Zufällige Bewegungen wie Diffusion sind ein allgegenwärtiges Phänomen, anzufinden nicht nur in der Physik. Das Hauptobjekt von Diffusionsmodellen ist oft die mittlere quadratische Verschiebung eines Teilchens, welche für sogenannte normal-diffusive Prozesse linear mit der Zeit anwächst. Anomale Diffusion bezeichnet Prozesse, für welche sie nicht-linear wächst; ein wichtiges Beispiel ist die Bewegung großer Moleküle in biologischen Zellen. Erscheinungen wie schwache Ergodizitätsbrechung sind ebenfalls bei anomaler Diffusion zu finden, und es gibt viele mathematische Modelle zu ihrer Beschreibung. Oft ist es schwierig für ein bestimmtes Experiment das "richtige" Modell, d.h. die physikalische Ursache der Anomalie, zu finden. Eine Methode zur Trennung oder Identifikation der physikalischen Ursachen wird also dringend benötigt. In dieser Arbeit stellten wir uns diesem Problem. Zuerst betrachteten wir ein recht allgemeines Modell zur Diffusion in ungeordneten Medien. Mithilfe der Netzwerktheorie trennten wir zwei Mechanismen, nämlich energetische und strukturelle Unordnung, welche beide zu anomaler Diffusion führen. Diese Klassen wurden dann in die Sprache der stochastischen Prozesse übertragen. Das erlaubte uns eine einfache Methode, die des fundamentalen Momentes, zu formulieren. Jene Methode ist in der Lage die energetischen und strukturellen Anteile eines Diffusionsprozesses voneinander zu trennen. Zuletzt behandelten wir Ergodizität und Ergodizitätsbrechung aus der Sicht der energetischen und strukturellen Unordnung. / Random motion, in particular diffusion, is a ubiquitous phenomenon that is encountered not only in physics. The main object of a diffusion model is usually the mean squared displacement (msd) of a particle, which for so-called normal diffusion grows linearly in time. Anomalous diffusion denotes processes, in which the msd grows non-linearly; an important example is the motion of large molecules in biological cells. Many interesting properties like weak ergodicity breaking are connected to anomalous diffusion, and there are many mathematical models exhibiting anomalous behaviour. Given an experiment, it is often difficult to decide, what is the "correct" model, i.e. the physical cause for the anomaly. Therefore, a method capable of separation and identification of different physical mechanisms is urgently required. This thesis approached the mentioned issue. First of all, we considered a quite general model for diffusion in disordered media. We used some network theory to distinguish two physical mechanisms - energetic and structural disorder. Both cause anomalous diffusion. Those classes of disorder were then translated into the language of stochastic processes. This put ourselves in position to propose a simple method, the fundamental moment, that is capable of separating the energetic and structural components of a diffusion process. At last, we discussed ergodicity and ergodicity breaking from the point of view of energetic and structural disorder.

Die Auswirkungen von anomalen Kopplungen bei den Prozessen der W-Paar- und der ZZ-Erzeugung werden untersucht. Analytische Ausdruecke fuer die differentiellen Wirkungsquerschnitte werden fuer beide Prozesse abgeleitet und numerische Ergebnisse werden praesentiert. Die analytischen Ergebnisse zur W-Paarerzeugung wurden in das Fortranprogramm GENTLE eingebaut, waehrend die Ergebnisse zur ZZ-Erzeugung in einem separaten Program ZAC zur Verfuegung stehen. Die numerischen Resultate werden mit den Vorhersagen des Standardmodells verglichen. Bei der W-Paarerzeugung sind Strahlungskorrekturen durch den Strukturfunktionszugang im Rahmen der Anfangszustandsabstrahlung beruecksichtig worden. Die Auswirkungen eines anomalen magnetischen Momentes a_tau des tau-Leptons auf die Endzustandsabstrahlung im Prozess der tau-Paarproduktion bei LEP1 wurden untersucht. Dieser Prozess erlaubt die Bestimmung des experimentellen Limits fuer das anomale magnetische Moment a_tau. Als ein Ergebnis erhalten wir, dass Beitraege, die linear in a_tau sind und als klein angesehen wurden, bei den heutigen Limits nicht mehr vernachlaessigt werden koennen. / Predictions are made for the effects of anomalous couplings in the processes of W-pair and ZZ production. Analytical expressions for the differential cross-sections are derived in both cases and numerical results are presented. The analytical results for W-pair production were implemented into the Fortran program GENTLE, while the ZZ production results are available in the stand-alone program ZAC. The numerical results are compared with the Standard Model predictions. For W-pair production radiative corrections are considered by using the structure function approach for the description of initial state radiation. Effects of an anomalous magnetic moment a_tau of the tau-lepton to the final state radiation in the process of tau-pair production at LEP1 are examined. This process allows to determine experimental limits for the anomalous magnetic moment of the tau. As a result we find that contributions linear in a_tau, which were believed to be small, cannot be neglegted at the present limits.

Wir stellen die Resultate einer Untersuchung von Strom-Strom-Korrelatoren beruhend auf den Grundprinzipien der Quantenchromodynamik vor. Wir benutzen die nicht-perturbativen Methoden der sogenannten twisted mass Gitter-QCD mit dynamischem up- und down-Quark unter Ausnutzung der automatischen O(a)-Verbesserung. Als Anwendung diskutieren wir die Berechnung des hadronischen Beitrags zur Korrektur in führender Ordnung in der elektromagnetischen Kopplung zum anomalen magnetischen Moment des Myons. Dieses gilt als eine sehr geeignete Größe für die aktuelle Suche nach neuer Physik jenseits des Standardmodells, besonders im Hinblick auf die Diskrepanz zwischen der Vorhersage aus dem Standardmodell und dem experimentell gemessenen Wert. Innerhalb der theoretischen Bestimmung ist der hadronische Anteil führender Ordnung mit der größten Unsicherheit behaftet und genießt derzeit somit naturgemäß Priorität. Wir beschreiben unsere Studie aller systematischen Unsicherheiten der Gitterrechnung auf Grundlage von drei Gittervolumina, zwei Gitterabständen, Pionmassen im Bereich von 650 MeV bis 290 MeV und den Quark-unverbundenen Beiträgen. Für die Extrapolation zum physikalischen Punkt stellen wir eine neue Methode vor, welche die Abhängigkeit von der Pionmasse hinreichend abschwächt und eine lineare Extrapolation ermöglicht. Im Ergebnis bestimmen wir den Beitrag von up- und down-Quark zu a_mu^hlo(N_f=2) = 5.69 (15) 10^(-8). Die dargelegten Methoden werden auf das Elektron- und das Tau-Lepton erweitert mit dem Resultat a_el^hlo(N_f=2) = 1.512 (43) 10^(-12) bzw. a_tau^hlo(N_f=2) = 2.635 (54) 10^(-6). Wir schätzen den Beitrag des charm-Quarks zu a_mu^hlo in der Partially Quenched tmLQCD mit dem Resultat a_mu^hlo(charm) = 1.447 (24) (30) 10^(-9) in Übereinstimmung mit der Vorhersage über die Dispersionsrelation unter Hinzunahme experimenteller Daten für das hadronische R-Verhältnis. / We present an investigation of hadronic current-current correlators based on the first principles of Quantum Chromodynamics. Specifically we apply the non-perturbative methods of twisted mass lattice QCD with dynamical up and down quark taking advantage of its automatic O(a) improvement. As a special application we discuss the calculation of the hadronic leading order contribution to the muon anomalous magnetic moment. The latter is regarded as a promising quantity for the search for physics beyond the standard model. The origin of the strong interest in the muon anomaly lies in the persistent discrepancy between the standard model estimate and its experimental measurement. In the theoretical determination the hadronic leading order part is currently afflicted with the largest uncertainty and a dedicated lattice investigation of the former can be of strong impact on future estimates. We discuss our study of all systematic uncertainties in the lattice calculation, including three lattice volumes, two lattice spacings, pion masses from 650 MeV to 290 MeV and the quark-disconnected contribution. We present a new method for the extrapolation to the physical point that softens the pion mass dependence of a_mu^hlo and allows for a linear extrapolation with small statistical uncertainty at the physical point. We determine the contribution of up and down quark as a_mu^hlo(N_f=2) = 5.69 (15) 10^(-8). The methods used for the muon are extended to the electron and tau lepton and we find a_el^hlo(N_f=2) = 1.512 (43) 10^(-12) and a_tau^hlo(N_f=2) = 2.635 (54) 10^(-6). We estimate the charm contribution to a_mu^hlo in partially quenched tmLQCD with the result a_mu^hlo(charm) = 1.447 (24) (30) 10^(-9) in very good agreement with a dispersion-relation based result using experimental data for the hadronic R-ratio.

Im ersten Teil dieser Dissertation untersuchen wir Formfaktoren von allgemeinen eichinvarianten lokalen zusammengesetzten Operatoren in der N=4 Super-Yang-Mills-Theorie bei verschiedenen Schleifenordnungen und Anzahlen externer Felder. Wir zeigen, wie Masseschalen-Methoden zu ihrer Berechnung genutzt werden können, und extrahieren aus ihnen insbesondere den Dilatationsoperator. Wir untersuchen auch die Eigenschaften der zugehörigen Rückstandsfunktionen. Des Weiteren verallgemeinern wir Masseschalen-Diagramme, Graßmann-Integrale und die integrabilitätsinspirierte Technik der R-Operatoren zur Anwendung auf Formfaktoren, wobei wir uns auf das Beispiel des chiralen Teils des Energie-Impuls-Tensors konzentrieren. Im zweiten Teil untersuchen wir die Beta- und die Gamma-i-Deformation. Bei diesen handelt es sich um die allgemeinste supersymmetrische beziehungsweise nicht-supersymmetrische feldtheoretische Deformation von N=4 Super-Yang-Mills-Theorie, welche auf der Ebene des asymptotischen Bethe-Ansatzes integrabel sind. Hierbei tritt ein neuer Effekt der endlichen Systemgröße auf, der durch Doppelspurstrukturen in der deformierten Lagrange-Dichte hervorgerufen wird und den wir Vorwickeln nennen. Während die Beta-Deformation für sich an ihren nicht-verschwindenden IR-Fixpunkten befindliche Doppelspurkopplungen konform invariant ist, weist die Gamma-i-Deformation rennende Doppelspurkopplungen ohne Fixpunkte auf, was die konforme Invarianz selbst im planaren Limes bricht. Nichtsdestotrotz erlaubt die Gamma-i-Deformation hochgradig nicht-triviale Tests der Integrabilität bei beliebig hohen Schleifenordnungen. / In the first part of this thesis, we study form factors of general gauge-invariant local composite operators in N=4 super Yang-Mills theory at various loop orders and for various numbers of external legs. We show how to use on-shell methods for their calculation and in particular extract the dilatation operator from the result. We also investigate the properties of the corresponding remainder functions. Moreover, we extend on-shell diagrams, a Graßmannian integral formulation and an integrability-based construction via R-operators to form factors, focussing on the chiral part of the stress-tensor supermultiplet as an example. In the second part, we study the beta- and the gamma-i-deformation, which were respectively shown to be the most general supersymmetric and non-supersymmetric field-theory deformations of N=4 super Yang-Mills theory that are integrable at the level of the asymptotic Bethe ansatz. For these theories, a new kind of finite-size effect occurs, which we call prewrapping and which emerges from double-trace structures that are required in the deformed Lagrangians. While the beta-deformation is conformal when the double-trace couplings are at their non-trivial IR fixed points, the gamma-i-deformation has running double-trace couplings without fixed points, which break conformal invariance even in the planar theory. Nevertheless, the gamma-i-deformation allows for highly non-trivial field-theoretic tests of integrability at arbitrarily high loop orders.

The way in which macroscopic transport results from microscopic dynamics is one of the important questions in statistical physics. Dynamical systems theory play a key role in a resent advance in this direction. Offering relatively simple models which are easy to study, dynamical systems theory became a standard branch of modern nonequilibrium statistical physics. In the present work the deterministic diffusion generated by simple dynamical systems is considered. The deterministic nature of these systems is more clearly expressed through the dependencies of the transport quantities as functions of systems parameters. For fully hyperbolic dynamical systems these dependencies were found to be highly irregular and, in fact, fractal. The main focus in this work is on nonhyperbolic and on intermittent dynamical systems. First, the climbing sine map is considered which is a nonhyperbolic system with many physical applications. Then we treat anomalous dynamics generated by a paradigmatic subdiffusive map. In both cases these systems display deterministic transport which, under variation of control parameters, is fractal. For both systems we give an explanation of the observed phenomena. The third part of the thesis is devoted to the relation between chaotic and transport properties of dynamical systems. This question lies at the heart of dynamical systems theory. For closed hyperbolic dynamical systems the Pesin theorem links the sum of positive Lyapunov exponents to the Kolmogorov-Sinai entropy. For open hyperbolic systems the escape rate formula is valid. In this work we have formulated generalizations of these formulas for a class of intermittent dynamical systems where the chaotic properties are weaker.

Particle physics deals with the elementary constituents of our universe and their interactions. The electroweak symmetry breaking mechanism in the Standard Model of Particle Physics is of paramount importance and it plays a central role in the physics programmes of current high-energy physics experiments at the Large Hadron Collider. The study of scattering processes of massive electroweak gauge bosons provides an approach complementary to the precise measurement of the properties of the recently discovered Higgs boson. Owing to the unprecedented energies achieved in proton-proton collisions at the Large Hadron Collider and the large amount of data collected, experimental studies of these processes become feasible for the first time. Especially the scattering of two W± bosons of identical electric charge is considered a promising process for an initial study due to its distinct experimental signature. In the course of this work, 20.3 fb−1 of proton-proton collision data recorded by the ATLAS detector at a centre-of-mass energy of √s = 8 TeV are analysed. An analysis of the production of two W± bosons of identical electric charge in association with two jets, pp → W ± W ± jj, is conducted in the leptonic decay channel of the W± bosons. Thereby, emphasis is put on the development of methods for the estimation of experimental backgrounds as well as on the optimisation of the event selection. As a result of this work, first experimental evidence for the existence of the aforementioned process is established with an observed significance of 4.9. Based on the number of observed events in the selected phase space the extracted fiducial cross section is σ(fid) = (2.3 ± 0.5(stat.) +0.4/−0.3 (sys.)) fb which is in agreement with the prediction of the Standard Model of σ(fid,SM) = (1.6 ± 0.2) fb. Of particular theoretical interest are electroweak contributions to the pp → W ± W ± jj process due to their sensitivity to the nature of the electroweak symmetry breaking mechanism. Criteria for a dedicated event selection are investigated and implemented in the analysis with the goal of enhancing the sensitivity to these contributions. First experimental evidence for the presence of electroweak contributions to the pp → W ± W ± jj process can be claimed with an observed significance of 4.1. The cross section extracted in the selected phase space region is found to be σ(fid) = (1.7 +0.5/−0.4 (stat.) ± 0.3(sys.)) fb which is 1.3 standard deviations above the theoretical prediction of the Standard Model of σ(fid,SM) = (1.0 ± 0.1) fb. A variety of extensions to the Standard Model predict modifications to the electroweak gauge sector. In the context of the electroweak chiral Lagrangian, which serves as an effective approximation of these theories in the energy regime E = 1 − 3 TeV, anomalous contributions to the quartic WWWW gauge coupling can be described by the parameters α4 and α5 . The selection of events is optimised again to enhance the sensitivity to these two parameters. On the basis of the number of events observed in this phase space region, the following one-dimensional confidence intervals at the 95% confidence level are derived: −0.09 ≤ α4 ≤ 0.10 and −0.15 ≤ α5 ≤ 0.15. At present, these limits represent the most stringent constraints on contributions from new physics processes to the quartic WWWW gauge coupling.

This work addresses properties of two-component lipid membranes on the experimentally relevant spatial scales of order of a micrometer and time intervals of order of a second by means of lattice-based Monte Carlo (MC) simulations. To be able to do that with reasonable computational efforts the lipid membrane is modeled as a square lattice of lipid molecules with next-neighbor interaction. This allows for efficient computation and thus provides a large-scale simulation with which it was possible to obtain important results previously not reported in simulation studies of lipid membranes. After properly tuning the next-neighbor interaction energies the simulation reproduces the experimental phase diagram of the DMPC/DSPC lipid system which is used as a model system in this work. Beyond that, the MC simulation provides a more detailed description of the phase behavior of the lipid mixture than the experimental data. It is found that, within a certain range of lipid compositions, the phase transition from the fluid phase to the fluid–gel phase coexistence proceeds via near-critical fluctuations, while for other lipid compositions this phase transition has a quasi-abrupt character. The complete combined state and component phase diagram is constructed by structure function analysis which confirms the existence of a critical point in the system. The dynamics of membrane coarsening after an abrupt temperature quench to the fluid–gel coexistence region of the phase diagram are studied. In this context, it is found that lateral diffusion of lipids plays an important role in the fluid–gel phase separation process. Dynamic scaling is observed only if the ratio of gel and fluid phase in the membrane stays constant in time. The line tension characterizing lipid domains in the fluid–gel coexistence region is found to be in the pN range thus matching values both predicted theoretically and measured experimentally. When approaching the critical point, the line tension, the inverse correlation length of fluid–gel spatial fluctuations, and the corresponding inverse order parameter susceptibility of the membrane vanish in agreement with recent experimental findings for model lipid membranes. By simulating single particle tracking and fluorescence correlation spectroscopy experiments it is found that in the presence of near-critical fluctuations lipid molecules show transient subdiffusive behavior, which is a new result important for understanding the origins of subdiffusion in cell membranes which are believed to be close to a critical point. The membrane–cytoskeleton interaction strongly affects phase separation, enhances subdiffusion, and eventually leads to hop diffusion of lipids. Thus, a minimum realistic model for membrane rafts showing the features of both microscopic phase separation and subdiffusion is established.

The Hall resistivity in ferromagnetic materials has an anomalous contribution proportional to the magnetization, which is defined as the anomalous Hall effect (AHE). Being a central topic in the study of ferromagnetic materials for many decades, the AHE was revived in recent years by generating many new understandings and phenomena, e.g. spin-Hall effect, topological insulators. The phase diagram of the AHE was shown recently to exhibit three distinct regions: a skew scattering region in the high conductivity regime, a scattering-independent normal metal regime, and an insulating regime. While the origin of the metallic regime scaling has been understood for many decades through the expected dependence of each contribution, the origin of the surprising scaling in the insulating regime was completely unexplained, leaving the primary challenge to the last step to understand fully the AHE. In this dissertation work we developed a theory to study the AHE in the disordered insulating regime, whose scaling relation is observed to be omega_xy^AH is proportional to omega_xx^(1.40∼1.75) in a large range of materials. This scaling is qualitatively different from the ones observed in metals. In the metallic regime where kFl > > 1, the linear response theory predicts that omega_xx is proportional to the quasi-particle lifetime tau, while omega_xy^AH scales as alpha*tau beta*tau^0, indicating that the upper limit of the scaling exponent is 1.0. Basing our theory on the phonon-assisted hopping mechanism and percolation theory, we derived a general formula for the anomalous Hall conductivity (AHC), and showed that the AHC scales with the longitudinal conductivity as omega_xy^AH ~ omega_xx^gamma with gamma predicted to be 1.33 <= gamma <= 1.76, quantitatively in agreement with the experimental observations. This scaling remains similar regardless of whether the hopping process is long range type (varible range hopping) or short range type (activation E3 hopping), or is influenced by interactions, i.e. Efros-Shklovskii (E-S) regime. Our theory completes the understanding of the AHE phase diagram in the insulating regime.

La loi de Moore est basée sur l’observation empirique qu’environ chaque deux années, le nombre de transistors dans des circuits denses intégrées double. Cette tendance s'est bien maintenue au cours des dernières décennies (années 1970 et suivantes). Cependant, la miniaturisation continue des transistors entraîne une augmentation significative des pertes d’énergie par le courant de fuite, ce qui augmente la consommation d'énergie de veille. Cette perte d’énergie est devenue un problème majeur dans la microélectronique pendant les dernières années, ce qui rend plus difficile le développement des nouvelles technologies. L’une des solutions est de placer des éléments mémoire non-volatile dans le puce, qui retiennent la configuration du transistor pendant la mise hors tension et permettent de le restaurer à la mise sous tension. Les Magnetic Random Access Memories (MRAM) sont considérées par l'ITRS comme un candidat crédible pour le remplacement potentiel de SRAM et de DRAM au-delà du nœud technologique de 20 nm. Bien que les exigences de base pour la lecture et l'écriture d'un élément de mémoire unique sont remplies, l'approche actuelle basée sur Spin Torque Transfer (STT) souffre d'un manque inné de la flexibilité. Le courant électrique entraine le retournement de l’aimantation de la couche ferromagnétique libre par le transfert du moment angulaire d’une couche ferromagnétique adjacent. Ainsi les éléments de mémoire basées sur STT ont deux terminaux dont les voies de courant pour « écriture » et « lecture » sont définies par la forme de «pillar». L’optimisation indépendant des paramètres d’écriture et de lecture reste, donc, très difficile. Au même temps, la densité de courant trop haute, nécessaire pour écrire, conduit à la vieillissement prémature du jonction tunnel. En conséquence, l’intégration MRAM dans la technologie du semi-conducteur reste, donc, difficile.Démonstrations récentes de reversement d’aimantation entrainées par l’injection d’un courant planaire dans des heterostructures métal lourd/ferromagnet ont attiré l’attention croissante sur les couples de spin basé sur le transfert du moment angulaire par l’effet Hall de spin et les effets d’interface. Contrairement à STT-MRAM, la SOT-MRAM a trois terminaux, dont les voies de courant pour « écriture » et « lecture » sont indépendantes. Cela permet d’améliorer les paramètres « écriture » et « lecture » de manière indépendante. Pour contrôler et optimiser les SOT il est nécessaire de comprendre très bien leur origine. Cela reste l’une des plus importantes questions dont on n’a pas une réponse définitive. Dans ce contexte, plusieurs études ont conclu sur un modèle basé seulement sur l’effet Hall de spin, en même temps que d’autres ont suggéré un modèle basé sur une contribution combiné de l’effet Hall de spin et l’effet d’interface.L’objectif de cette thèse est de réaliser une étude systématique sur les effets d’interface sur les SOT dans des heterostructures métal lourde/ferromagnet a base de Pt, avec aimantation planaire.Dans ce but, cette thèse explore trois voies différentes. Premièrement nous avons modifié le rapport entre les effets d’interface et les effets bulk en changeant l’épaisseur de la couche de Pt et en suivant l’évolution des SOT. En deuxième nous avons exploré des différents empilements métal lourde/ferromagnet afin d’étudier différentes interfaces. Finalement, nous avons changé les propriétés des interfaces soit par changer la structure cristalline soit par oxydation. La technique de mesure, la méthode d’analyse de données associé et les aspects théoriques nécessaires pour l’interprétation des données sont aussi détaillés dans ce manuscrit. / Moore’s law is based on empirical observation and states that every two years approximately, the number of transistors in dense integrated circuits doubles. This trend has held up well in the past several decades (1970s and onwards). However, the continuous miniaturisation of transistors brings about a significant increase in leakage current, which increases the stand-by power consumption. This energy loss has become a major problem in microelectronics during the last several years, making the development of new technologies more difficult. One of the solutions that can address this issue is to place non-volatile memory elements inside the chip, that retain the configuration of the transistor during power-off and allow to restore it at power-on. Magnetic Random Access Memories (MRAM) are considered by the ITRS as a credible candidate for the potential replacement for SRAM and DRAM beyond the 20 nm technological node. Though the basic requirements for reading and writing a single memory element are fulfilled, the present approach based on Spin Transfer Torque (STT) suffers from an innate lack of flexibility. The electric current drives the magnetization switching of a free ferromagnetic layer by transferring angular momentum from an adjacent ferromagnet. Therefore, STT-based memory elements are two terminal devices in which the “pillar” shape defines both the “read” and the “write” current paths. Independent optimisation of the reading and writing parameters is therefore difficult, while the large writing current density injected through the tunnel barrier causes its accelerated ageing, particularly for fast switching. Consequently, the integration of MRAM into semiconductor technology poses significant difficulties.Recent demonstrations of magnetization switching induced by in-plane current injection in heavy metal (HM)/ferromagnet (FM) heterostructures have drawn increasing attention to spin-torques based on orbital-to-spin momentum transfer induced by Spin Hall and interfacial effects (SOTs). Unlike STT-MRAM, the in-plane current injection geometry of SOT-MRAM allows for a three-terminal device which decouples the “read” and “write” mechanisms, allowing the independent tuning of reading and writing parameters. However, an essential first step in order to control and optimise the SOTs for any kind of application, is to better understand their origin. The origin of the SOTs remains one of the most important unanswered questions to date. While some experimental studies suggest a SHE (Spin Hall Effect)-only model for the SOTs, others point towards a combined contribution of the bulk (SHE) and interface (Rashba Effect and Interfacial SHE). At the same time, many studies start with a SHE only hypothesis and do not consider interfacial effects. Furthermore, there are not so many systematic studies on the effects of interfaces. This thesis tries to fill in this gap, by providing a systematic study on the effects of interfaces on the SOTs, in Pt-based NM/FM/HM multilayers with in-plane magnetic anisotropy. For this purpose, this thesis explores three different, but related avenues. First, we changed the interface/bulk effect ratio by modifying the Pt thickness and following the evolution of the SOTs. Second, we explored different HM/FM/NM combinations, in order to study different interfaces. And third, we changed the properties of the interfaces by changing the crystallographic structure of the interface and by oxidation. The measurement technique and associated data analysis method, as well as the theoretical considerations needed for the interpretation of the results are also detailed in this manuscript.

Cette thèse est consacrée à l'analyse asymptotique d'équations aux dérivées partielles issues de modèles de déplacement sous-diffusif en biologie cellulaire. Notre motivation biologique est fondée sur les nombreuses observation récentes de protéinescytoplasmiques dont le déplacement aléatoire dévié de la diffusion Fickienne normale. Dans la première partie, nous étudions la décroissance auto-similaire de la solution d'une équation de renouvellement à queue lourde vers un état stationnaire. Les idéesmises en jeu sont inspirées de méthodes d'entropie relative. Nos principaux apports sont la preuve d'un taux de décroissance en norme L1 vers la loi de l'arc-sinus et l'introduction d'une fonction pivot spécifique dans une méthode d'entropie relative.La seconde partie porte sur la limite hyperbolique d'une équation de renouvellement structurée en âge et à sauts en espace. Nous y prouvons un résultat de « stabilité » : les solutions des problèmes rééchelonnés à ε > 0 convergent lorsque ε --> 0 vers la solution de viscosité de l'équation de Hamilton-Jacobi limite des problèmes à ε > 0. Les outilsmis en jeu proviennent de la théorie des équations de Hamilton-Jacobi.Ce travail présente trois idées intéressantes. La première est celle de prouver le résultat de convergence sur la condition de bord du problème plutôt que d'utiliser des fonctions test perturbées. La deuxième consiste en l'introduction de termes correcteurslogarithmiques en temps dans des estimations a priori ne découlant pas directementdu principe du maximum. Cela est dû à la non-existence d'un équilibre du problèmehomogène en espace. La troisième est une estimation précise de la décroissance de l'influence de la condition initiale sur le terme de renouvellement. Elle correspond à une estimation fine d'une version non-locale de la dérivée temporelle de la solution. Au cours de cette thèse, des simulations numériques de type Monte Carlo, schémas volumes finis, Lax-Friedrichs et Weighted Essentially Non Oscillating ont été réalisées. / This thesis is devoted to the asymptotic analysis of partial differential equations modelling subdiffusive random motion in cell biology. The biological motivation for this work is the numerous recent observations of cytoplasmic proteins whose random motion deviates from normal Fickian diffusion. In the first part, we study the self-similar decay towards a steady state of the solution of a heavy-tailed renewal equation. The ideas therein are inspired from relative entropy methods. Our main contributions are the proof of an L1 decay rate towards the arc-sine distribution and the introduction of a specific pivot function in a relative entropy method.The second part treats the hyperbolic limit of an age-structured space-jump renewal equation. We prove a "stability" result: the solutions of the rescaled problems at ε > 0 converge as ε --> 0 towards the viscosity solution of the limiting Hamilton-Jacobi equation of the ε > 0 problems. The main mathematical tools used come from the theory of Hamilton-Jacobi equations. This work presents three interesting ideas. The first is that of proving the convergence result on the boundary condition of the studied problem rather than using perturbed test functions. The second consists in the introduction of time-logarithmic correction termsin a priori estimates that do not follow directly from the maximum principle. That is due to the non-existence of a suitable equilibrium for the space-homogenous problem. The third is a precise estimate of the decay of the inuence of the initial condition on the renewal term. This is tantamount to a refined estimate of a non-local version of the time derivative of the solution. Throughout this thesis, we have performed numerical simulations of different types: Monte Carlo, finite volume schemes, Lax-Friedrichs schemes and Weighted Essentially Non Oscillating schemes.