Nesta tese, o limite não re1ativistico em teorias quânticas de campos em 2+1 dimensões é discutido1 perturbativamente, através da introdução de um corte intermediário que permite 0 cálculo de.expansão /P/m das amplitudes quânticas. especificando a origem, no espaço dos estados intermediários, de cada uma. das contribuições. Este procedimento é aplicado à teoria 4 e um esquema de redução a nível das amplitudes, que identifica a contribuição do setor de baixas energias com 0 resultado da teoria não re1ativistica, é proposto. Quando aplicado á teoria de Chern-Simons escalar, este procedimento sugere correlações relativísticas para o espalhamento Aharonov-Bohm. / n this thesis, the nonrelativistic limit of quantum field theories in 2 + 1 dimensions is discussed, perturbatively, through the introduction of an intermediate cutoff which generates the /p/m expansion of the quantum amplitudes and specifies the origin of each contribution in the space of the intermediary states. This scheme is applied to the theory 4 and a reduction procedure for the amplitudes that identify the low energy sector contribution with the results of the nonrelativistic theory is proposed. When applied to the scalar Chern-Simons theory, this procedure gives relativistic corrections to the Aharonov- Bohm scattering.

<p>The present thesis concerns applications of first principles electronic structure calculations in conjunction with methods of statistical mechanics for simulations of transition metal alloys both in the bulk and at surfaces.</p><p>A fully relativistic generalization of the exact muffin-tin orbitals (EMTO) method has been developed. The method accurately takes into account spin-orbit coupling and allows one to calculate orbital polarization and magneto-crystalline anisotropy in magnetic systems as well as increasing the range of applicability of the EMTO method to heavy elements. A new direct-exchange Monte Carlo (DEMC) method has been proposed, which is capable to tackling effectively statistical simulations of surface segregations in disordered and ordered alloys.</p><p>The applications of relativistic methods include calculations of spin and orbital magnetization in iron-cobalt disordered and partially ordered alloys, as well as computation of the core-level shifts (CLS) in transition metal alloys. It has been found, that relativistic corrections are important for CLS calculations in 5-d metal alloys. Properties of a Ni monolayer deposited on a Cu surface have been studied. The monolayer is found to be unstable in the top layer, and its magnetization depends greatly on the surface orientation. Two distinct energy levels have been found to exist Co/Cu/Ni trilayers deposited on the (100) Cu surface, which correspond to a completely paramagnetic trilayer and the case when only Ni is paramagnetic.</p><p>Vacancy ordering in substoichometric titanium carbides TiC_x have been simulated. Existence of three ordered phases in the range of carbon concentration x=0.5 ÷1.0 has been revealed and a theoretical phase diagram has been proposed. Surface segregations have been calculated in disordered Ni₅₀Pt₅₀ and Ni₅₀Pd₅₀ as well as in ordered NiPt alloys. Segregation reversal has been observed in the Ni₅₀Pt₅₀ alloy with Pt segregation at the (111) surface and Ni segregation at the (110). In the ordered NiPt alloys segregation behaviour is found to be affected greatly by small deviations from the exact stoichiometric composition in bulk. Surface magnetization in PdV and MoV bcc alloys have been studied. It has been found, that in PdV alloys surface segregations suppress magnetic order at the surface, while in MoV alloys magnetization is substantially enhanced due to the segregation.</p>

In order to understand some of the superconducting mechanisms involving external electric fields at nanometric scales, a Lorentz-covariant extension of the phenomenological Ginzburg-Landau theory has been developed by analogy with the Higgs model of particle physics. Among the specific properties of this model, it has been shown that the phase diagram of some particular geometry submitted to crossed electric and magnetic fields in a stationary situation provides a criterion involving the applied electric field, which could discriminate between the usual Ginzburg-Landau theory and its covariant extension. A sub-microscopic device has been manufactured using microelectronics lithography techniques and was used to perform transport measurements at very low temperatures. However, the experimental measurements of the phase diagram do not reproduce the expectations based whether on the usual or the extended model, suggesting a screening of the electric field by some mechanism which is not accounted for by these phenomenological approaches. A microscopic approach has therefore been developed to extend the s-wave channel of the BCS theory in a relativistic framework, using the functional integral formalism of Finite Temperature Field Theory. In particular, the effective action related to the Ginzburg-Landau free energy was obtained up to second order in the fluctuations of the electromagnetic field and of the superconducting condensate density. This allowed for the identification of the electric and magnetic penetration lengths, inclusive of their dependences on temperature and the chemical potential, which fully explain the experimental results. Several analytic expressions have also been provided for the effective potential in the full range of temperatures between 0 K and the critical temperature, among which the Ginzburg-Landau potential was shown to reproduce this effective potential within the limited range of temperatures where it is expected to be valid.

The present thesis concerns applications of first principles electronic structure calculations in conjunction with methods of statistical mechanics for simulations of transition metal alloys both in the bulk and at surfaces. A fully relativistic generalization of the exact muffin-tin orbitals (EMTO) method has been developed. The method accurately takes into account spin-orbit coupling and allows one to calculate orbital polarization and magneto-crystalline anisotropy in magnetic systems as well as increasing the range of applicability of the EMTO method to heavy elements. A new direct-exchange Monte Carlo (DEMC) method has been proposed, which is capable to tackling effectively statistical simulations of surface segregations in disordered and ordered alloys. The applications of relativistic methods include calculations of spin and orbital magnetization in iron-cobalt disordered and partially ordered alloys, as well as computation of the core-level shifts (CLS) in transition metal alloys. It has been found, that relativistic corrections are important for CLS calculations in 5-d metal alloys. Properties of a Ni monolayer deposited on a Cu surface have been studied. The monolayer is found to be unstable in the top layer, and its magnetization depends greatly on the surface orientation. Two distinct energy levels have been found to exist Co/Cu/Ni trilayers deposited on the (100) Cu surface, which correspond to a completely paramagnetic trilayer and the case when only Ni is paramagnetic. Vacancy ordering in substoichometric titanium carbides TiCx have been simulated. Existence of three ordered phases in the range of carbon concentration x=0.5 ÷1.0 has been revealed and a theoretical phase diagram has been proposed. Surface segregations have been calculated in disordered Ni50Pt50 and Ni50Pd50 as well as in ordered NiPt alloys. Segregation reversal has been observed in the Ni50Pt50 alloy with Pt segregation at the (111) surface and Ni segregation at the (110). In the ordered NiPt alloys segregation behaviour is found to be affected greatly by small deviations from the exact stoichiometric composition in bulk. Surface magnetization in PdV and MoV bcc alloys have been studied. It has been found, that in PdV alloys surface segregations suppress magnetic order at the surface, while in MoV alloys magnetization is substantially enhanced due to the segregation.

Tesi doctoral - Universitat de Barcelona. Facultat de Física, 1980 / A la relativitat, a diferència de la mecànica newtoniana, no trobem exemples senzills de sistemes dinàmics de diverses partícules. La formulació covariant Lorentz de les equacions del moviment per a sistemes de partícules en interacció, directament en termes de les variables de les partícules és l'objecte de les teories d'acció a distància. Les dificultats d'aquestes teories consisteixen a que les equacions que donen no són equacions diferencials ordinàries, per a les quals hom no sap formular teoremes d'existència i unicitat ni tampoc cap mètode de solució (ni tan sols numèric). Això mateix passa amb qualsevol teoria de camps. L'acció a distància instantània té dues branques. Una és la iniciada per Dirac, consistent en buscar una formulació Hamiltoniana utilitzant per a tal fí l'estructura del grup de Poincaré, i demanant que les transformacions d'aquest grup siguin canòniques. L'interès d'una formulació Hamiltoniana rau en que permet de quantificar la teoria fàcilment. La segona branca, dins de la qual es situa aquest treball és la Mecànica Relativista Predictiva. El punt de partença és mantenir fermament la invariància de les línies d'univers de les partícules i demanar unes equacions del moviment estrictament Newtonianes: acceleracions instantànies en termes de posicions i velocitats instantànies de les partícules. El fet que la simultaneïtat no sigui un concepte covariant fa que aquest punt de vista sembli inacceptable. No obstant hom demostra que les equacions de tipus newtonià són compatibles amb la invariància sota el grup de Poincaré. Aquest prejudici ha fet que la dinàmica relativista de N partícules no sigui desenvolupada fins molt tard, molt després de la formulació de la relativitat restringida per Einstein. Podem trobar un. fonament formal per això a l'electrodinàmica mateixa. Eliminant els camps i fent desenvolupaments de Taylor en les càrregues hom arriba a equacions del moviment del tipus Newtonià. La propietat de covariància sota el grup de Lorentz, que tenien les equacions de partença, es manté per tant en la versió derivada instantània (encara que aquesta instantaneitat sigui totalment formal) Tornant al cas general, la dificultat de la no-covariància de la simultaneïtat rau en que posicions i velocitats que són simultànies en un sistema de referència no ho són en un altra sistema en moviment respecte del primer; i per que la dinàmica en el sistema mòbil tingui la mateixa forma que en el primer sistema considerat, hem de prendre noves posicions i velocitats, desplaçades al llarg de cada línia d'univers de les partícules, tal de que siguin simultànies en el sistema mòbil. Això exigeix integrar les equacions del moviment per obtenir les òrbites. Aquesta situació sembla insuperable. Però solament ens cal considerar transformacions infinitesimals, perquè tota transformació finita de Poincaré pot ésser descomposta com una seqüència de transformacions infinitesimals. Així obtenim fàcilment condicions necessàries i suficients que garanteixen la covariància de la dinàmica de tipus Newtonià proposada. En el primer capítol d'aquest treball farem un resum del que és la mecànica relativista predictiva per passar després a aplicar-la al cas de dues partícules en interacció electromagnètica, amb radiació, al capítol 3. En el camp de les teories d'acció a distància, aquests darrers anys han apaeagut diferents treballs sobre models L~grangians singulars. Un Lagrangià singular és aquell per al qual la matriu Hessiana respecte de les velocitats generalitzades és singular; això fa que hom no pugui aïllar directament les acceleracions a partir de les equacions d'Euler-Lagrange. La teoria d'aquests sistemes arriba a unes equacions del moviment (a les quals hi apareixen funcions arbitràries), vàlides solament sobre una subvarietat de l'espai de les fases. Els avantatges d'aquestes teories consisteixen en que hom pot desenvolupar un formalisme Hamiltonià que permet de quantificar fàcilment la teoria. Els teoremes de no interacció no es poden aplicar, ja que les posicions de les partícules no són variables canòniques i les equacions del moviment obtingudes són vàlides únicament sobre una subvarietat de l'espai de les fases. Ara bé, les equacions del moviment que hom deriva d'aquestes teories no són equacions diferencials de segon ordre, ja que contenen funcions arbitràries; a més les condicions inicials no poden ésser qualsevulles, sinò que han de estar sobre la subvarietat abans esmentada. Una altra dificultat es presenta quan escrivim les triacceleracions que s'observen des d'un sistema inercial. Per a alguns sistemes aquestes acceleracions seran instantànies (en el sentit de que venen descrites en termes de posicions i velocitats simultànies de la resta de partícules) mentre que per d'altres no. Però des del punt de vista de la mecànica relativista predictiva, desitgem que no hi hagi cap observador inercial privilegiat. Així, la segona part d'aquest treball està dedicada a buscar un sistema predictiu que coincideixi amb el sis tema dinàmic que es deriva d'un Lagrangià singular donat. Trobarem condicions generals sota les quals tal cosa és possible, i aplicarem els resultats al model de Dominici-Gomis-Longhi (al capítol 5). La motivació d'aquests treballs és aprofundir els coneixements de la dinàmica relativista de sistemes de N partícules (des del punt de vista de la Mecànica Predictiva), ja que pensem que part de les dificultats de la Teoria Quàntica de Camps (eliminació d'estats d'energia negativa; impossibilitat de tractar estats lligats i d'altres) tenen origen relativista i no quàntic. Una mostra d'això són els models Lagrangians singulars proposats per explicar la interacció entre els quarks, els quals permeten d'eliminar els estats no físics (norma negativa) i presenten potencials relativistes que permeten d'explicar el confinament dels quarks.

In this thesis, entanglement under fully relativistic settings are discussed. The thesis starts with a brief review of the relativistic quantum mechanics. In order to describe the effects of Lorentz transformations on the entangled states, quantum mechanics and special relativity are merged by construction of the unitary irreducible representations of Poincar&eacute / group on the infinite dimensional Hilbert space of state vectors. In this framework, the issue of finding the unitary irreducible representations of Poincar&eacute / group is reduced to that of the little group. Wigner rotation for the massive particles plays a crucial role due to its effect on the spin polarization directions. Furthermore, the physical requirements for constructing the correct relativistic spin operator is also studied. Then, the entanglement and Bell type inequalities are reviewed. The special attention has been devoted to two historical papers, by EPR in 1935 and by J.S. Bell in 1964. The main part of the thesis is based on the Lorentz transformation of the Bell states and the Bell inequalities on these transformed states. It is shown that entanglement is a Lorentz invariant quantity. That is, no inertial observer can see the entangled state as a separable one. However, it was shown that the Bell inequality may be satisfied for the Wigner angle dependent transformed entangled states. Since the Wigner rotation changes the spin polarization direction with the increased velocity, initial dichotomous operators can satisfy the Bell inequality for those states. By choosing the dichotomous operators taking into consideration the Wigner angle, it is always possible to show that Bell type inequalities can be violated for the transformed entangled states.

It has been noted by several authors that General Relativistic frame dragging in rotating neutron stars is a first order effect which has to be included in a self-consistent model of pulsar magnetospheric structure and associated radiation and transport processes. To this end, I undertook the present study with the aim of investigating the effect of General Relativity (GR) on millisecond pulsar (MSP) visibility. I developed a numerical code for simulating a pulsar magnetosphere, incorporating the GR-corrected expressions for the electric potential and field. I included curvature radiation (CR) due to primary electrons accelerated above the stellar surface, as well as inverse Compton scattering (ICS) of thermal X-ray photons by these electrons. I then applied the model to PSR J0437-4715, a prime candidate for testing the GR-Electrodynamic theory, and examined its visibility for the H.E.S.S. telescope. I also considered the question of whether magnetic photon absorption would take place for this particular pulsar. In addition, I developed a classical model for comparison with the GR results. I found that the typical electron energies and associated CR photon energies are functions of position above the polar cap (PC). These energies are also quite smaller in the GR case than in the classical case due to the different functional forms of the GR and classical electric fields. I found the CR energy cut-off to be ~ 4 GeV compared to the well-known classical value of ~ 100 GeV. Since the H.E.S.S. energy threshold is ~ 100 GeV, it seems as though the CR component will not be visible, contrary to wide-held opinion. However, the ICS component seems to be well in excess of the H.E.S.S. energy threshold and is expected to be visible. I also found that no pair production will take place for PSR J0437-4715. Hopefully, forthcoming H.E.S.S. observations will provide validation of these results. KEY WORDS: General relativistic frame dragging, GR electrodynamics, millisecond pulsar visibility, non-thermal radiation processes, pair production, H.E.S.S., individual pulsars: PSR J0437-4715. / Thesis (M.Sc. (Physics))--North-West University, Potchefstroom Campus, 2004.

It has been noted by several authors that General Relativistic frame dragging in rotating neutron stars is a first order effect which has to be included in a self-consistent model of pulsar magnetospheric structure and associated radiation and transport processes. To this end, I undertook the present study with the aim of investigating the effect of General Relativity (GR) on millisecond pulsar (MSP) visibility. I developed a numerical code for simulating a pulsar magnetosphere, incorporating the GR-corrected expressions for the electric potential and field. I included curvature radiation (CR) due to primary electrons accelerated above the stellar surface, as well as inverse Compton scattering (ICS) of thermal X-ray photons by these electrons. I then applied the model to PSR J0437-4715, a prime candidate for testing the GR-Electrodynamic theory, and examined its visibility for the H.E.S.S. telescope. I also considered the question of whether magnetic photon absorption would take place for this particular pulsar. In addition, I developed a classical model for comparison with the GR results. I found that the typical electron energies and associated CR photon energies are functions of position above the polar cap (PC). These energies are also quite smaller in the GR case than in the classical case due to the different functional forms of the GR and classical electric fields. I found the CR energy cut-off to be ~ 4 GeV compared to the well-known classical value of ~ 100 GeV. Since the H.E.S.S. energy threshold is ~ 100 GeV, it seems as though the CR component will not be visible, contrary to wide-held opinion. However, the ICS component seems to be well in excess of the H.E.S.S. energy threshold and is expected to be visible. I also found that no pair production will take place for PSR J0437-4715. Hopefully, forthcoming H.E.S.S. observations will provide validation of these results. KEY WORDS: General relativistic frame dragging, GR electrodynamics, millisecond pulsar visibility, non-thermal radiation processes, pair production, H.E.S.S., individual pulsars: PSR J0437-4715. / Thesis (M.Sc. (Physics))--North-West University, Potchefstroom Campus, 2004.

No description available.

Les noyaux actifs de galaxie (NAG) sont les objets les plus énergétiques de l'univers. Cette incroyable puissance provient de l'énergie gravitationnel de matière en rotation autour d'un trou noir super-massif siégeant au centre des galaxies. Environ 10% des NAG sont pourvus de jets relativistes émanant de l'objet central (trou noir et matière environnante) et s'étalant sur des échelles de l'ordre de la galaxie hôte. Ces jets sont observés à toutes les longueurs d'ondes, de la radio aux rayons gamma les plus énergétiques. En dépit de nombreuses études et d'instruments de plus en plus précis depuis leur découverte dans les années 1950, les NAG sont encore très mal compris et la formation, la composition et l'accélération des jets sont des questions encore pleinement ouvertes. Le modèle le plus répandu visant à reproduire l'émission des NAG, le modèle "une zone" repose souvent sur des hypothèse ad-hoc et ne parvient pas à apporter une modélisation satisfaisante.Le paradigme du "two-flow" (deux fluides) développé à l'IPAG et basé sur une idée originale de Sol et al (1989) a pour but de fournir une vision unifiée et cohérente des jets de NAG. Cette théorie repose sur une l'hypothèse principale que les jets seraient en fait composés de deux fluides co-axiaux: une colonne centrale composée d'un plasma purement leptonique (électrons/positrons) se déplaçant à des vitesses relativistes et responsable pour la grande partie de l'émission non thermique observée entourée par une enveloppe composée d'un plasma baryonique (électrons/protons), régie pas la magnéto-hydrodynamique, se déplaçant à des vitesses sous-relativistes mais transportant la majorité de l'énergie. Cette hypothèse est basée sur des indices observationnels ainsi que sur des arguments théoriques et permet d'expliquer nombre des caractéristiques des NAG.Afin d'étudier plus en profondeur le paradigme du two-flow, un modèle numérique basé sur ses concepts et produisants des observables comparables aux observations est nécessaire.Durant ma thèse, j'ai participé au développement de ce modèle, m'intéressant notamment à la diffusion Compton inverse de photons provenant de l'extérieur du jet. Ce processus, primordial dans la modélisation des NAG, est aussi central dans le paradigme du two-flow car il est à l'origine de l'accélération de la colonne via l'effet fusée Compton. Pour cela, j'ai du développer des nouvelles approximations analytiques de la diffusion Compton d'une distribution thermique de photons.En m'intéressant à l'effet fusée Compton, j'ai pu montré que dans le champ de photon thermique d'un NAG, le facteur de Lorentz d'ensemble du plasma pouvait être sujet à des variations le long du jet en fonction de la distance à l'objet central. Ces variations peuvent avoir un effet important sur l'émission observée et peuvent induire de la variabilité spatiale et temporelle. J'ai également montré que les facteurs de Lorentz terminaux obtenus étaient compatibles avec les conditions physiques attendus dans les jets et avec les observations.Le modèle complet produit des DES directement comparables aux observations. Néanmoins, le modèle est par nature erratique et il est quasiment impossible de relier directement les paramètres du modèles avec les DES produites. Malheureusement, les procédures standards d'adaptation automatique aux données (e.g. basé sur les méthodes de gradient) ne sont pas adaptées au modèle à cause de son grand nombre de paramètres, de sa non-linéarité et du temps de calcul important. Afin de palier à ce problème, j'ai développé une procédure d'adaptation automatique basée sur les algorithmes génétiques. L'utilisation de cet outil a permis la reproduction de plusieurs DES par le modèle. J'ai également montré que le modèle était capable de reproduire les DES observées avec des facteurs de Lorentz d'ensemble relativement bas, ce qui pourrait potentiellement apporter une harmonisation entre les observations et les nécessités théoriques. / Active galactic nuclei (AGN) are the most energetic objects known in the universe. Their fantastic energy is due to efficient conversion of gravitational energy of mass accreted on super-massive black-holes at the center of galaxy into luminous energy. 10% of AGN are even more incredible as they display relativistic jets on galaxy scales. Those jets are observed at all energies, from far radio to highest gamma-rays. Despite intense study since their discovery in the 50's and more and more observations, favored by rapid progress in instrumentation, AGN are still widely misunderstood. The questions of formation, composition, and acceleration of jets are central but still a matter of debates. Models aiming at reproducing observed emission have been developed throughout the years. The most common one, the one-zone model, often relies on ad hoc hypothesis and does not provide a satisfactory answer.The two-flow paradigm developed at IPAG and based on an original idea from Sol et al (1989) aims at giving a more coherent and physical representation of AGN jets. The principal assumption is that jets are actually composed of two coaxial flows: an inner spine made of a pure pair plasma, moving at relativistic speed and responsible for the non-thermal observed emission surrounded by an external sheath, made of a baryonic MHD plasma, midly relativistic but carrying most of the power. The two-flow paradigm finds roots in observations as well as theoretical arguments and has been able to explain many AGN features.During my PhD, I studied this paradigm and contributed to the development of a numerical model based on its concepts. I have been particularly interested in the inverse Compton scattering of thermal photons, fundamental process in the modeling of AGN emission, as well as the Compton rocket effect, key to the acceleration of the spine in the two-flow paradigm.However, taking into account the inverse Compton emission, with the complete cross-section (including the Klein-Nishina regime) and the anisotropy can be very time consuming. To accomplish fast and efficient computation of the external Compton emission, I have had to formulate new analytical approximations of the scattering of a thermal distribution of photons.I have also studied the Compton rocket effect, responsible for the acceleration of the inner spine in the two-flow paradigm. I showed that the resulting bulk Lorentz factor of the flow in the complex photon field of an AGN is subject to variations along the jet as a function of the distance to the central engine. These variations can have drastic effects on the observed emission and could induce variability, both spatially and temporally.I also showed that the terminal bulk Lorentz factor obtained are compatible with physical conditions expected in jets and with observations.The complete model produce spectral energy distribution (SED) comparable to observed ones. However, the model is by nature erratic and it is difficult to make a direct link between the model parameters (input) and the SED (output). Unfortunately, standard data fitting procedures (e.g. based on gradient methods) are not adapted to the model due to its important number of parameters, its important computing time and its non-linearity. In order to circumvent this issue, I have developed a fitting tool based on genetic algorithms. The application of this algorithm allowed me to successfully fit several SED. In particular, I have also showed that the model, because based on a structured jet model, can reproduce observations with low bulk Lorentz factor, thus giving hope to match observations and theoretical requirements in this matter.