properties and Judd-Ofelt theory analysis of Dy3+ doped oxyfluoride silicate glass

Dy3+ doped oxyfluoride silicate glass was prepared and its optical absorption, 1.3 mu m emission, and upconversion luminescence properties were studied. Furthermore, the Judd-Ofelt [Phys. Rev. 127, 750 (1962); J. Chem. Phys. 37, 511 (1962)] intensity parameters, oscillator strengths, spontaneous transition probability, fluorescence branching ratio and radiative lifetime were calculated by Judd-Ofelt theory, while stimulated emission cross section of H-6(9/2)+F-6(11/2)-> H-6(15/2) transition was calculated by McCumber theory [Phys. Rev. A. 134, 299 (1964)]. According to the obtained Judd-Ofelt intensity parameters Omega(2)=2.69x10(-20) cm(2), Omega(4)=1.64x10(-20) cm(2), and Omega(6)=1.64x10(-20) cm(2), the radiative lifetime was calculated to be 810 mu s for 1.3 mu m emission, whose full width at half maximum and sigma(e) were 115 nm and 2.21x10(-20)cm(2), respectively. In addition, near infrared to visible upconversion luminescence was observed and evaluated. The results suggest that Dy3+ doped oxyfluoride silicate glass can be used as potential host material for developing broadband optical amplifiers and laser applications.