In this thesis we study GaAs one dimensional hole systems with strong spin-orbit interaction effects. The primary focus is the Zeeman splitting of 1D subbands in the two orthogonal in-plane magnetic field directions. We study two types of 1D hole systems based on different (311)A grown heterostructures: a modulation doped GaAs/AlGaAs square quantum well and an undoped induced GaAs/AlGaAs triangular quantum well. The results from the modulation doped 1D wire show enhanced anisotropy of the effective Lande g-factor for the two in-plane field directions (parallel and perpendicular to the wire), compared to that in 2D hole systems. This enhancement is explained by the confinement induced reorientation of the total angular momentum ^ J from perpendicular to the 2D plane to in-plane and parallel to the wire. We use the intrinsic anisotropy of the in-plane g-factors to probe the 0:7 structure and the zero bias anomaly in 1D hole wires. We find that the behaviour of the 0:7 structure and the ZBA are correlated and depend strongly on the orientation of the in-plane field. This result proves the connection between the 0:7 and the ZBA and their relation to spin. We fabricate the first induced hole 1D wire with extremely stable gate characteristics and characterize this device. We also fabricate devices with two orthogonal induced hole wires on one chip, to study the interplay between the confinement, crystallographic anisotropy and spin-orbit coupling and their effect on the Zeeman splitting. We find that the ratios of the g-factors in the two orthogonal field directions for the two wires show opposite behaviour. We compare absolute values of the g-factors relative to the magnetic field direction. For B || [011] the g-factor is large for the wire along [011] and small for the wire along [233]. Whereas for B || [233], the g-factors are large irrespective of the wire direction. The former result can be explained by reorientation of ^ J along the wire, and the latter by an additional off-diagonal Zeeman term, which leads to the out-of-plane component of ^ J when B || [233], and as a result, to enhanced g-factors via increased exchange interactions.

The main objective of this thesis is to study the behavior of black objects in external fields, for example black holes and black strings in 4 and 5-dimensional spacetimes respectively. In particular, to analyze how external fields affect horizons and the internal structure of such objects, to study their properties, and tocunderstand how the spacetime fabric works. The thesis contains three chapters. In Chapters 1 and 2 we study the interior of 4-dimensional static, axisymmetric, electrically neutral and electrically charged distorted black holes. We analyze how external static and axisymmetric distortions affect the interior of such black holes. In particular, we study the behavior of the interior solution of an electrically neutral black hole near its horizon and singularity. The analysis shows that there exists a certain duality between the event horizon and the singularity. As a special example, we study the interior of a compactified 4-dimensional Schwarzschild black hole. In the case of an electrically charged black hole, a similar duality exists between its event and Cauchy horizons. The duality implies that the Cauchy horizon remains regular, provided the distortion is regular at the event horizon. Extension of the general theory of relativity to higher dimensional spacetimes brings a large variety of black objects whose boundary, the event horizon, may be of a complicated structure. One such object is a black string. In Chapter 3 we discuss the so-called Gregory-Laflamme instability of 5-dimensional black strings in a spacetime with one compact dimension and their topological phase transitions. Here we consider black strings with electric or magnetic charge. Linear static perturbations of these objects indicate the presence of a threshold unstable mode. An analysis of such mode shows that an electrically charged black string is less stable than a neutral one. The situation is opposite for a magnetically charged black string. An analysis of 5-dimensional extremal black string with electric charge shows a continuous spectrum of unstable threshold modes. The results presented in this thesis may have applications in the theory of classical 4-dimensional black holes and in the modern theoretical models of higher dimensions.

No description available.

Upon dimensional reduction, certain supergravity theories exhibit symmetries otherwise undetected, called hidden symmetries. Not only do these symmetries teach us about the structure of the corresponding theories but moreover they provide methods to construct black hole solutions. In this thesis, we study the hidden symmetries of supergravity theories of particular interest and how these help constructing black hole solutions in dimensions D>4. We focus on three representative cases that are the symmetries appearing upon dimensional reduction to three, two and one dimensions. They are respectively described by finite, affine and hyperbolic algebras. In the first two cases, we develop and apply solution generating techniques. The first part of this thesis introduces the background concepts. We start with an introduction to black holes and other black objects in dimensions D>4. We present their subtleties, the known solutions and the conjectured ones. We insist on stationary axisymmetric solutions of vacuum and to the corresponding solution generating technique. The next chapter gives an introduction to Kac-Moody algebras. These indeed play a central role in this thesis as the symmetries appearing in three, two and one dimensions are described by three types of Kac-Moody algebras called respectively finite, affine and hyperbolic. In the second part, we first review the notion of dimensional reductions and how the hidden symmetries can be uncovered. The rest of the thesis contains three applications of these hidden symmetries. The first two concern five-dimensional minimal supergravity. Upon dimensional reduction to three dimensions, this theory exhibits a symmetry under the exceptional finite Kac-Moody algebra g2. This 14-dimensional algebra is the smallest exceptional finite Kac-Moody algebra. We use this duality to generate solutions while focussing mainly on black strings. After reduction to two dimensions, the symmetry becomes infinite-dimensional and is described by the affine extension of g2. Moreover, the two-dimensional theory is integrable, which allows us to develop another type of solution generating technique, hitherto applied only to vacuum gravity. In this work we generalize it to a case with matter fields. Finally, the notion of dimensional reduction to one dimension provides the necessary intuition for the conjecture of an algebraic formulation of M-theory, candidate to the unification of all interactions, based on the hyperbolic Kac-Moody algebra e10. In the last chapter of this thesis, we study an aspect of this correspondence, namely the e10 symmetry of massive type IIA supergravity in ten dimensions. / On sait depuis longtemps que par un processus appelé réduction dimensionnelle, on peut faire apparaître dans certaines théories de gravitation des symétries autrement indétectées. On les appelle des symétries cachées. La mise en évidence de ces symétries non seulement nous informe sur la structure de ces théories, mais de plus elle permet d'élaborer des méthodes de construction de solutions de trous noirs. Dans cette thèse, nous étudions les symétries cachées de certaines théories de supergravité en dimensions supérieures à quatre. Nous nous concentrons sur trois cas représentatifs que sont les symétries apparaissant après réduction à trois, deux et une dimensions. Dans les cas des symétries apparaissant à trois et à deux dimensions nous développons et appliquons des méthodes de construction de solutions. La première partie introduit les concepts préliminaires. Nous commençons par une introduction aux trous noirs et autres objets noirs en dimensions supérieures à quatre. Nous en présentons les subtilités, les solutions connues à ce jour et celles qui ne sont encore que conjecturées. Nous insistons particulièrement sur les solutions stationnaires à symétrie axiale dans le vide et à la méthode de construction de solutions correspondante. Le chapitre suivant présente une introduction aux algèbres de Kac-Moody. Celles-ci jouent en effet un rôle central dans cette thèse puisque les symétries apparaissant à trois, deux et une dimensions sont décrites par trois types d'algèbres de Kac-Moody appelées respectivement finies, affines et hyperboliques. Dans la deuxième partie, nous rentrons dans le vif du sujet, en commençant par rappeler le principe des réductions dimensionnelles et la mise en évidence des différents types de symétries cachées. Les trois derniers chapitres contiennent ensuite trois applications de ces symétries cachées. Dans deux d'entre eux, nous nous concentrons sur la théorie de supergravité minimale à cinq dimensions. Après réduction à trois dimensions, cette théorie présente un symétrie cachée sous le groupe G2 qui, avec quatorze dimensions, est le plus petit des groupes de Lie exceptionnels. Nous utilisons cette dualité pour engendrer des solutions, en nous focalisant essentiellement sur les solutions de cordes noires. A deux dimensions, la symétrie est décrite par l'extension affine de G2. De plus, la théorie est alors complètement intégrable. Cela conduit à un autre type de méthode de construction de solutions, jusqu'alors uniquement appliquée à des théories dans le vide. Dans ce travail, nous la généralisons donc à un cas avec champs de matière. Enfin, la notion de réduction à une dimension fournit l'intuition d'une conjecture selon laquelle la théorie M, candidate à l'unification de toutes les interactions, pourrait être reformulée en une théorie basée sur l'algèbre de Kac-Moody hyperbolique e10. Dans le dernier chapitre de cette thèse, nous étudions un aspect de cette correspondance, à savoir, la symétrie sous e10 de la supergravité massive de type IIA à dix dimensions.

In this dissertation, we investigate the macroscopic magnetic properties of bulk high-temperature superconductors (HTS) containing an array of artificial holes in view of enhancing their performances. The study involves a numerical modelling part and an experimental characterization part. In each part, novel concepts are highlighted and detailed. In particular, we develop a three-dimensional finite-element method (FEM) for calculating the magnetic field penetration in HTS where a single time-step is used in the case of a linearly varying applied magnetic field, and we probe the magnetic field in the volume of drilled samples with the help of microcoils inserted inside the holes. The thesis starts with an introductory chapter that describes the general concept of high-temperature superconductivity and particularly draws the attention on the interests and on the synthesis of drilled structures. Then, we detail the modelling tools that are used for evaluating the magnetic properties of drilled samples. Three models are taken into account: (1) the numerical Bean model which is a generalization of the Bean model for arbitrary cross sections where the samples are assumed to have an infinite height; (2) a 2D finite element model implemented in the open source solver GetDP for samples with an infinite height and assuming a power law relationship, that is characterized by a critical exponent n, between the electric field, E, and the current density, J; (3) a 3D finite element model with the same equations as those of model (2), but where these are solved in a three-dimensional sample with a finite height. For large values of n, both FEM models use the properties of a slow magnetic diffusion to reduce the number of time steps. In particular, the trapped flux can be calculated with only two time-steps: during the first step, the applied magnetic flux density is increased with a constant sweep rate to a maximum value, it then decreases to zero with the same sweep rate during the second step. The models are first used in simple geometries where they are compared to other available techniques. These are next applied to drilled samples. A systematic numerical study of the influence of the holes on the magnetic properties of the sample is reported. A single hole perturbs the critical current flow over an extended region that is bounded by a discontinuity line, where the direction of the current density changes abruptly. In samples with several holes and a given critical current density, we demonstrate that the trapped magnetic flux is maximized when the centre of each hole is positioned on one of the discontinuity lines produced by the neighbouring holes. For a cylindrical sample, we construct a polar triangular hole pattern that exploits this principle; in such a lattice, the trapped field is 20% higher than in a squared lattice, for which the holes do not lie on discontinuity lines. These results are experimentally validated. Two parallelepipedic samples are drilled with two different hole lattices. The trapped magnetic flux density of these samples is characterized by a Hall probe mapping before and after drilling holes. The sample in which the holes are aligned on the discontinuity lines exhibits the smallest magnetization drop that results from the hole drilling. Then, we resort to a novel experimental technique using microcoils inside the holes to characterize the local magnetic properties in the volume of drilled samples. In a given hole, three different penetration regimes can be observed when the sample is subjected to an AC magnetic field: (i) the shielded regime, where no magnetic flux threads the hole; (ii) the gradual penetration regime, where the amplitude of the magnetic field scales with the applied field; and (iii) the flux concentration regime, where the magnetic field exceeds that of the applied field. A comparison of the measurements with simple models assuming an infinite height shows that the holes may serve as a return path for the demagnetizing field lines. In the case of a pulsed field excitation, that measurement technique also allows us to estimate the trapped magnetic flux density in the volume of the sample and compare it with that on the surfaces. Moreover, the penetration of a magnetic pulse from hole to hole is described in the median plane and on the surface and the differences of penetration speeds are explained. Finally, we investigate the magnetic properties of drilled samples whose holes are filled with a ferromagnetic powder. To this aim, we use experimental techniques (Hall probe mapping techniques, together with measurements of the volume magnetization and of the levitation force between the HTS sample and a permanent magnet) and a numerical model (3D FEM) to characterize the modification of the magnetic properties resulting from the impregnation of the holes with AISI 410 ferromagnetic powder. Numerical results support the experimental observations and give clues to understand the mutual interaction between the HTS sample and the ferromagnetic powder inserted in its holes. In particular, the Hall probe mappings of the distribution of the trapped flux above the non-impregnated and impregnated samples reveal an increase of trapped flux after impregnation that is confirmed by simulations.

Collisions of black holes and neutron stars, named mixed binaries in the following, are interesting because of at least two reasons. Firstly, it is expected that they emit a large amount of energy as gravitational waves, which could be measured by new detectors. The form of those waves is expected to carry information about the internal structure of such systems. Secondly, collisions of such objects are the prime suspects of short gamma ray bursts. The exact mechanism for the energy emission is unknown so far. <br><br> In the past, Newtonian theory of gravitation and modifications to it were often used for numerical simulations of collisions of mixed binary systems. However, near to such objects, the gravitational forces are so strong, that the use of General Relativity is necessary for accurate predictions. <br><br> There are a lot of problems in general relativistic simulations. However, systems of two neutron stars and systems of two black holes have been studies extensively in the past and a lot of those problems have been solved. One of the remaining problems so far has been the use of hydrodynamic on excision boundaries. Inside excision regions, no evolution is carried out. Such regions are often used inside black holes to circumvent instabilities of the numerical methods near the singularity. Methods to handle hydrodynamics at such boundaries have been described and tests are shown in this work. <br><br> One important test and the first application of those methods has been the simulation of a collapsing neutron star to a black hole. The success of these simulations and in particular the performance of the excision methods was an important step towards simulations of mixed binaries. <br><br> Initial data are necessary for every numerical simulation. However, the creation of such initial data for general relativistic situations is in general very complicated. In this work it is shown how to obtain initial data for mixed binary systems using an already existing method for initial data of two black holes. <br><br> These initial data have been used for evolutions of such systems and problems encountered are discussed in this work. One of the problems are instabilities due to different methods, which could be solved by dissipation of appropriate strength. Another problem is the expected drift of the black hole towards the neutron star. It is shown, that this can be solved by using special gauge conditions, which prevent the black hole from moving on the computational grid. <br><br> The methods and simulations shown in this work are only the starting step for a much more detailed study of mixed binary system. Better methods, models and simulations with higher resolution and even better gauge conditions will be focus of future work. <br><br> It is expected that such detailed studies can give information about the emitted gravitational waves, which is important in view of the newly built gravitational wave detectors. In addition, these simulations could give insight into the processes responsible for short gamma ray bursts. / Zusammenstöße eines schwarzen Lochs und eines Neutronensterns, im Folgenden "gemischte Zusammenstöße" genannt, sind aus wenigstens zwei Gründen interessant. Erstens wird erwartet, dass dabei große Mengen Energie als Gravitationswellen freigesetzt werden und diese mit neuen Detektoren gemessen werden können. Die Form dieser Wellen verrät viel über die Beschaffenheit eines solchen Systems und stellt neben elektromagnetischen Wellen eine wichtige Informationsquelle dar. Zweitens sind Zusammenstöße von kompakten Objekten wie Neutronensternen und schwarze Löchern sehr wahrscheinlich die Ursache sogenannter kurzer Gammastrahlungsblitze. Deren genauer Mechanismus für die Umwandlung der gewaltigen Energiemengen, die bei diesen Blitzen ausgesandt werden, ist jedoch bisher unbekannt. <br><br> Computersimulationen von Zusammenstößen eines gemischten Systems wurden bisher oft unter Benutzung der Newtonschen Gravitationstheorie, bzw. Korrekturen dazu, durchgeführt. In der Nähe so kompakte Objekte wie schwarzer Löcher oder Neutronensterne ist jedoch die Gravitationswirkung so stark, dass Näherungen wie die erwähnten Korrekturen der Newtonschen Gravitationstheorie zu ungenau sind. Eine Benutzung der allgemeinen Relativitätstheorie ist daher für dieses Problem unumgänglich. <br><br> Die Probleme allgemein-relativistischer Simulationen sind vielfältig. Jedoch wurden Binärsysteme zweier schwarzer Löcher und zweier Neutronensterne schon eingehend untersucht, und so viele Probleme, die auch Simulationen gemischter Systeme betreffen, gelöst. Eins der bisher ausstehenden Probleme war die Behandlung der Hydrodynamik an Ausschneiderändern; Rändern zu Gebieten, die in der Zeitentwicklung der Simulation ignoriert werden. Solche Ränder werden zum Beispiel innerhalb eines schwarzen Lochs benutzt, um Instabilitäten des Programms in der Nähe der Singularität zu vermeiden. Methoden, solche Ränder zu behandeln wurden in der Arbeit entwickelt, getestet und gezeigt, dass sie verlässlich arbeiten. <br><br> Ein wichtiger Test für diese Methoden, der gleichzeitig der Gewinnung neuer Erkenntnisse diente, war deren Anwendung auf Simulationen von zu schwarzen Löchern kollabierenden, rotierenden Sternen. Der Erfolg, diese Simulationen ohne Probleme mit den erwähnten Methoden durchzuführen, war ein wichtiger Schritt zu Simulationen gemischter Binärsysteme. <br><br> Für Computersimulationen sind Anfangsdaten notwendig, die das gewünschte Problem beschreiben. Die Erstellung solcher Anfangsdaten ist jedoch unter Benutzung der allgemeinen Relativitätstheorie ausser in Spezialfällen sehr komplex. Wir zeigen, wie man einen schon vorhandenen Algorithmus für Anfangsdaten für zwei schwarze Löcher ändern kann, um Anfangsdaten für ein gemischtes Binärsystem zu erhalten. <br><br> Diese Anfangsdaten wurden für Simulationen eines gemischten Binärsystems benutzt. Während dieser Simulationen traten mehrere Probleme auf. Zwei dieser Probleme waren numerische Instabilitäten unterschiedlicher Herkunft. Beide konnten jedoch mit angepasst starker Dissipation (der künstliche Entnahme von hochfrequenter Energie aus dem System) unterdrückt werden. Ein weiteres Problem war die erwartete Bewegung des schwarzen Lochs in Richtung des Neutronensterns. Da ein Teil des Simulationsgebietes innerhalb des schwarzen Lochs ausgeschnitten wird und das verwendete Programm bewegte Ausschneidegebiete nicht behandeln kann, darf sich das schwarze Loch jedoch auf dem Gitter kaum bewegen. Wir haben dieses Problem durch eine an das Problem angepasste Eichbedingung gelöst, die auf Bewegungen des scheinbaren Horizons reagiert und die Position des schwarzen Lochs auf diese Weise nahezu konstant hält. <br><br> Die Methoden und Simulationen dieser Arbeit sind nur der Anfangspunkt einer ausführlichen Studie von Binärsystemen eines schwarzen Lochs und eines Neutronensterns. Bessere Methoden, Modelle und Simulationen mit höherer Auflösung und besser an das System angepassten Koordinaten werden Mittelpunkt zukünftiger Arbeit sein. <br><br> Es wird erwartet, dass solche detailierten Studien Erkenntnisse über die abgestrahlten Gravitationswellen liefern, die gerade in Hinblick auf die neuen Gravitationswellendetektoren wichtig sind. Weiterhin könnten diese Simulationen dabei helfen, die Prozesse, die kurze Gammastrahlungsblitze hervorrufen, und über die im Moment kaum etwas bekannt ist, aufzuklären.

We study the effects of loop quantum gravity motivated corrections in classical systems. Computational methods are used to simulate black hole formation from the gravitational collapse of a massless scalar field in Painleve-Gullstrand coordinates. Singularities present in the classical case are resolved by a radiation-like phase in the quantum collapse. The evaporation is not complete but leaves behind an outward moving shell of mass that disperses to infinity. We reproduce Choptuik scaling showing the usual behaviour for the curvature scaling, while observing previously unseen behaviour in the mass scaling. The quantum corrections are found to impose a lower limit on black hole mass and generate a new universal power law scaling relationship. In a parallel study, we quantize the Hamiltonian for a particle in the singular $1/r^2$ potential, a form that appears frequently in black hole physics. In addition to conventional Schrodinger methods, the quantization is performed using full and semiclassical polymerization. The various quantization schemes are in excellent agreement for the highly excited states but differ for the low-lying states, and the polymer spectrum is bounded below even when the Schrodinger spectrum is not. / May 2009

No description available.

We study a proposed statistical explanation for the Bekenstein-Hawking entropy of a black hole in which entropy arises quantum-mechanically as a result of entanglement. Arguments for the identification of black hole entropy with entanglement entropy are reviewed in the framework of quantum field theory, emphasizing the role of renormalization and the need for a physical short-distance cutoff. Our main novel contribution is a calculation of entanglement entropy in loop quantum gravity. The kinematical Hilbert space and spin network states are introduced, and the entanglement entropy of these states is calculated using methods from quantum information theory. The entanglement entropy is compared with the density of states previously computed for isolated horizons in loop quantum gravity, and the two are found to agree up to a topological term. We investigate a conjecture due to Sorkin that the entanglement entropy must be a monotonically increasing function of time under the assumption of causality. For a system described by a finite-dimensional Hilbert space, the conjecture is found to be trivial, and for a system described by an infinite-dimensional Hilbert space a counterexample is provided. For quantum states with Euclidean symmetry, the area scaling of the entanglement entropy is shown to be equivalent to the strong additivity condition on the entropy. The strong additivity condition is naturally interpreted in information-theoretic terms as a continuous analog of the Markov property for a classical random variable. We explicitly construct states of a quantum field theory on the one-dimensional real line in which the area law is exactly satisfied.

We study a proposed statistical explanation for the Bekenstein-Hawking entropy of a black hole in which entropy arises quantum-mechanically as a result of entanglement. Arguments for the identification of black hole entropy with entanglement entropy are reviewed in the framework of quantum field theory, emphasizing the role of renormalization and the need for a physical short-distance cutoff. Our main novel contribution is a calculation of entanglement entropy in loop quantum gravity. The kinematical Hilbert space and spin network states are introduced, and the entanglement entropy of these states is calculated using methods from quantum information theory. The entanglement entropy is compared with the density of states previously computed for isolated horizons in loop quantum gravity, and the two are found to agree up to a topological term. We investigate a conjecture due to Sorkin that the entanglement entropy must be a monotonically increasing function of time under the assumption of causality. For a system described by a finite-dimensional Hilbert space, the conjecture is found to be trivial, and for a system described by an infinite-dimensional Hilbert space a counterexample is provided. For quantum states with Euclidean symmetry, the area scaling of the entanglement entropy is shown to be equivalent to the strong additivity condition on the entropy. The strong additivity condition is naturally interpreted in information-theoretic terms as a continuous analog of the Markov property for a classical random variable. We explicitly construct states of a quantum field theory on the one-dimensional real line in which the area law is exactly satisfied.