121 |
The infrared behavior of lattice QCD green's functions / a numerical study of lattice QCD in Landau gaugeSternbeck, André 15 August 2006 (has links)
Diese Arbeit untersucht im Rahmen der Gittereichtheorie verschiedene Aspekte der QCD in der Landau-Eichung, insbesondere solche, die mit den Gluon- und Geist-Propagatoren bei kleinen Impulsen zusammenhängen. Die Eichgruppe ist SU(3). Wir analysieren den Einfluss unterschiedlicher systematischer Effekte. Wir zeigen, dass der Formfaktor des Geist-Propagators bei kleinen Impulsen systematisch von der Wahl der Eichkopien (Gribov-Kopien) abhängt. Hingegen können wir einen solchen Einfluss auf den Gluon-Propagator nicht feststellen. Ebenfalls wird die Verteilung der kleinsten Eigenwerte des Faddeev-Popov-Operators durch die Wahl der Eichkopien beeinflusst. Wir zeigen außerdem, dass der Einfluss dynamischer Wilson-Fermionen auf den Geist-Propagator für die untersuchten Impulse vernachlässigbar ist. Für den Gluon-Propagator können wir jedoch einen deutlichen Einfluss für große und mittlere Impulse feststellen. Zusätzlich wurden beide Propagatoren auf asymmetrischen Gittern gemessen und mit den Daten von symmetrischen Gittern verglichen. Wir vergleichen unsere Ergebnisse mit denen aus Studien von Dyson-Schwinger-Gleichungen für den Gluon- und Geist-Propagator. Wir zeigen, dass das in dieser Arbeit gefundene Niedrigimpulsverhalten im Einklang mit verschiedenen Kriterien für Confinement (Einschluss von Farbladungen) ist. Wir berechnen die laufende Kopplung, die sich als eine renormierungsgruppeninvariante Kombination der Gluon- und Geist-Formfaktoren ergibt. Unsere Ergebnisse zeigen, dass im Bereich kleiner Impulse die laufende Kopplung kleiner wird und so vermutlich kein endlicher Infrarot-Fixpunkt im Grenzfall Impuls Null angestrebt wird. Wir präsentieren außerdem eine erste nichtstörungstheoretische Berechnung der Renormierungskonstante des SU(3) Ghost-Gluon-Vertex. Wir berichten über Untersuchungen zu spektralen Eigenschaften des Faddeev-Popov-Operators. Dazu haben wir eine Reihe der kleinsten Eigenwerte und Eigenvektoren dieses Operators berechnet. / Within the framework of lattice QCD we investigate different aspects of QCD in Landau gauge using Monte Carlo simulations. In particular, we focus on the low momentum behavior of gluon and ghost propagators. The gauge group is SU(3). Different systematic effects on the gluon and ghost propagators are studied. We demonstrate the ghost dressing function to systematically depend on the choice of Gribov copies at low momentum, while the influence on the gluon dressing function is not resolvable. Also the eigenvalue distribution of the Faddeev-Popov operator is sensitive to Gribov copies. We show that the influence of dynamical Wilson fermions on the ghost propagator is negligible at the momenta available to us. On the contrary, fermions affect the gluon propagator at large and intermediate momenta. In addition, we analyze data for both propagators obtained on asymmetric lattices and compare these results with data obtained on symmetric lattices. We compare our data with results from studies of Dyson-Schwinger equations for the gluon and ghost propagators. We demonstrate that the infrared behavior of both propagators, as found in this thesis, is consistent with different criteria for confinement. However, the running coupling constant, given as a renormalization-group-invariant combination of the gluon and ghost dressing functions, does not expose a finite infrared fixed point. Rather the data are in favor of an infrared vanishing coupling constant. We also report on a first nonperturbative computation of the SU(3) ghost-gluon-vertex renormalization constant. We present results of an investigation of the spectral properties of the Faddeev-Popov operator. For this we have calculated the low-lying eigenvalues and eigenmodes of the Faddeev-Popov operator.
|
122 |
Gluon and ghost propagator studies in lattice QCD at finite temperatureAouane, Rafik 14 May 2013 (has links)
Die im infraroten Impulsbereich der Quantenchromodynamik (QCD) berechneten Gluon- und Ghost-Propagatoren spielen eine große Rolle für das sogenannte Confinement der Quarks und Gluonen. Sie sind Gegenstand intensiver Foschungen dank nicht-perturbativer Methoden basierend auf Dyson-Schwinger- (DS) und funktionalen Renormierungsgruppen-Gleichungen (FRG). Darüber hinaus sollte es deren Verhalten bei endlichen Temperaturen erlauben, den chiralen und Deconfinement-Phasenübergang bzw. das Crossover in der QCD besser aufzuklären. Unser Zugang beruht auf der gitter-diskretisierten QCD (LQCD), die es als ab-initio-Methode gestattet, verschiedenste störungstheoretisch nicht zugängliche QCD-Observablen der hadronischen Welt zu berechnen. Wir untersuchen das Temperaturverhalten der Gluon- und Ghost-Propagatoren in der Landau-Eichung für die reine Gluodynamik und die volle QCD. Für den Gluon-Propagator berechnen wir deren longitudinale (DL) sowie transversale (DT) Komponenten. Ziel ist es, Datensätze in Form von Fit-Formeln zu liefern, welche als Input für die DS- (oder FRG-) Gleichungen verwendet werden können. Wir beschäftigen uns mit der vollen (Nf=2) LQCD unter Verwendung der sogenannten twisted mass Fermiondiskretisierung. Von der tmfT-Kollaboration wurden uns dafür Eichfeldkonfigurationen für Temperaturen im Crossover-Bereich sowie jeweils für drei fixierte Pion-Massenwerte im Intervall [300, 500] MeV bereitgestellt. Schließlich berechnen wir innerhalb der reinen SU(3) Eichtheorie (bei T=0) den Landau Gluon-Propagator unter Verwendung verschiedener Eichfixierungskriterien. Unser Ziel ist es, den Einfluss von Eich-Kopien mit minimalen (nicht-trivialen) Eigenwerten des Faddeev-Popov-Operators zu verstehen. Eine solche Studie soll klären, wie Gribov-Kopien das Verhalten der Gluon- und Ghost-Propagatoren im infraroten Bereich prinzipiell beeinflussen. / Gluon and ghost propagators in quantum chromodynamics (QCD) computed in the infrared momentum region play an important role to understand quark and gluon confinement. They are the subject of intensive research thanks to non-perturbative methods based on Dyson-Schwinger (DS) and functional renormalization group (FRG) equations. Moreover, their temperature behavior might also help to explore the chiral and deconfinement phase transition or crossover within QCD at non-zero temperature. Our prime tool is the lattice discretized QCD (LQCD) providing a unique ab-initio non-perturbative approach to deal with the computation of various observables of the hadronic world. We investigate the temperature dependence of Landau gauge gluon and ghost propagators in pure gluodynamics and in full QCD. Regarding the gluon propagator, we compute its longitudinal DL as well its transversal DT components. The aim is to provide a data set in terms of fitting formulae which can be used as input for DS (or FRG) equations. We deal with full (Nf=2) LQCD with the twisted mass fermion discretization. We employ gauge field configurations provided by the tmfT collaboration for temperatures in the crossover region and for three fixed pion mass values in the range [300,500] MeV. Finally, within SU(3) pure gauge theory (at T=0) we compute the Landau gauge gluon propagator according to different gauge fixing criteria. Our goal is to understand the influence of gauge copies with minimal (non-trivial) eigenvalues of the Faddeev-Popov operator.
|
123 |
A quantum hall effect without landau levels in a quasi one dimensional systemBrand, Janetta Debora 12 1900 (has links)
Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: The experimental observation of the quantum Hall effect in a two-dimensional electron gas posed
an intriguing question to theorists: Why is the quantization of conductance so precise, given the
imperfections of the measured samples? The question was answered a few years later, when a
connection was uncovered between the quantum Hall effect and topological quantities associated
with the band structure of the material in which it is observed. The Hall conductance was revealed
to be an integer topological invariant, implying its robustness to certain perturbations.
The topological theory went further than explaining only the usual integer quantum Hall effect
in a perpendicular magnetic field. Soon it was realized that it also applies to certain systems in
which the total magnetic flux is zero. Thus it is possible to have a quantized Hall effect without
Landau levels.
We study a carbon nanotube in a magnetic field perpendicular to its axial direction. Recent
studies suggest that the application of an electric field parallel to the magnetic field would induce
a gap in the electronic spectrum of a previously metallic carbon nanotube. Despite the quasi onedimensional
nature of the carbon nanotube, the gapped state supports a quantum Hall effect and
is associated with a non zero topological invariant. This result is revealed when an additional
magnetic field is applied parallel to the axis of the carbon nanotube. If the flux due to this
magnetic field is varied by one flux quantum, exactly one electron is transported between the
ends of the carbon nanotube. / AFRIKAANSE OPSOMMING: Die eksperimentele waarneming van die kwantum Hall effek in ’n twee-dimensionele elektron gas
laat ’n interessante vraag aan teoretiese fisikuste: Waarom sou die kwantisasie van die geleiding
so presies wees al bevat die monsters, waarop die meetings gedoen word, onsuiwerhede? Hierdie
vraag word ’n paar jaar later geantwoord toe ’n konneksie tussen die kwantum Hall effek en
topologiese waardes, wat verband hou met die bandstruktuur van die monster, gemaak is. Dit
is aan die lig gebring dat die Hall geleiding ’n heeltallige topologiese invariante is wat die robuustheid
teen sekere steurings impliseer. Die topologiese teorie verduidelik nie net die gewone
kwantum Hall effek wat in ’n loodregte magneetveld waargeneem word nie. Dit is ook moontlik
om ’n kwantum Hall effek waar te neem in sekere sisteme waar die totale magneetvloed nul is.
Dit is dus moontlik om ’n gekwantiseerde Hall effek sonder Landau levels te hˆe.
Ons bestudeer ’n koolstofnanobuis in ’n magneetveld loodreg tot die aksiale rigting. Onlangse
studies dui daarop dat die toepassing van ’n elektriese veld parallel aan die magneetveld ’n
gaping in die elektroniese spektrum van ’n metaliese koolstofnanobuis induseer. Ten spyte van
die een-dimensionele aard van die koolstofnanobuis ondersteun die gapings-toestand steeds ’n
kwantum Hall effek en hou dit verband met ’n nie-nul topologiese invariante. Hierdie resultaat
word openbaar wanneer ’n bykomende magneetveld parallel tot die as van die koolstofnanobuis
toegedien word. Indien die vloed as gevolg van hierdie magneetveld met een vloedkwantum
verander word, word presies een elektron tussen die twee kante van die koolstofnanobuis vervoer.
|
124 |
On study of deterministic conservative solvers for the nonlinear boltzmann and landau transport equationsZhang, Chenglong 24 October 2014 (has links)
The Boltzmann Transport Equation (BTE) has been the keystone of the kinetic theory, which is at the center of Statistical Mechanics bridging the gap between the atomic structures and the continuum-like behaviors. The existence of solutions has been a great mathematical challenge and still remains elusive. As a grazing limit of the Boltzmann operator, the Fokker-Planck-Landau (FPL) operator is of primary importance for collisional plasmas. We have worked on the following three different projects regarding the most important kinetic models, the BTE and the FPL Equations. (1). A Discontinuous Galerkin Solver for Nonlinear BTE. We propose a deterministic numerical solver based on Discontinuous Galerkin (DG) methods, which has been rarely studied. As the key part, the weak form of the collision operator is approximated within subspaces of piecewise polynomials. To save the tremendous computational cost with increasing order of polynomials and number of mesh nodes, as well as to resolve loss of conservations due to domain truncations, the following combined procedures are applied. First, the collision operator is projected onto a subspace of basis polynomials up to first order. Then, at every time step, a conservation routine is employed to enforce the preservation of desired moments (mass, momentum and/or energy), with only linear complexity. The asymptotic error analysis shows the validity and guarantees the accuracy of these two procedures. We applied the property of ``shifting symmetries" in the weight matrix, which consists in finding a minimal set of basis matrices that can exactly reconstruct the complete family of collision weight matrix. This procedure, together with showing the sparsity of the weight matrix, reduces the computation and storage of the collision matrix from O(N3) down to O(N^2). (2). Spectral Gap for Linearized Boltzmann Operator. Spectral gaps provide information on the relaxation to equilibrium. This is a pioneer field currently unexplored form the computational viewpoint. This work, for the first time, provides numerical evidence on the existence of spectral gaps and corresponding approximate values. The linearized Boltzmann operator is projected onto a Discontinuous Galerkin mesh, resulting in a ``collision matrix". The original spectral gap problem is then approximated by a constrained minimization problem, with objective function the Rayleigh quotient of the "collision matrix" and with constraints the conservation laws. A conservation correction then applies. We also study the convergence of the approximate Rayleigh quotient to the real spectral gap. (3). A Conservative Scheme for Approximating Collisional Plasmas. We have developed a deterministic conservative solver for the inhomogeneous Fokker-Planck-Landau equations coupled with Poisson equations. The original problem is splitted into two subproblems: collisonless Vlasov problem and collisonal homogeneous Fokker-Planck-Landau problem. They are handled with different numerical schemes. The former is approximated using Runge-Kutta Discontinuous Galerkin (RKDG) scheme with a piecewise polynomial basis subspace covering all collision invariants; while the latter is solved by a conservative spectral method. To link the two different computing grids, a special conservation routine is also developed. All the projects are implemented with hybrid MPI and OpenMP. Numerical results and applications are provided. / text
|
125 |
Défauts de vorticité dans un supraconducteur en présence d'impuretésDos Santos, Mickaël 09 December 2010 (has links) (PDF)
Cette thèse est consacrée à l'étude mathématique de quelques modèles suggérés par la théorie de la supraconductivité. Plus spécifiquement, nous étudions le modèle de Ginzburg-Landau simplifié (sans champ magnétique) en présence de condition de type Dirichlet ou du type degrés prescrits. Dans une première partie nous traitons le problème d'existence de minimiseurs locaux dans un domaine multiplement connexe du plan pour des conditions de type degrés prescrits. La deuxième partie traite l'effet d'un terme de chevillage dans l'énergie de Ginzburg-Landau (GL) bi-dimensionnelle en imposant une condition de type Dirichlet. Cette partie se décompose en trois chapitres. On commence par l'étude d'un terme de chevillage qui est étagé et qui prend une valeur différente de 1 uniquement en un nombre fixe de sous domaines (aussi appelés inclusions) dont la taille tend vers zéro. Dans le chapitre suivant, nous considérons le cas d'un terme de chevillage sans hypothèse de structure particulière dans le cas où la donnée au bord est de degré nul. Dans le dernier chapitre de la deuxième partie, nous traitons le cas d'un terme de chevillage étagé et uniformément distribué avec une condition de type Dirichlet de degré non nul. On montre que la vorticité est quantifiée et localisée dans les inclusions. La dernière partie s'intéresse à l'effet d'un terme de chevillage étagé dans un domaine tridimensionnel avec une condition de Dirichlet. Les résultats préliminaires que nous présentons permettent d'appréhender la manière dont les filaments de vorticité sont "tordus" par l'effet du terme de chevillage.
|
126 |
Vorticité dans le modèle de Ginzburg-Landau et quelques contributions en théorie de point fixeAydi, Hassen 02 June 2012 (has links) (PDF)
Cette habilitation porte sur l'étude de la vorticité dans le modèle de Ginzburg-Landau et quelques contributions en théorie de point fixe
|
127 |
Nonlinear solutions of the amplitude equations governing fluid flow in rotating spherical geometriesBlockley, Edward William January 2008 (has links)
We are interested in the onset of instability of the axisymmetric flow between two concentric spherical shells that differentially rotate about a common axis in the narrow-gap limit. The expected mode of instability takes the form of roughly square axisymmetric Taylor vortices which arise in the vicinity of the equator and are modulated on a latitudinal length scale large compared to the gap width but small compared to the shell radii. At the heart of the difficulties faced is the presence of phase mixing in the system, characterised by a non-zero frequency gradient at the equator and the tendency for vortices located off the equator to oscillate. This mechanism serves to enhance viscous dissipation in the fluid with the effect that the amplitude of any initial disturbance generated at onset is ultimately driven to zero. In this thesis we study a complex Ginzburg-Landau equation derived from the weakly nonlinear analysis of Harris, Bassom and Soward [D. Harris, A. P. Bassom, A. M. Soward, Global bifurcation to travelling waves with application to narrow gap spherical Couette flow, Physica D 177 (2003) p. 122-174] (referred to as HBS) to govern the amplitude modulation of Taylor vortex disturbances in the vicinity of the equator. This equation was developed in a regime that requires the angular velocities of the bounding spheres to be very close. When the spherical shells do not co-rotate, it has the remarkable property that the linearised form of the equation has no non-trivial neutral modes. Furthermore no steady solutions to the nonlinear equation have been found. Despite these challenges Bassom and Soward [A. P. Bassom, A. M. Soward, On finite amplitude subcritical instability in narrow-gap spherical Couette flow, J. Fluid Mech. 499 (2004) p. 277-314] (referred to as BS) identified solutions to the equation in the form of pulse-trains. These pulse-trains consist of oscillatory finite amplitude solutions expressed in terms of a single complex amplitude localised as a pulse about the origin. Each pulse oscillates at a frequency proportional to its distance from the equatorial plane and the whole pulse-train is modulated under an envelope and drifts away from the equator at a relatively slow speed. The survival of the pulse-train depends upon the nonlinear mutual-interaction of close neighbours; as the absence of steady solutions suggests, self-interaction is inadequate. Though we report new solutions to the HBS co-rotation model the primary focus in this work is the physically more interesting case when the shell velocities are far from close. More specifically we concentrate on the investigation of BS-style pulse-train solutions and, in the first part of this thesis, develop a generic framework for the identification and classification of pulse-train solutions. Motivated by relaxation oscillations identified by Cole [S. J. Cole, Nonlinear rapidly rotating spherical convection, Ph.D. thesis, University of Exeter (2004)] whilst studying the related problem of thermal convection in a rapidly rotating self-gravitating sphere, we extend the HBS equation in the second part of this work. A model system is developed which captures many of the essential features exhibited by Cole's, much more complicated, system of equations. We successfully reproduce relaxation oscillations in this extended HBS model and document the solution as it undergoes a series of interesting bifurcations.
|
128 |
Modélisation et simulation numérique multi-échelle du transport cinétique électroniqueDuclous, Roland 24 November 2009 (has links)
Ce manuscrit est dédié au transport relativiste cinétique sous influence de champs magnétiques, identifié comme obstacle pour la modélisation et la simulation intégrée, dans le cadre de la Fusion par Confinement Inertiel (FCI). Une réalisation importante concerne le développement d'un code déterministe de référence, 2Dx-3Dv, de type Maxwell-Fokker-Planck-Landau, permettant la prise en compte de fonctions de distribution à large degré d'anisotropie. Ce travail se situe à l'interface de l'analyse numérique, des mathématiques appliquées, et de la physique des plasmas. Un deuxième résultat marquant concerne la dérivation d'un modèle collisionel multi-échelle, pour le transport d'électrons relativistes dans la matière dense. Des processus importants sont mis en évidence pour la FCI, et une analogie est menée vis-à-vis des processus de transport collisionels connus en radiothérapie. Enfin, un modèle mésoscopique aux moments angulaires, avec fermeture entropique, a été dérivé et utilisé pour le dépôt de dose pour la radiothérapie. Des schémas numériques précis, d'ordre élevé, et robustes, ont été développé dans ce cadre. / This manuscript is dedicated to the relativistic kinetic transport, under the influence of the magnetic field, identified as a barrier for the modeling and integrated simulations, in the frame of the Inertial Confinement Fusion (ICF). An important achievement concerns the development of a deterministic, reference code, 2Dx-3Dv, of Maxwell-Fokker-Planck-Landau type, that permits the treatment of distribution functions with large anisotropy degree. This work is at the interface between the numerical analysis, applied mathematics, and plasma physics. Another milestone result concerns the derivation of a multi-scale, collisional model, for the transport of relativistic electrons in dense matter. A set of processes is demonstrated to be of importance for ICF, and an analogy is conducted with respect to well-known collisional transport processes in radiotherapy. Finally, a mesoscopic angular moment model, with entropic closure, is derived and employed for radiotherapy dose computation. High order precise and robust numerical schemes are then developed in this framework.
|
129 |
Study of Magnetization Switching for MRAM Based Memory TechnologiesPham, Huy 20 December 2009 (has links)
Understanding magnetization reversal is very important in designing high density and high data transfer rate recording media. This research has been motivated by interest in developing new nonvolatile data storage solutions as magnetic random access memories - MRAMs. This dissertation is intended to provide a theoretical analysis of static and dynamic magnetization switching of magnetic systems within the framework of critical curve (CC). Based on the time scale involved, a quasi-static or dynamic CC approach is used. The static magnetization switching can be elegantly described using the concept of critical curves. The critical curves of simple uncoupled films used in MRAM are discussed. We propose a new sensitive method for CC determination of 2D magnetic systems. This method is validated experimentally by measuring experimental critical curves of a series of Co/SiO2 multilayers systems. The dynamics switching is studied using the Landau-Lifshitz-Gilbert (LLG) equation of motion. The switching diagram so-called dynamic critical curve of Stonerlike particles subject to short magnetic field pulses is presented, giving useful information for optimizing field pulse parameters in order to make ultrafast and stable switching possible. For the first time, the dynamic critical curves (dCCs) for synthetic antiferromagnet (SAF) structures are introduced in this work. Comparing with CC, which are currently used for studying the switching in toggle MRAM, dCCs show the consistent switching and bring more useful information on the speed of magnetization reversal. Based on dCCs, better understanding of the switching diagram of toggle MRAM following toggle writing scheme can be achieved. The dynamic switching triggered by spin torque transfer in spin-torque MRAM cell has been also derived in this dissertation. We have studied the magnetization's dynamics properties as a function of applied current pulse amplitude, shape, and also as a function of the Gilbert damping constant. The great important result has been obtained is that, the boundary between switching/non-switching regions is not smooth but having a seashell spiral fringes. The influence of thermal fluctuation on the switching behavior is also discussed in this work.
|
130 |
Diamagnétisme des gaz quantiques quasi-parfaits / Diamagnetism of quasi-perfect quantum gasesSavoie, Baptiste 24 November 2010 (has links)
La majeure partie de cette thèse concerne l’étude de la susceptibilité diamagnétique en champ magnétique nul d’un gaz d’électrons de Bloch à température et densité fixées dans la limite de sfaibles températures. Pour les électrons libres (i.e. en l’absence de potentiel périodique), la susceptibilité diamagnétique a été calculée par L. Landau en 1930 ; le résultat est connu sous le nom de formule de Landau. Quant au cas des électrons de Bloch, E.R. Peierls montra en 1933 que dans l’approximation des électrons fortement liés, la formule pour la susceptibilité diamagnétique reste la même en remplaçant la masse de l’électron par sa ”masse effective” ; ce résultat est connu sous le nom de formule de Landau-Peierls. Depuis, de nombreuses tentatives pour clarifier les hypothèses de validité de la formule de Landau-Peierls ont vu le jour. Le résultat principal de cette thèse établit rigoureusement qu’à température nulle, lorsque la densité d’électrons tend vers zéro, la contribution dominante à la susceptibilité diamagnétique est donné par la formule de Landau-Peierls avecla masse effective de la plus petite bande d’énergie de Bloch. / The main part of this thesis deals with the zero-field diamagnetic susceptibility of a Blochelectrons gas at fixed temperature and fixed density in the limit of low temperatures. For a freeelectrons gas (that is when the periodic potential is zero), the steady diamagnetic susceptibilityhas been computed by L. Landau in 1930 ; the result is known as Landau formula. As for the Blochelectrons, E.R. Peierls in 1933 showed that under the tight-binding approximation, the formula forthe diamagnetic susceptibility remains the same but with the mass of the electron replaced by its”effective mass” ; this result is known as the Landau-Peierls formula. Since, there were very manyattempts in order to clarify the assumptions of validity of the Landau-Peierls formula. The mainresult of this thesis establishes rigorously that at zero temperature, as the density of electrons tendsto zero, the leading contribution of the diamagnetic susceptibility is given by the Landau-Peierlsformula with the effective mass of the lowest Bloch energy band.
|
Page generated in 0.0378 seconds