L'interprétation causale de la mécanique quantique a été décrite en premier lieu par les historiens comme une conséquence de l'influence croissante du marxisme chez les physiciens des pays occidentaux. En effet, au cours des années 1950, le noyau du groupe de physiciens impliqués dans le programme causal autour de Jean-Pierre Vigier et Louis de Broglie à l'Institut Henri Poincaré est majoritairement constitué soit de membres, soit de sympathisants du PCF. Leurs travaux sont fortement influencés par les critiques soviétiques contre l'interprétation dominante de la mécanique quantique, l'interprétation dite de Copenhague. Entre autres, Vigier critique le pragmatisme qui règne dans la physique de l'après-guerre et pense que le manque de réflexion philosophique est en grande partie responsable de la crise que traverse la physique fondamentale, telle que le problème de la renormalisation. Le groupe a également porté la question de l'interprétation de la théorie au sein du PCF d'où est née une controverse au sein du parti qui a soulevé la problématique de la relation entre le marxisme et la science.La théorie fait également partie d'un programme de recherche plus global lié aux questions contemporaines en physique. Ce point est souvent oublié, ce qui mène à la conclusion erronée que la motivation du groupe IHP est seulement de nature idéologique et, par conséquent, que leur activité est hors de la science. Dès 1957, en collaboration avec des physiciens japonais, le groupe a proposé une théorie des particules élémentaires et un système de classification, à une époque où une théorie consensuelle manque encore / The Causal Interpretation of Quantum Mechanics was in the first place described by historians as a consequence of the growing influence of Marxism among physicists in Western countries. Indeed, during the 1950s, the core of the group of physicists involved in the Causal program around Jean-Pierre Vigier and Louis de Broglie at the Institut Henri Poincaré was mainly constituted either of members or sympathizers of the PCF. Their works were strongly influenced by critics from Soviet Union against the mainstream interpretation of Quantum Mechanics, the so called Copenhagen interpretation. Vigier criticized the pragmatism which prevailed in the Postwar physics and thought that the lack of philosophical considerations was in great part responsible for the crisis in fundamental physics, such as the problem of renormalization. They also put the issue of the interpretation of the theory inside the PCF and created a controversy inside the party which raised the relationship between Marxism and science. The theory was also part of a more global research program linked with contemporary questions in physics. This point is often forgotten which leads to the erroneous conclusion that the motivation of the IHP group was only ideological and, therefore, their activity was out of science. As early as 1957, in collaboration with Japanese physicists, the group proposed a theory for elementary particles and a method of their classification, in a period in where a standard theory was still missing

Nous entendons confronter pratique des mathématiques et réflexions sur les mathématiques dans l'œuvre de Weyl. Nous étudierons : (a) ses monographies en analyse complexe, en relativité générale et en mécanique quantique, (b) les articles en lien avec ces ouvrages, (c) certains de ses cours, (d) sa correspondance avec divers scientifiques, principalement A. Einstein, E. Cartan, J. von Neumann. Nous voulons savoir si les théories mathématiques qu'il investit conditionnent ses positions sur les fondements des mathématiques. Inversement, nous montrerons que les philosophies auxquelles il se réfère – essentiellement le criticisme kantien, l'idéalisme fichtéen et la phénoménologie de Husserl – conditionnent ses recherches. Tout d'abord, nous reviendrons sur Die Idee der Riemannschen Fläche (première éd. 1913). Nous montrerons qu'il opte alors pour un formalisme mitigé. Il se revendique de deux traditions incarnées par Klein et par Hilbert. Ensuite, nous étudierons les éditions successives de Raum, Zeit, Materie (1918-1923). Nous aborderons le projet d'une géométrie purement infinitésimale qui permet à Weyl de proposer une théorie unifiée des champs, cette dernière étant réfutée par Einstein, Pauli, Reichenbach, Hilbert and Eddington. Nous décrirons aussi la construction et la résolution de son « problème de l'espace » (1921-1923). Nous indiquerons comment la référence aux philosophies de Fichte et de Husserl permet d'éclairer ces deux projets. Enfin, nous commenterons l'article de Weyl sur les groupes de Lie (1925-1926) ainsi que son ouvrage Gruppentheorie und Quantenmechanik (1928, 1931). Son article sur les groupes de Lie manifeste la voie moyenne entre formalisme et intuitionnisme qu'il adopte en 1924. Son ouvrage en mécanique quantique incarne quant à lui un « tournant empirique » dans son épistémologie qu'il conviendra de comparer \`a l'« empirisme logique ». / Our purpose consists in comparing Weyl's mathematical practice with his philosophical reflections on mathematics. We will study (a) his monographs on complex analysis, general relativity and quantum mechanics, (b) the articles which are linked to these books, (c) some of his lecture courses, (d) his correspondence with different scientists, mainly A. Einstein, E. Cartan, J. von Neumann. We will show that his mathematical research has a strong influence on the different stands he successively takes regarding the foundations of mathematics. Conversely, we will show that the philosophical systems he refers to (mainly kantian criticism, fichtean idealism and husserlian phenomenology) have a real impact on his investigations in mathematics. We will first analyse Die Idee der Riemannschen Fläche (first edition 1913). In this book, Weyl seems to take up a formalist point of view, but this is partly true. In fact, he is influenced by two traditions respectively embodied by Hilbert and Klein. Then, we will study the successive editions of Raum, Zeit, Materie (1918-1923). We will describe Weyl's project of a “purely infinitesimal geometry”. Thanks to this geometrical framework, he builds a unified fields theory, which will be disproved by Einstein, Pauli, Reichenbach, Hilbert and Eddington. During this short period, Weyl also constructs and solves the so-called space problem (1921-1923). Weyl's references to Fichte and Husserl have a significant impact on these two projects. Finally, we will comment Weyl's main article on Lie groups (1925-1926) and his monograph on quantum mechanics, i.e. Gruppentheorie und Quantenmechanik (1rst ed. 1928, 2nd ed. 1931). Weyl's article on Lie groups is in accordance with his compromise between intuitionism and formalism (1924). On the other hand, Weyl's book on quantum mechanics encapsulates an “empirical turn” in his epistemology, which will be compared with the so-called empirical logicism.

A presente dissertação tem como objeto de estudo sistemas da física da matéria condensada que sejam capazes de simular sistemas gravitacionais, tais como buracos negros e universos em expansão, onde processos quânticos tomam parte. Neste estudo nos debruçamos principalmente sobre o modelo do fluido e condensados de Bose-Einstein. No modelo do fluido exploramos a geometria efetiva que surge e os problemas de back-reaction e dos modos trans-planckianos de campos quânticos. No modelo baseado em condensados exploramos sua faceta cosmológica e a possibilidade de campos maciços. Além destes dois modelos de grande relevância na literatura, ainda expomos os análogos em cordas elásticas e os baseados em ondas na superfícies de fluidos e uma análise geral baseada no formalismo lagrangeano para campos. / This dissertation has as object of study systems of condensate-matter physics which can simulate gravitational systems like black holes and expanding universes where quantum processes take place. In this study we lay attention mainly on the fluid model and on Bose-Einstein-condensate-based models. In the fluid model we explore the features of the emergent geometry and other problems like the back-reaction and the trans-planckian modes of quantum fields. In the condensate-based models we explore their cosmological aspects and the possibility for massive fields. Moreover, we shall present two other models, the elastic string and the surface-wave-based models in fluids, and a very general analysis based on the Lagrangean formalism for fields.

Made available in DSpace on 2016-04-25T19:21:07Z (GMT). No. of bitstreams: 1 Pablo Nogueira.pdf: 1921895 bytes, checksum: 8fae9708904e9ea1b48d7e0381c03b62 (MD5) Previous issue date: 2010-05-27 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The objective of this dissertation is to discuss the religious elements in the work of Indian physicist Amit Goswami. Goswami became a familiar figure in the New Age movement because of his proposal to interpret quantum mechanics −based on the idea of a non-local and transcendent conscience as the foundation of reality − and for his advocacy of a synthesis between spirituality and scientific discourse. The text begins with a history of connections between science and religion proposed since the mid 19th century until the rise of New Age in the 1970s. Its main focus is the dialogue between science and religion which began to be settled with the development of quantum mechanics. The dissertation approaches the work of Goswami with the intent of highlighting its main ideas: the criticism of materialist realism, the mystical origin of religions, their inability to adequately convey the essential truth of the mystical experience, his confidence that certain experiments could support the belief in a transcendent dimension of reality and the moral crisis experienced by modern societies. Next, the dissertation uses the definition of religion proposed by Geertz and makes evident the religious element of Goswami´s speech characterized by its quest to link cosmology and ethos in order to substantiate a new ethic for contemporary societies. Finally, Hanegraaff´s definitions of spirituality and religion allow distinguish his Goswami s work as an example of spirituality based on a secular symbolic system / O objetivo desta dissertação é discutir o elemento religioso presente na obra do físico indiano Amit Goswami. Goswami tornou-se uma figura conhecida dentro do movimento Nova Era por sua proposta de interpretar a mecânica quântica tendo como fundamento da realidade a ideia de uma consciência não-local e transcendente, e por sua defesa de uma síntese entre espiritualidade e discurso científico. O texto começa por apresentar um histórico das aproximações entre ciência e religião propostas desde meados do século 19 até o surgimento da Nova Era nos anos 1970, tendo como foco principal o diálogo entre ambas que começou a ser estabelecido a partir do desenvolvimento da mecânica quântica. Apresenta-se um recorte da obra de Goswami com o objetivo de evidenciar suas principais idéias: a crítica ao realismo materialista, a origem mística das religiões, a incapacidade delas em transmitir de forma adequada a verdade essencial da experiência mística, sua crença de que certos experimentos poderiam sustentar a crença numa dimensão transcendente da realidade e a crise moral vivida pelas sociedades modernas. A seguir, recorrendo à definição de religião proposta por Geertz evidencia-se o elemento religioso do discurso de Goswami, caracterizado por sua busca de associar ethos e cosmologia a fim de fundamentar uma nova ética para as sociedades contemporâneas. Por fim, as definições de espiritualidade e de religião de Hanegraaff permitem caracterizar seu trabalho como exemplo de espiritualidade que se assenta sobre um sistema simbólico secular

Ce travail est centré sur la charactérisation de certaines classes de processus aléatoires par des formules de dualité. En particulier on considérera des processus réciproques à sauts, un cas jusqu'à présent négligé dans la littérature.Dans la première partie nous formulons de façon innovante une charactérisation des processus à accroissements indépendants. Celle-ci est basée sur une formule de dualité pour des processus infiniment divisibles, déjà connue dans le cadre du calcul de Malliavin. On va présenter deux nouvelles méthodes pour prouver cette formule, qui n'utilisent pas la décomposition en chaos de l'espace des fonctionnelles de carré intégrable. Une méthode s'appuie sur une formule d'intégration par parties satisfaite par des vecteurs aléatoires infiniment divisibles. Sous cet angle, notre charactérisation est une généralization du lemme de Stein dans le cas Gaussien et du lemme de Chen dans le cas Poissonien. La généralité de notre approche nous permet de plus, de présenter une charactérisation des mesures aléatoires infiniment divisibles.Dans la deuxième partie de notre travail nous nous concentrons sur l'étude des classes réciproques de processus de Markov avec ou sans sauts, et sur leur charactérisation. On commence avec un résumé des résultats déjà existants concernant les classes réciproques de diffusions browniennes comme solutions d'une formule de dualité. Nous obtenons notamment une nouvelle interprétation des classes réciproques comme les solutions d'une équation de Newton. Cela nous permet de relier nos résultats à la mécanique stochastique d'une part et à la théorie du contrôle optimale, d'autre part. La formule de dualité nous permet aussi de prouver une propriété d'invariance par retournement du temps de la classe réciproque d'une diffusion brownienne.En outre nous obtenons une série de nouveaux résultats concernant les processus de sauts purs. Nous décrivons d'abord la classe réciproque associée à un processus markovien de comptage, c'est-à-dire un processus de sauts de taille un, puis en présentons une charactérisation par une formule de dualité. Cette formule contient une dérivée stochastique, une intégrale stochastique compensée, et une fonctionnelle qui est une grandeur invariante de la classe réciproque. De plus nous livrons une interprétation de la classe réciproque comme ensemble des solutions d'un problème de contrôle optimal. Enfin, par une utilisation appropriée de la formule de dualité, nous montrons que la classe réciproque d'un processus markovien de comptage est invariante par retournement du temps.Quelques-uns de ces résultats restent valables pour des processus de sauts purs dont les sauts sont de taille variée. En particulier nous montrons que certaines fonctionnelles dites invariants réciproques permettent de distinguer différentes classes réciproques. Notre dernier résultat est la charactérisation de la classe réciproque d'un processus de Poisson composé dès lors que les (tailles des) différents sauts sont incommensurables. / This work is concerned with the characterization of certain classes of stochastic processes via duality formulae. In particular we consider reciprocal processes with jumps, a subject up to now neglected in the literature. In the first part we introduce a new formulation of a characterization of processes with independent increments. This characterization is based on a duality formula satisfied by processes with infinitely divisible increments, in particular Lévy processes, which is well known in Malliavin calculus. We obtain two new methods to prove this duality formula, which are not based on the chaos decomposition of the space of square-integrable functionals. One of these methods uses a formula of partial integration that characterizes infinitely divisible random vectors. In this context, our characterization is a generalization of Stein's lemma for Gaussian random variables and Chen's lemma for Poisson random variables. The generality of our approach permits us to derive a characterization of infinitely divisible random measures.The second part of this work focuses on the study of the reciprocal classes of Markov processes with and without jumps and their characterization. We start with a resume of already existing results concerning the reciprocal classes of Brownian diffusions as solutions of duality formulae. As a new contribution, we show that the duality formula satisfied by elements of the reciprocal class of a Brownian diffusion has a physical interpretation as a stochastic Newton equation of motion. Thus we are able to connect the results of characterizations via duality formulae with the theory of stochastic mechanics by our interpretation, and to stochastic optimal control theory by the mathematical approach. As an application we are able to prove an invariance property of the reciprocal class of a Brownian diffusion under time reversal.In the context of pure jump processes we derive the following new results. We describe the reciprocal classes of Markov counting processes, also called unit jump processes, and obtain a characterization of the associated reciprocal class via a duality formula. This formula contains as key terms a stochastic derivative, a compensated stochastic integral and an invariant of the reciprocal class. Moreover we present an interpretation of the characterization of a reciprocal class in the context of stochastic optimal control of unit jump processes. As a further application we show that the reciprocal class of a Markov counting process has an invariance property under time reversal. Some of these results are extendable to the setting of pure jump processes, that is, we admit different jump-sizes. In particular, we show that the reciprocal classes of Markov jump processes can be compared using reciprocal invariants. A characterization of the reciprocal class of compound Poisson processes via a duality formula is possible under the assumption that the jump-sizes of the process are incommensurable.

Made available in DSpace on 2016-04-28T14:16:34Z (GMT). No. of bitstreams: 1 Douglas Guilherme Schmidt.pdf: 995968 bytes, checksum: 1a8192151fc433a54ec422f421249ac4 (MD5) Previous issue date: 2008-09-15 / Secretaria da Educação do Estado de São Paulo / This historical research analyses the initial period of construction of wave mechanics, as propounded by the Austrian physicist Erwin Schrödinger (1887- 1961), emphasizing his work from December 1925 to February 1926. During these months Schrödinger created the basis of his quantum theory and wrote his two earlier papers on this subject. They were published in the Annalen der Physik. The present dissertation analyses those two papers, and some of their precedents and immediate consequences. Special attention is given to the influence of the theory of matter waves of the French physicist Louis de Broglie (1892-1987) upon the development of Schrödinger s theory, as well as other works and relevant circumstances that contributed to the creation of wave mechanics. The dissertation also discusses the interpretation given by Schrödinger to his own theory, comparing it to the approach of other physicists of that time / O presente trabalho histórico investiga a fase inicial da construção da mecânica ondulatória formulada pelo físico austríaco Erwin Schrödinger (1887- 1961), dando especial atenção aos trabalhos por ele realizados de dezembro de 1925 até fevereiro de 1926. Nesse período, Schrödinger concebeu as bases de sua teoria quântica e redigiu os dois primeiros artigos sobre o assunto, publicados na revista Annalen der Physik. Esta dissertação analisa esses dois artigos, bem como alguns de seus precedentes e repercussões. É analisada em especial a influência da teoria de ondas de matéria do físico francês Louis de Broglie (1892- 1987) no desenvolvimento da teoria de Schrödinger, bem como outros trabalhos e circunstâncias importantes que contribuíram para a elaboração da mecânica ondulatória. Discute-se também a interpretação que o próprio Schrödinger deu à sua teoria, comparando-a com o enfoque adotado por outros físicos da época

Previous research in InGaN/GaN light emitting diodes (LEDs) employing semi-classical drift-diffusion models has used reduced polarization constants without much physical explanantion. This paper investigates possible physical explanations for this effective polarization reduction in InGaN LEDs through the use of the simulation software SiLENSe. One major problem of current LED simulations is the assumption of perfectly discrete transitions between the quantum well (QW) and blocking layers when experiments have shown this to not be the case. The In concentration profile within InGaN multiple quantum well (MQW) devices shows much smoother and delayed transitions indicative of indium diffusion and drift during common atomic deposition techniques (e.g. molecular beam epitaxy, chemical vapor deposition). In this case the InGaN square QW approximation may not be valid in modeling the devices' true electronic behavior. A simulation of a 3QW InGaN/GaN LED heterostructure with an AlGaN electron blocking layer is discussed in this paper. Polarization coefficients were reduced to 70% and 40% empirical values to simulate polarization shielding effects. QW shapes of square (3 nm), trapezoidal, and triangular profiles were used to simulate realistic QW shapes. The J-V characteristic and electron-hole wavefunctions of each device were monitored. Polarization reduction decreased the onset voltage from 4.0 V to 3.0 V while QW size reduction decreased the onset voltage from 4.0 V to 3.5 V. The increased current density in both cases can be attributed to increased wavefunction overlap in the QWs.

Methods for performing large-scale parallel Molecular Dynamics(MD) simulations are investigated. A perspective on the field of parallel MD simulations is given. Hardware and software aspects are characterized and the interplay between the two is briefly discussed. A method for performing ab initio MD is described; the method essentially recomputes the interaction potential at each time-step. It has been tested on a system of liquid water by comparing results with other simulation methods and experimental results. Different strategies for parallelization are explored. Furthermore, data-parallel methods for short-range and long-range interactions on massively parallel platforms are described and compared. Next, a method for treating electrostatic interactions in MD simulations is developed. It combines the traditional Ewald summation technique with the nonuniform Fast Fourier transform---ENUF for short. The method scales as N log N, where N is the number of charges in the system. ENUF has a behavior very similar to Ewald summation and can be easily and efficiently implemented in existing simulation programs. Finally, an outlook is given and some directions for further developments are suggested.

The progess in NMRQIP can be outlined in to four parts.1) Implementation of theoretical protocols on small number of qubits. 2) Demonstration of QIP on various NMR systems. 3) Designing and implementing the algorithms for mixed initial states. 4) Developing the techniques for coherent and decoherent control on higher number(up to 15) of qubits. This thesis contains some efforts in the direction of first three points. Quantum-state discrimination has important applications in the context of quantum communication and quantum cryptography. One of the characteristic features of quantum mechanics is that it is impossible to devise a measurement that can distinguish nonorthogonal states perfectly. However, one can distinguish them with a finite probability by an appropriate measurement strategy. In Chapter 2, we describe the implementation of a theoretical protocol of programmable quantum-state discriminator, on a two-qubit NMR System. The projective measurement is simulated by adding two experiments. This device does the unambiguous discrimination of a pair of states of the data qubit that are symmetrically located about a fixed state. The device is used to discriminate both linearly polarized states and eillipitically polarized states. The maximum probability of successful discrimination is achieved by suitably preparing the ancilla quubit. The last step of any QIP protocol is the readout. In NMR-QIP the readout is done by using density matrix tomography. It was first proposed by Ernst and co-workers that a two-dimensional method can be used to correlate input and output states. This method uses an extra (aniclla) qubit, whose transitions indicate the quantum states of the remaining qubits. The 2D spectrum of ancilla qubit represent the input and output states along F1 and F2 dimensions respectively. However the 2D method requires several t1 increments to achieve the required spectral width and resolution in the indirect dimension, hence leads to large experimental time. In chapter 3, the conventional 2D NMRQIP method is speeded-up by using Hadamard spectroscopy. The Hadamard method is used to implement various two-, three-qubit gates and qutrit gates. We also use Hadamard spectroscopy for information storage under spatial encoding and to implement a parallel search algorithm. Various slices of water sample can be spatially encoded by using a multi-frequency pulse under the field gradient. Thus the information of each slice is projected to the frequency space. Each slice represents a classical bit, where excitation and no excitation corresponds to the binary values 0 and 1 respectively. However one has to do the experiment for each binary information, by synthesizing a suitable multi-frequency pulse. In this work we show that by recording the data obtained by various Hadamard encoded multi-frequency pulses, one can suitably decode it to obtain any birnary information, without doing further experiments. Geometric phases depend only on the geometry of the path executed in the projective Hilbert space, and are therefore resilient to certain types of errors. This leads to the possibility of an intrinsically fault-tolerant quantum computation. In liquid state NMRQIP. Controlled phase shift gates are achieved by using qubit selective pulses and J evolutions, and also by using geometir phases. In order to achieve higher number of qubits in NMR, one explores dipolar couplings which are larger in magnitude, yielding strongly coupled spectra. In such systems since the Hamiltonian consists of terms, it is difficult to apply qubit selective pulses. However such systems have been used for NMRQIP by considering 2n eigen states as basis states of an n-qubit system. In chapter 4, it is shown that non-adiabatic geometric phases can be used to implement controlled phase shift gates in strongly dipolar coupled systems. A detailed theoretical explanation of non-adiabatic geometric phases in NMR is given, by using single transition operators. Using such controlled phase shift gates, the implementation of Deutsch-Jozsa and parity algorithms are demonstrated. Search algorithms play an important role in the filed of information processing. Grovers quantum search algorithm achieves polynomial speed-up over the classical search algorithm. Bruschweiler proposed a Liouville space search algorithm which achieve polymonial speed-up. This algorithm requires a weakly coupled system with a mixed initial state. In chapter 5 we modified the Bruschweiler’s algorithm, so that it can be implemented on a weakly as well as strongly coupled system. The experiments are performed on a strongly dipolar coupled four-qubit system. The experiments from four spin-1/2 nuclei of a molecule oriented in a liquid crystal matrix. Chapter 6 describes the implementation of controlled phase shift gates on a quadrupolar spin-7/2 nucleus, using non-adiabatic geometric phases. The eight energy levels of spin-7/2 nucleus, form a three qubit system. A general procedure is given, for implementing a controlled phase shift gate on a system consisting of any number of energy levels. Finally Collin’s version of three-qubit DJ algorithm using multi-frequency pulses, is implemented in the spin-7/2 system.

The work of this Ph.D. thesis in mathematics concerns the problem of determining existence, uniqueness, and structure of zero-energy states in supersymmetric matrix models, which arise from a quantum mechanical description of the physics of relativistic membranes, reduced Yang-Mills gauge theory, and of nonperturbative features of string theory, respectively M-theory. Several new approaches to this problem are introduced and considered in the course of seven scientific papers, including: construction by recursive methods (Papers A and D), deformations and alternative models (Papers B and C), averaging with respect to symmetries (Paper E), and weighted supersymmetry and index theory (Papers F and G). The mathematical tools used and developed for these approaches include Clifford algebras and associated representation theory, structure of supersymmetric quantum mechanics, as well as spectral theory of (matrix-) Schrödinger operators. / QC20100629