Die Transporteigenschaften eines Elektronengases mit reduzierter Dimensionalität werden von den Welleneigenschaften der Elektronen bestimmt. Dies ermöglicht es, verschiedene Quanteneffekte, wie Quanteninterferenz, zu beobachten. Im ersten Teil dieser Arbeit werden geätzte Quantenringe und eindimensionale (1D) Verengungen, basierend auf AlxGa1-xAs/GaAs-Heterostrukturen, hinsichtlich ihrer Transporteigenschaften untersucht. Messungen des thermischen Rauschens im Gleichgewichtszustand zeigen, dass der Erwartungswert mit den Rauschspektren aller 1D Verengungen übereinstimmt, jedoch um bis zu 60 % bei allen Quantenringen überschritten wird. Rauschmessungen im thermischen Nichtgleichgewicht ergeben, dass der Wärmefluss in Quantenringen mithilfe einer globalen Steuerelektrode (Topgate) an- und ausgeschaltet werden kann. Die magnetische Widerstandsänderung der Quantenringe zeigt Oszillationen, die dem Aharonov-Bohm-Effekt zugeordnet werden. Die Beobachtbarkeit dieser Oszillationen hängt stark von dem Abkühlvorgang der Probe ab und die Oszillationen zeigen Hinweise auf ein Schwebungsmuster sowie auf Phasenstarre. Im zweiten Teil der Arbeit werden die Oberflächenzustände von exfolierten Bi2Se3 Mikroflocken untersucht. Für Mikroflocken mit metallischen Temperaturabhängigkeiten des Widerstandes wurde schwache Anti-Lokalisierung beobachtet. Diese Beobachtung deutet darauf hin, dass sich die magnetische Widerstandsänderung weniger ausschließlich aus den 2D Oberflächenkanälen als vielmehr aus einem geschichtetem Transport von 2D Kanälen im Volumenkörper zusammensetzt. Eine Mikroflocke mit halbleitenden Eigenschaften zeigt keine Hinweise auf solch einen geschichteten 2D Transport und es wird angenommen, dass ihre magnetische Widerstandsänderung ausschließlich von den 2D Oberflächenzuständen verursacht wird. / The transport properties of an electron gas with reduced dimensionality are dominated by the electron’s wave nature. This allows to observe various quantum effects, such as quantum interference. In the first part of this thesis etched quantum rings and one-dimensional (1D) constrictions, based on AlxGa1-xAs/GaAs heterostructures, are investigated with respect to their transport properties. Thermal noise measurements in equilibrium show that the expectation value agrees with the noise spectra of all 1D constrictions but is exceeded by up to 60 % for the noise spectra of all quantum rings. Noise measurements in thermal non-equilibrium reveal that the heat flow can be switched on and off for a quantum ring by a global top-gate. The measured magnetoresistance of the quantum rings shows oscillations that are attributed to the Aharonov-Bohm effect. The observability of these oscillations strongly depends on the cooling process of the sample and the oscillations show indications of a beating as well as phase rigidity. In the second part of the thesis the surface states of exfoliated Bi2Se3 microflakes are studied. For microflakes that show a metallic temperature dependence of the resistance weak anti-localization is observed. This observation suggests that the magnetoresistance is a result of layered transport of 2D channels in the bulk rather than just the surface 2D channels. A microflake with semiconducting characteristics does not show indications of such a 2D layered transport and its magnetoresistance is considered to be carried by the 2D surface states only.

Percolation theory is a relevant area of research in Nanotechnology because of its wide applications in nanoelectronics based on thin films of nanoparticles and composites, amongst others. In nanotechnology, systems are often explored through modelling and simulations. Thin films of the emerging low-dimensional nanomaterials, such as the 1D nanowires/nanotubes and 2D graphene, as well as their composites, can generally be simulated through a two dimensional percolation system of homogeneous or heterogeneous ellipses. The critical phenomena, i.e., the percolation threshold of the systems, is now obtained using the Monte Carlo simulation method, which, need extensive amounts of time. This project is an interdisciplinary one, wherein an attempt is made to use a certain amount of the data from the Monte Carlo simulations to train a machine learning model to predict the threshold of all the 2D ellipse systems with the maximum relative error < 10%, thus reducing the time taken when gathering the data. This project investigates different algorithms such as Linear Regression, Polynomial Regression, Multi-layer Perceptron Neural Networks, Random Forests, Extreme Gradient Boosted Trees, Support Vector Machines and K-Nearest Neighbours. Weaknesses in the results are identified and overcome by specific additional sample generation. Finally, a comparison is made between the algorithms marking the Multi-layer Perceptron and Extreme Gradient Boosted Trees as successful, with the Multi-layer Perceptron being the clear winner. The algorithm is successful within the defined 10% relative error, performing even better with all samples having relative prediction errors less than 7%. The model can be downloaded and used from https://github.com/NiravSurajlal/ PercolationAI. / Perkolationsteori är ett relevant forskningsområde inom nanoteknik på grund av dess breda tillämpningar inom nanoelektronik, bland annat baserade på tunna filmer av nanopartiklar och kompositer. Inom nanoteknik undersöks system ofta genom modellering och simuleringar. Tunna filmer av de framväxande lågdimensionella nanomaterialen, såsom 1D-nanotrådar / nanorör och 2Dgrafen, liksom deras kompositer, kan i allmänhet simuleras genom ett tvådimensionellt perkolationssystem av homogena eller heterogena ellipser. De kritiska fenomenen, dvs. systemets perkolationströskel, erhålls nu med hjälp av Monte Carlosimuleringsmetoden, som kräver omfattande tidsperioder. Detta projekt är ett tvärvetenskapligt projekt, där man försöker använda en viss mängd data från Monte Carlo-simuleringarna för att träna en maskininlärningsmodell för att förutsäga tröskeln för alla 2D-ellipssystem med det maximala relativa felet <10%vilket minskar den tid det tar att samla in data. Detta projekt undersöker olika algoritmer som linjär regression, polynomregression, flerlagers Perceptron-neuronnätverk, slumpmässiga skogar, extrema gradientförstärkta träd, stöd för vektormaskiner och K-närmaste grannar. Svagheter i resultaten identifieras och övervinns genom specifik ytterligare provgenerering. Slutligen görs en jämförelse mellan algoritmerna som markerar Multi-layer Perceptron och Extreme Gradient Boosted Trees som framgångsrika, med Multi-layer Perceptron som den tydliga vinnaren. Algoritmen är framgångsrik inom det definierade 10 % relativfelet och presterar ännu bättre med alla prover som har relativa prediktionsfel mindre än 7 %. Modellen kan laddas ner och användas från https://github.com/NiravSurajlal/PercolationAI.

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The thesis is devoted to the study of in-chain impurities in spin 1/2 antiferromagnetic Heisenberg chains (S=1/2 aHC's)---a model which accompanies the research on magnetism since the early days of quantum theory and which is one of the few integrable spin systems. With respect to impurities it is special insofar as an impurity perturbs the system strongly due to its topology: there is no way around the defect. To what extend the one-dimensional picture stays a good basis for the description of real materials even if the chains are disturbed by in-chain impurities is an interesting question which is addressed in this work. For this purpose, Cu Nuclear Magnetic Resonance (NMR) measurements on the cuprate spin chain compounds SrCuO2 and Sr2CuO3 intentionally doped with nickel (Ni), zinc (Zn) and palladium (Pd) are presented. These materials are well known to be among the best realizations of the S=1/2 aHC model and their large exchange coupling constants allow the investigation of the low-energy dynamics within experimentally easily feasible temperatures. NMR provides the unique ability to study the static and dynamic magnetic properties of the spin chains locally which is important since randomly placed impurities break the translational invariance. Because copper is the magnetically active ion in those materials and the copper nuclear spin is most directly coupled to its electron spin, the NMR measurements have been performed on the copper site. The measurements show in all cases that there are changes in the results of these measurements as compared to the pure compounds which indicate the opening of gaps in the excitation spectra of the spin chains and the emergence of oscillations of the local susceptibility close to the impurities. These experimental observations are compared to theoretical predictions to clarify if and to what extend the already proposed model for these doped systems---the finite spin chain---is suitable to predict the behavior of real materials. Thereby, each impurity shows peculiarities. While Zn and Pd are know to be spin 0 impurities, it is not clear if Ni carries spin 1. To shed some light on this issue is another scope of this work. For Zn impurities, there are indications that they avoid to occupy copper sites, other than in the layered cuprate compounds. Also this matter is considered.

"Fluid-structure interaction arises in a wide array of technological applications including naval and marine hydrodynamics, civil and wind engineering and flight vehicle aerodynamics. When a fluid flows over a bluff body such as a circular cylinder, the periodic vortex shedding in the wake causes fluctuating lift and drag forces on the body. This phenomenon can lead to fatigue damage of the structure due to large amplitude vibration. It is widely believed that the wake structures behind the structure determine the hydrodynamic forces acting on the structure and control of wake structures can lead to vibration control of the structure. Modeling this complex non-linear interaction requires coupling of the dynamics of the fluid and the structure. In this thesis, however, the vibration of the flexible cylinder is prescribed, and the focus is on modeling the fluid dynamics in its wake. Low-dimensional iterative circle maps have been found to predict the universal dynamics of a two-oscillator system such as the rigid cylinder wake. Coupled map lattice (CML)models that combine a series of low-dimensional circle maps with a diffusion model have previously predicted qualitative features of wake patterns behind freely vibrating cables at low Reynolds number. However, the simple nature of the CML models implies that there will always be unmodelled wake dynamics if a detailed, quantitative comparison is made with laboratory or simulated wake flows. Motivated by a desire to develop an improved CML model, we incorporate self-learning features into a new CML that is trained to precisely estimate wake patterns from target numerical simulations and experimental wake flows. The eventual goal is to have the CML learn from a laboratory flow in real time. A real-time self-learning CML capable of estimating experimental wake patterns could serve as a wake model in a future anticipated feedback control system designed to produce desired wake patterns. A new convective-diffusive map that includes additional wake dynamics is developed. Two different self-learning CML models, each capable of precisely estimating complex wake patterns, have been developed by considering additional dynamics from the convective-diffusive map. The new self-learning CML models use adaptive estimation schemes which seek to precisely estimate target wake patterns from numerical simulations and experiments. In the first self-learning CML, the estimator scheme uses a multi-variable least-squares algorithm to adaptively vary the spanwise velocity distribution in order to minimize the state error (difference between modeled and target wake patterns). The second self-learning model uses radial basis function neural networks as online approximators of the unmodelled dynamics. Additional unmodelled dynamics not present in the first self-learning CML model are considered here. The estimator model uses a combination of a multi-variable normalized least squares scheme and a projection algorithm to adaptively vary the neural network weights. Studies of this approach are conducted using wake patterns from spectral element based NEKTAR simulations of freely vibrating cable wakes at low Reynolds numbers on the order of 100. It is shown that the self-learning models accurately and efficiently estimate the simulated wake patterns within several shedding cycles. Next, experimental wake patterns behind different configurations of rigid cylinders were obtained. The self-learning CML models were then used for off-line estimation of the stored wake patterns. With the eventual goal of incorporating low-order CML models into a wake pattern control system in mind, in a related study control terms were added to the simple CML model in order to drive the wake to the desired target pattern of shedding. Proportional, adaptive proportional and non-linear control techniques were developed and their control efficiencies compared."

This work presents a joint theoretical and experimental investigation of the electronic structure of quasi one-dimensional cuprates and vanadates. Electron energy-loss spectroscopy in transmission was employed to measure the momentum-dependent loss function of Li2CuO2, CuGeO3, V2O5 and NaV2O5. The comparison between the experimental data and the results from bandstructure as well as cluster calculations allows an explanation of the mobility and correlations of the electrons in these systems. The investigation of the electronic structure of the structurally related cuprates Li2CuO2 and CuGeO3 is exemplary for the study of the transition from a quasi zero-dimensional to a quasi one-dimensional system. In contrast to Li2CuO2 where the electron transitions are strongly localized, the excited states in CuGeO3 can be assigned to the electron hopping to the nearest-neighboured CuO4 plaquettes. The shift of spectral weight from the high energy to the low energy region with increasing coupling between the plaquettes, observed in edge-sharing CuO2 chains, is confirmed by the applied cluster modell. The momentum dependent loss functions of NaV2O5 deliver information about the mobility and correlations of electrons in a quarter-filled ladder system which determine the transition from the charge ordered state into the unordered state at 34 K. Thcontributions of the 3d electrons to the EELS spectra of NaV2O5 are filtered by comparing these spectra with the loss functions of the structurally related V2O5 (d0 configuration). For NaV2O5 the picture of linear chains of V-O-V rungs containing a single d electron in a molecular orbital-like state is confirmed. The comparison of the experimentally determined optical conductivities and those derived from the bandstructrure calculations yield a good agreement upon adoption of an on-site Coulomb interaction U = 2-3 eV. In contrast to the strongly anisotropic hopping within the ladder plane the intersite Coulomb interactions V are about the same size. These interactions are the driving force for the transition from an unordered state at room temperature into a zigzag ordered state observed at low temperatures. / In einer Kombination aus experimentellen und theoretischen Methoden wurden in dieser Arbeit die Elektronenstrukturen von quasi-eindimensionalen Kupraten und Vanadaten untersucht. Dazu wurde die impulsabhängige Verlustfunktion mit Hilfe der Elektronen-Energieverlustspektroskopie in Transmission an Einkristallen von Li2CuO2, CuGeO3, V2O5 und NaV2O5 gemessen. Der Vergleich der experimentellen Daten mit Ergebnissen aus Bandstruktur- und Cluster-Rechnungen erlaubte Rückschlüsse auf die Beweglichkeit und Korrelationen der Elektronen in diesen Systemen. Die Untersuchung der elektronischen Anregungen in den strukturell sehr ähnlichen Kupraten Li2CuO2 und CuGeO3 ist beispielhaft für das Studium des Übergangs von einem quasi-nulldimensionalen zu einem quasi-eindimensionalen System. In Li2CuO2 finden die elektronischen Übergänge vorwiegend lokal auf der CuO4-Plakette statt. Dagegen findet man in CuGeO3 angeregte Zustände, die als das Hüpfen der Elektronen auf benachbarte Plaketten interpretiert werden können. Das angewandte Cluster-Modell bestätigt für eine zunehmende Kopplung zwischen den Plaketten die in eckenverbundenen Kupratketten beobachtete Verschiebung des spektralen Gewichts vom hoch- zum niederenergetischen Bereich. Die Verlustfunktionen von NaV2O5 liefern wertvolle Informationen über die Freiheitsgrade und Korrelationen der Elektronen in einem viertelgefüllten Leitersystem, die wesentlich den Phasenübergang zwischen geordneter und ungeordneter Ladung bei 34 K bestimmen. Die Beiträge der 3d-Elektronen von NaV2O5 zu den EELS-Spektren konnten durch eine vergleichende Studie der Verlustfunktionen des strukturell verwandten V2O5, das keine d-Elektronen besitzt, separiert werden. Die Beschreibbarkeit der Elektronenstruktur in NaV2O5 durch ein effektives Modell einfach besetzter, molekülähnlicher V-O-V-Sprossen wird bestätigt. Die Coulomb-Wechselwirkung U kann in diesem Modell auf den Wertebereich zwischen 2 und 3 eV eingeschränkt werden. Im Gegensatz zu den stark anisotropen Hüpfwahrscheinlichkeiten in der Leiterebene sind die Coulomb-Wechselwirkungen V zwischen Elektronen auf benachbarten Vanadiumplätzen nahezu von gleicher Größe. Diese Wechselwirkungen sind die treibende Kraft für den Übergang von einem ungeordneten Zustand bei Raumtemperatur in einen zickzackgeordneten Grundzustand bei tiefen Temperaturen.

We report experimentally results on the low temperature properties of two classes of materials with a special emphasizes near the QCP induced by substitution and magnetic 1.field: (1) the HF systems YbRh2(Si0.95Ge0.05)2, Yb1-yLayRh2Si2 (y = 0.05, 0.1),and YbIr2Si2 with tetragonal structures and CeIn3-xSnx (x = 0.55, 0.6, 0.65, 0.7, 0.8) with cubic structure; (2) the quantum spin systems: Cs2CuCl4 and Cs2CoCl4. In all the HF compounds we have observed NFL behavior in zero magnetic field close to the QCP. The La substituted system does not show an antiferromagnetic (AFM) transition down to the lowest accessible temperature (0.03 K) while in YbRh2(Si1-xGex)2 with x = 0 and x = 0.05 AFM transitions occur at TN =0.07 K and 0.02 K, respectively. For Yb0.9La0.1Rh2Si2 we observe below 0.07 K saturation of DeltaC/T indicating clearly a LFL state for this concentration. For YbIr2Si2, DeltaC/T saturates below 0.5 K. In contrast to the Yb based compounds in the vicinity of the QCP, CeIn3-xSnx shows no evidence of a divergence in Delta C/T, with B or with x. Furthermore, we used specic heat measurements in the mK temperature range and at high fields (up to 12 T) to probe the phase diagrams in the low dimensional quantum antiferromagnets Cs2CuCl4 and Cs2CoCl4. In applied magnetic field, we have presented experimental evidence that in Cs2CuCl4 the field dependence of the critical temperature Tc(B) ~ (Bc-B)^1-Phi close to the critical field Bc = 8.51 T is well described with Phi=1.5. This is in very good agreement with the exponent expected in the mean-field approximation and support the notion of a Bose-Einstein condensation of magnons in Cs2CuCl4.

Due to recent progress in theory and the growing number of physical realizations, low-dimensional quantum magnets continue to receive a considerable amount of attention. They serve as model systems for investigating numerous physical phenomena in spin systems with cooperative ground states, including the field-induced evolution of the ground-state properties and the corresponding rearrangement of their low-energy excitation spectra. This work is devoted to systematic studies of recently synthesized low-dimensional quantum spin systems by means of multi-frequency high-field electron spin resonance (ESR) investigations. In the spin- 1/2 chain compound (C6H9N2)CuCl3 [known as (6MAP)CuCl3] the striking incompatibility with a simple uniform S = 1/2 Heisenberg chain model employed previously is revealed. The observed ESR mode is explained in terms of a recently developed theory, revealing the important role of the alternation and next-nearest-neighbor interactions in this compound. The excitations spectrum in copper pyrimidine dinitrate [PM·Cu(NO3)2(H2O)2]n, an S = 1/2 antiferromagnetic chain material with alternating g-tensor and Dzyaloshinskii-Moriya interaction, is probed in magnetic fields up to 63 T. To study the high field behavior of the field-induced energy gap in this material, a multi-frequency pulsed-field ESR spectrometer is built. Pronounced changes in the frequency-field dependence of the magnetic excitations are observed in the vicinity of the saturation field, B ∼ Bs = 48.5 T. ESR results clearly indicate a transition from the soliton-breather to a spin-polarized state with magnons as elementary excitations. Experimental data are compared with results of density matrix renormalization group calculations; excellent agreement is found. ESR studies of the spin-ladder material (C5H12N)2CuBr4 (known as BPCB) completes the determination of the full spin Hamiltonian of this compound. ESR results provide a direct evidence for a pronounced anisotropy in this compound, that is in contrast to fully isotropic spin-ladder model employed previously for BPCB. Our observations can be of particular importance for describing the rich temperature-field phase diagram of this material. The frequency-field diagram of magnetic excitations in the quasi-two dimensional S = 1/2 compound [Cu(C4H4N2)2(HF2)]PF6 in the AFM-ordered state is studied. The AFM gap is observed directly. Using high-field magnetization and ESR results, parameters of the effective spin-Hamiltonian (exchange interaction, anisotropy and g-factor) are obtained and compared with those estimated from thermodynamic properties of this compound.

Η παρούσα εργασία αφορά στη μελέτη Χαμιλτώνιων συστημάτων Ν μη γραμμικών ταλαντωτών, όπως είναι αυτό των Fermi Pasta και Ulam (FPU), με στόχο την βαθύτερη κατανόηση της δυναμικής των σχεδόν-περιοδικών τροχιών και του ρόλου των αντίστοιχων τόρων στο χώρο φάσεων, καθώς αυξάνουμε την ενέργεια Ε και τον αριθμό βαθμών ελευθερίας Ν του συστήματος. Το βασικό μας αποτέλεσμα είναι ότι υπάρχουν τόροι χαμηλής διάστασης, που προκύπτουν από τη συνέχεια των αντίστοιχων του γραμμικού συστήματος, οι οποίοι ευθύνονται για τις FPU επαναλήψεις και εμποδίζουν την ισοκατανομή της ενέργειας μεταξύ όλων των κανονικών τρόπων ταλάντωσης. Αναλύοντας ευστάθεια αυτών των τόρων, μπορέσαμε να δώσουμε μια πληρέστερη ερμηνεία στο Παράδοξο των FPU, συνδέοντας και συμπληρώνοντας έτσι δύο από τις επικρατέστερες ερμηνείες του εν λόγω φαινομένου. / The present work concerns the study of Hamiltonian systems of N nonlinear coupled oscillators, as it is the one by Fermi Pasta and Ulam (FPU), in order to understand the dynamics of quasi-periodic orbits and the role of their corresponding tori in phase space, as we increase the energy E and the number N of the degrees of freedom. Our fundamental result is that there exist tori of low dimension, that come from the continuation of the corresponding tori of the linear system, which are responsible for the FPU recurrences and prevent the system from equipartition of the energy among all normal modes. By investigating the stability of these tori, we achieved to provide a more complete explanation for the FPU paradox, connecting and supplementing in this way two of the most dominant approaches for this paradox.

Cette thèse porte sur l'utilisation de plusieurs techniques de diffusion de neutrons polarisés pour la conduite d'expériences de diffraction et de spectroscopie inélastique à haute résolution. Nous décrivons de façon exhaustive l'option à écho de spin neutronique résonant ZETA, installée sur le spectromètre triple axe thermique CRG IN22 à l'Institut Laue Langevin. Grâce à elle, nous étudions la structure nucléaire et la dynamique de spin de plusieurs systèmes modèles. Dans un premier temps, nous nous intéressons à la série BaM2(XO4)2 (M = Co, Ni; X = As, P) dont les membres sont de bons exemples de systèmes magnétiques quasi-bidimensionnels. L'effet de la mise en ordre magnétique sur leurs paramètres de maille est révélé par diffraction de Larmor. De plus, nous montrons que l'évolution thermique de la durée de vie du mode de magnon optique dans BaNi2(PO4)2 est fortement affecté par la présence de défauts dans sa structure. Ensuite, nous abordons le composé à chaînes et échelles de spin 1/2 Sr14Cu24O41. Nous nous focalisons d'abord sur l'étude du pic inélastique associé au gap de spin des échelles et présentons une méthode capable de montrer de façon directe la dégénérescence de la transition concernée. Ensuite, nous évaluons sa largeur énergétique intrinsèque et observons l'effet des différentes mises en ordre de charge sur la structure cristallographique du matériau. Finalement, nous adaptons l'instrumentation disponible pour mener des expériences de réflectométrie résolues en temps, par le biais de la méthode MIEZE, sur une multicouche magnétique pouvant posséder des propriétés intéressante pour des applications en spintronique / This thesis is mainly concerned with the use of several polarized neutron scattering techniques for carrying high resolution diffraction and inelastic spectroscopy experiments. We describe exhaustively our neutron resonant spin-echo option ZETA, installed on the thermal triple-axis spectrometer CRG IN22 at Institut Laue Langevin. Through it, we study the nuclear structure and spin dynamics of several model systems. First, we are interested in the BaM2(XO4)2 (M = Co, Ni; X = As, P)-family which members are good prototypes of quasi-2D magnetic systems. The effect of magnetic ordering on lattice constants is revealed thanks to Larmor diffraction. Moreover, we show that the thermal evolution of optic magnon lifetime in BaNi2(PO4)2 is strongly affected by the presence of defects in its structure. Then, we address the spin-chain and -ladder compound Sr14Cu24O41. We first focus on the study of the inelastic peak associated with the spin gap in the ladders spectrum and introduce a method capable of showing directly the degeneracy of the associated spin transition. We also evaluate its intrinsic linewidth and observe the effect of different charge ordering process on the material crystallographic structure. Ultimately, we adapt our instrumentation to perform time-resolved reflectometry experiments on a magnetic multilayer which can possess interesting properties for spintronics applications, through the so-called MIEZE technique.