Proefschrift Universiteit van Amsterdam. / Met lit.opg. en samenvatting in het Nederlands.

El asunto de la presente investigación pretende abordar el tema de la materia en el físico contemporáneo Werner Heisenberg. Partiendo de la tesis de que la física ha buscado siempre la unidad en la formulación de teorías frente a la multiplicidad fenoménica, se busca estudiar la teoría cuántica desde una perspectiva filosófica, como un intento más por alcanzar dicha unidad. Dado que la ciencia, desde la perspectiva de Popper, es un saber conjetural, a lo largo de la historia se ha tenido que reformular y restringir la validez de las teorías a la luz de nuevos resultados experimentales. La historia de las ideas científicas está marcada por diversos hitos que han llevado a un claro diálogo interdisciplinario entre ciencia y filosofía. Uno de estos “momentos” es la elaboración de la teoría cuántica. Al interior de dicho momento se encuentra Heisenberg. Así, la búsqueda por la unidad en toda teoría física es inherente a su propia estructura. Ahora bien, la física contemporánea surgió como consecuencia del descubrimiento de una serie de fenómenos que no eran posibles de abordar mediante la física clásica. De este modo, el estudio de las estructuras atómicas volvió a sacar a luz la vieja interrogante, ¿de qué están hechas las cosas?. Dicho de otro modo, ¿es posible concebir un mundo físico que se sustente en un fundamento material único y que a su vez sea posible conocerlo, es decir, de acceder a él? Con todo, la tesis consiste en mostrar la filosofía de la física que se encuentra, en muchos puntos implícita, en la obra de Werner Heisenberg y circunscribirla al problema de la materia; entendiendo por tal problemática, la pregunta por el fundamento de la realidad. Con ello se pretende mostrar cómo el pensamiento de Platón y Aristóteles determinan, filosóficamente hablando, la búsqueda por el fundamento último del mundo físico en el mencionado autor. Teniendo presente este desarrollo hemos pretendido mostrar que a través de dicho diálogo interdisciplinario entre física y filosofía, Heisenberg elabora una concepción simbólica de la materia muy en la línea de un idealismo platónico, aunque matizado en muchos punto por un realismo aristotélico.

The physics of the one-dimensional (I-D) Ising, XY and Heisenberg systems as well as the two-dimensional (2-D) Heisenberg and XY systems differ from the 2-D Ising and three-dimensional (3-D) Heisenberg magnets in that they do not show magnetic order in the presence of magnetic short-range correlations for T --70 K. Small deviations from ideal behaviour induced by single-ion anisotropy, magnetic dipole interaction or intrachainar, intraplanar superexchange, can result in the introduction of long-range (3-D) magnetic ordering. The lattice geometry in conjunction with the anisotropy of the spin system may introduce magnetic frustration effects, chirality ordering or Kosterlitz-Thouless behaviour. In this thesis a collection of papers is presented on different aspects of the magnetic ordering behaviour in quasi 1-0 and 2-D magnetic model systems with XY -like anisotropy where in the case of the quasi I -0 hexagonal ABX3 ternary halides additional low-dimensional aspects are introduced in the magnetic ordering behaviour due to the 2-D network - a triangular lattice - of the magnetic ions perpendicular to the chain-axis. Consequently, frustration effects as well as chirality ordering can be observed for particular compounds. The magnetic ordering phenomena in the quasi 1-0 AFeX3 halides will be presented. These systems show singlet groundstate or induced moment behaviour. Their magnetic ordering behaviour can be influenced by an external order parameter such as an applied magnetic field (HI/c) or an applied uniaxial pressure (P//a). The ordering behaviour is strongly dependent on relatively small changes in the structural parameters. The magnetic ordering behaviour for a diluted induced-moment system is investigated for the solid solution RbFel-xMgxCl3 and mixed ferro-antiferromagnetic induced-moment system for the solid solution RbFeCI3-xBrx. The magnetic phase diagrams for these sytems have been determined. The effect of the magnetic ordering on the magnetic excitations was studied for the singlet groundstate system CsFeBr3 in the presence of an applied field along the chain direction and perpendicular to the chain direction as well as for the induced moment system RbFeBr3. The influence of a slight structural distortion of the trigonal basal plane and its influence on the magnetic ordering behaviour and excitations at the magnetic soft mode point have been investigated. In the case of triangular antiferromagnets with XY anisotropy, geometrical frustration leads to magnetic structures of the 120' type. The magnetic moments in such a system are condensed into the basal plane where the magnetic moments form plaquettes of spins which rotate 120' either clockwise or anti-clockwise. This chirality order introduces an extra degree of freedom which results in new universality classes for the critical exponents of such a type of system. On symmetry grounds it has been shown that the chiral ordering can be removed in the presence of an electric field along the direction of the magnetic ordering vector. Experimental evidence has been presented to underwrite this theoretical prediction. The 2-D XY model does not sustain long-range order for T - OK. However, Berezinskii, Kosterlitz and Thouless have shown that for this model a phase transition to low temperature phase does exist. This phase has an infinite correlation length but no spontaneous order. Evidence for the existence of such a phase in the quasi 2-D ferromagnet Rb2CrCl4 has been presented. A similar behaviour may be present in the in the quasi 2-D weak ferromagnets AMnP03.H20: A += NH4, ND4, K, CnH2n+ I. Magnetisation data are presented in support of this hypothesis.

Desde o surgimento da mecânica quântica no início do século XX, ela vem sendo alvo de diversos estudos e suas característcas fazem com que a mesma seja descrita de forma totalmente diferente da teoria clássica. Com o aprofundamento em suas áreas, surgiram novos conceitos e a compreensão sobre a teoria da informação e computação quântica foi radicalmente mudada devido a uma propriedade básica da mecânica quântica, o emaranhamento. Assim, a popularização da ideia do computador quântico trouxe consigo uma série de pesquisas relacionadas a informação quântica e suas aplicações no mundo real. Nesta dissertação apresentamos um estudo sobre a construção de um critério de emaranhamento geral, no qual podemos aplicá-lo a quaisquer sistemas possuindo um Hamiltoniano descrito por cadeias de spins, seja ele bipartido ou multipartido. Esse critério é baseado na covariância de um observável geral que pode ou não possuir termos de interações entre os spins. Entretanto, esse critério pode ser facilmente reduzido a variância, uma vez que esta é muito mais adequada para a aplicação em sistemas físicos. Desta maneira, podemos utilizar a susceptibilidade magnética e o calor específico como testemunhas de emaranhamento para o critério, em razão da sua facilidade de medidas experimentais. / Since the advent of quantum mechanics in the early twentieth century, it has been the subject of several studies and their features cause it to be described quite differently from classical theory. With the deepening in their fields, there were new concepts and understanding about information theory and quantum computing has been radically changed due to a basic property of quantum mechanics, the entanglement. Thus, the popularization of the idea of the quantum computer has brought a lot of research related to quantum information and its applications in the real world. In this thesis we present a study about a construction of a general criterion of entanglement, in which we can apply it to any system having a Hamiltonian described by spin chains, either bipartite or multipartite. This criterion is based on general observables covariance that may or may not possess terms of interactions between spins. However, this criterion can be easily reduced to the variance, since this is more suitable for use in physical systems. In this way, we can use the magnetic susceptibility and the specific heat as witnesses of entanglement for the criterion, because of their ease of experimental measurements.

Desde o surgimento da mecânica quântica no início do século XX, ela vem sendo alvo de diversos estudos e suas característcas fazem com que a mesma seja descrita de forma totalmente diferente da teoria clássica. Com o aprofundamento em suas áreas, surgiram novos conceitos e a compreensão sobre a teoria da informação e computação quântica foi radicalmente mudada devido a uma propriedade básica da mecânica quântica, o emaranhamento. Assim, a popularização da ideia do computador quântico trouxe consigo uma série de pesquisas relacionadas a informação quântica e suas aplicações no mundo real. Nesta dissertação apresentamos um estudo sobre a construção de um critério de emaranhamento geral, no qual podemos aplicá-lo a quaisquer sistemas possuindo um Hamiltoniano descrito por cadeias de spins, seja ele bipartido ou multipartido. Esse critério é baseado na covariância de um observável geral que pode ou não possuir termos de interações entre os spins. Entretanto, esse critério pode ser facilmente reduzido a variância, uma vez que esta é muito mais adequada para a aplicação em sistemas físicos. Desta maneira, podemos utilizar a susceptibilidade magnética e o calor específico como testemunhas de emaranhamento para o critério, em razão da sua facilidade de medidas experimentais. / Since the advent of quantum mechanics in the early twentieth century, it has been the subject of several studies and their features cause it to be described quite differently from classical theory. With the deepening in their fields, there were new concepts and understanding about information theory and quantum computing has been radically changed due to a basic property of quantum mechanics, the entanglement. Thus, the popularization of the idea of the quantum computer has brought a lot of research related to quantum information and its applications in the real world. In this thesis we present a study about a construction of a general criterion of entanglement, in which we can apply it to any system having a Hamiltonian described by spin chains, either bipartite or multipartite. This criterion is based on general observables covariance that may or may not possess terms of interactions between spins. However, this criterion can be easily reduced to the variance, since this is more suitable for use in physical systems. In this way, we can use the magnetic susceptibility and the specific heat as witnesses of entanglement for the criterion, because of their ease of experimental measurements.

Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / FundaÃÃo Cearense de Apoio ao Desenvolvimento Cientifico e TecnolÃgico / Nesta dissertaÃÃao, estudamos as superfÃcies mÃnimas do grupo de Heisenberg tridimensional, bem como a aplicaÃÃo de Gauss destas superfÃcies. Inicialmente à feito uma breve exposiÃÃo sobre a geometria do grupo de Heisenberg. EntÃo, mostramos que, em tal espaÃo: as Ãnicas superfÃcies com aplicaÃÃo de Gauss constante sÃo os planos verticais; nÃo existem superfÃcies totalmente umbÃlicas nem superfÃcies mÃnimas compactas; toda superfÃcie mÃnima Ã, necessariamente, estÃvel. Mostramos, ainda, que as Ãnicas superfÃcies mÃnimas verticais sÃo os planos verticais. Por fim, apresentamos uma classificaÃÃo das superfÃcies com aplicaÃÃo de Gauss de posto constante, igual a zero ou um. / In this report, we study minimal surfaces of the tridimensional Heisenberg group, as well as their Gauss maps. We begin with a short presentation of the geometry of the Heisenberg group. Then, we show that, in this space: the only surfaces with constant Gauss map are the vertical planes; there are no totally umbilical surfaces nor compact minimal surfaces; every minimal surface is, necessarily, stable. We also show that the only vertical minimal surfaces are vertical planes. Finally, we present a classification of the surfaces with Gauss map of constant rank, equal to zero or one.

Imagine a crystalline world of tiny, discrete "cells", each knowing only what its nearest neighbors do. Each volume of space contains only a finite amount of information, because space and time come in discrete units. In such a universe, we'll construct analogs of particles and fields ??d ask what it would mean for these to satisfy constraints like conservation of momentum. In each case classical mechanics will break down ?? scales both small and large, and strange phenomena emerge: a maximal velocity, a slowing of internal clocks, a bound on simultaneous measurement, and quantum-like effects in very weak or intense fields. This fantasy about conservation in cellular arrays was inspired by this first conference on computation and physics, a subject destined to produce profound and powerful theories. I wish this essay could include one such; alas, it only portrays images of what such theories might be like. The "cellular array" idea is popular already in such forms as Ising models, renormalization theories, the "Game of Life" and Von Neumann's work on self-producing machines. This essay exploits many unpublished ideas I got from Edward Fredkin. The ideas about field and particle are original; Richard Feynman persuaded me to consider fields instead of forces, but is not responsible for my compromise on potential surfaces. I also thank Danny Hillis and Richard Stallman for other ideas.

There is no abstract available for this thesis.

Thesis (Ph. D.)--University of Texas at Austin, 1999. / Vita. Includes bibliographical references (leaves 93-94). Available also in a digital version from Dissertation Abstracts.

Universiẗat, Diss., 2004--Mainz.