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Subject: search.filters.subject.530Publication Type: search.filters.UBSTyp.Abschlussarbeit (Master)Start date: 2020

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Now showing 1 - 10 of 24
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    Spin-orbit coupled states arising in the half-filled t2g shell
    (2023) Schönleber, Marco
    Strongly correlated and spin-orbit coupled t2g systems have been extensively investigated. By coupling orbital and spin angular momentum into one quantity, spin-orbit coupling (SOC) tends to reduce orbital degeneracy, e.g. for the widely studied case of one hole in the t2g shell. However, the opposite has to be expected at half filling. Without spin-orbit coupling, all orbitals are half filled, no orbital degree of freedom is left and coupling to the lattice can be expected to be small. At dominant spin-orbit coupling, in contrast, one of the j=3/2 states is empty and the system couples to the lattice. We investigate this issue. One finding is that the low-energy manifold evolves smoothly from the four S=3/2 states in the absence of SOC to the four j=3/2 states with dominant SOC. These four states are always separated from other states by a robust gap. We then discuss a relevant superexchange mechanism to assess the interplay between spin-orbit coupling and coupling to the lattice.
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    Collective variables in data-centric neural network training
    (2023) Nikolaou, Konstantin
    Neural Networks have become beneficial tools for physics research. While they provide a powerful tool for data-driven modeling, their success is accompanied by a lack of interpretability. This thesis aims to add transparency to the opaque nature of NNs by means of collective variables, a concept well-known in the field of statistical physics. Three collective variables are introduced that emerge from the interactions between neurons and data. These observables enable one to capture holistic behavior of the network and are used to conduct an analysis of neural network training, focusing on data. Through the investigations, the collective variables are applied to selections from a novel sampling method: Random Network Distillation (RND). Besides studying collective variables, the investigation of Random Network Distillation as a data selection method composes the second part of this thesis. The method is analyzed and optimized with respect to its components, aiming to understand and improve the data selection process. It is shown that RND can be used to select data sets that are beneficial for neural network training, giving rise to its application in fields like active learning. The collective variables are leveraged to further investigate the selection method and its effect on neural network training, revealing previously unknown properties of RND-selected data sets. The potential of the collective variables is demonstrated and discussed from a data-centric perspective. They are shown to be discriminative towards the information content of data and give rise to novel insights into the nature of neural network training. In addition to fundamental research on neural networks, the collective variables offer several potential applications including the identification of adversarial attacks and facilitating neural architecture search.
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    Thermodynamical stability analysis of a model quasicrystal
    (2022) Holzwarth, Moritz
    The thermodynamical stability of a simple 2D model quasicrystal is analysed using the theory of the phason elastic free energy. Atoms in the crystal interact via a double-well potential called the Lennard-Jones Gauß-potenital. The essential mechanisms that support the quasicrystal's free energy are atom jumps called phasonic flips. The distribution of such flips in a crystal is computed in dependency of the crystal lattice, which is parameterized by a 2x2-matrix called the phasonic strain. This computation is fully analytic and is based on the popular cut-and-project-scheme for quasicrystals. The quasicrystal is found to be instable at low temperature but stabilized at high temperature due to large entropy. This is in accordance with an MD-simulation from 2008 that used the LJG-Interaction-potential for the first time.
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    Lasertreatment of Al-Cu materials
    (2023) Kümmel, Simon
    In this work, the bond strength and stability of aluminium, copper and their alloys are investigated upon excitation using DFT calculations. In particular, free energy curves, elastic constants and phonon spectra are used to identify changes in the bond strength and the density of states at different degrees of excitation are used to explain the changes. We find nearly no change in bond strength in aluminium, a strong increase in bond strength in copper and bond hardening of certain modes in the AlCu alloys.
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    Microwave properties of superconducting SrTiO3 at mK-temperatures
    (2022) Beydeda, Cenk
    In this thesis the properties of superconducting Nb-doped SrTiO3 are investigated, more concrete the optical conductivity was obtained as function of temperature, magnetic flux density and frequency. Superconducting Stripline resonators were used to probe the optical properties of Nb:SrTiO3. The optical conductivity of Nb:SrTiO3 reveals features that are typically associated with a dirty single-gap superconductor. At low frequencies the coherence peak predicted by the BCS theory is observed. In the type II superconductor Nb:SrTiO3 two critical magnetic flux densities are observed that correspond to two superconducting bands. The real part of the optical conductivity displays a strong initial increase in dependence of magnetic flux density even at lowest achieved temperature to values multiple times of the DC conductivity. The critical magnetic flux densities and the critical temperatures show a dome-shaped dependence on the Nb-doping.
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    Simulation studies of selective laser melting
    (2022) Gorgis, Azad
    The technology of SLM is used to layer three-dimensional functional components. Studying and refining the factors that influence the melting of Al layer. The layer is made up of six distinct Al atom sizes in the shape of a sphere (ball) with various diameters (40˚A, 80˚A, 160˚A, 220˚A, 440˚A, 880˚A). The simulation depends mainly on MD to simulate the melting process. Although the sample sizes change, system parameters must be scaled to accommodate two distinct sample sizes. The whole melting of the Al layer has been recorded, using both sample 1 (40˚A, 80˚A, 160˚A) and sample 2 (220˚A, 440˚A, 880˚A), where with and without Ar gas, to explore the influence of Ar in the system. It is expected that the findings of this study will serve as a platform for further research into complex systems with several layers, and that the methodological style used in this work will serve as a model for systematic studies into other structures. In the near future, this research might aid materials design for next-generation in 3D printing.
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    Übergangsraten eines getriebenen Spinsystems unter Berücksichtigung von Relaxation
    (2021) Maihöfer, Michael
    Der Magnetismus hat die Menschen schon lange fasziniert. Obwohl viele Aspekte des Magnetismus geklärt sind, ist dieser in der Festkörperphysik auch heute noch ein offenes und aktives Forschungsgebiet. Das liegt nicht zuletzt daran, dass der Magnetismus ein kollektives Phänomen sehr vieler miteinander interagierender Teile bildet, deren magnetische Eigenschaften sich oft von denen der zugrundeliegenden Atome unterscheiden. Ein Trend der Forschung in diesem Gebiet ist es dabei, die Dimensionen des Festkörpers bis auf die Größenordnung von wenigen Atomen schrumpfen zu lassen und die dabei auftretenden magnetischen Eigenschaften von niedrigdimensionalen Festkörpern zu untersuchen. Diese Bemühungen waren auch sehr fruchtbar, und es wurde, um ein Beispiel zu nennen, der Giant Magnetoresistance Effect entdeckt, was seinen Entdeckern Albert Fert und Peter Grünberg 2007 den Nobelpreis in Physik einbrachte. Der Effekt bezeichnet das Auftreten eines magnetfeldrichtungsabhängigen elektrischen Widerstands in einem aus sich abwechselnden ferromagnetischen und nicht-magnetischen Dünnschichten bestehenden Material. Der Trend der Größenreduktion setzte sich fort, sodass nun auch die lateralen Dimensionen unterhalb der Größenordnung der charakteristischen Längenskalen, wie z.B. der Größe der magnetischen Domänen, gebracht wurden. Damit war das Feld des Mikromagnetismus (engl. micromagnetics) geboren. In gewisser Hinsicht vereinfacht dies die Beschreibung des Systems: Einerseits ist das System nun klein genug, sodass magnetische Domänen relevant werden, andererseits ist es groß genug, dass eine quantenmechanische Beschreibung noch nicht zwingend vonnöten ist. Oftmals reicht daher eine semiklassische Beschreibung des Makrospins über die bereits im Jahre 1955 phänomenologisch aufgestellte Landau-Lifshitz-Gilbert (LLG) Gleichung aus. Neuere Experimente legen allerdings nahe, dass im Bereich von Pikosekunden Abweichungen von Voraussagen der LLG-Gleichung auftreten und diese durch einen zusätzlichen Relaxationsterm ergänzt werden muss. Die in diesem Gebiet gewonnenen Erkenntnisse sind für viele technische Anwendungen relevant. Für die Entwicklung von magnetischen bzw. magnetooptischen Speichern ist die Erhöhung der Speicherdichte und der Lese- und Schreibgeschwindigkeit durch ein besseres Verständnis der magnetischen Anordnung und der Magnetisierungsumkehr, relevant. Ferner besteht die Hoffnung der Spintronics (abgeleitet aus den englischen Wörtern spin und electronics) die Informationsverarbeitung nicht mehr – wie in der Elektronik – durch elektrische Ladungen oder Ströme zu realisieren, sondern durch die Ausrichtung des magnetischen Moments der Elektronen. Demnach ist die Untersuchung der Umklappprozesse der Magnetisierung von zentralem Interesse. Ziel der vorliegenden Arbeit ist es die Rate zu bestimmen, mit der solche Umklappprozesse in einem Zweischichtenmodell stattfinden. Dies wird mithilfe der Methoden der Transition State Theory untersucht. Dieselbe Fragestellung wurde für die LLG-Gleichung bereits bearbeitet. Im Vergleich dazu wird nun in dieser Arbeit die um den Relaxationsterm erweiterte LLG-Gleichung herangezogen. Im Gegensatz zur LLG-Gleichung, die eine Differentialgleichung erster Ordnung ist, erlaubt die erweiterte LLG-Gleichung als Differentialgleichung zweiter Ordnung eine reichere Dynamik des Spinsystems. Die Transition State Theory (TST) wurde ursprünglich in der Chemie zur Bestimmung von Übergangsraten von chemischen Reaktionen entwickelt. Die grundlegende Idee der Transition State Theory ist dabei, den Ablauf einer chemischen Reaktion als eine klassische Trajektorie zwischen einem Ausgangs- und einem Endzustand zu beschreiben. Dabei muss diese Bahn eine Potentialhürde überwinden, die der Aktivierungsenergie der chemischen Reaktion entspricht. Die wesentliche Dynamik findet in der Nähe des Sattelpunktes statt, also der energiegünstigsten Stelle der Potentialhürde. Diese lokale Dynamik ist dann auch für die Übergangsrate zwischen den beiden Zuständen wesentlich und wird im Rahmen dieser Arbeit für das getriebene Spinsystem näher untersucht. Die Methoden der TST können auch die Landau-Lifshitz-Gilbert Gleichung bzw. der erweiterten LLG-Gleichung mit Relaxation hergestellt werden. Diese Bewegungsgleichung, zusammen mit einem effektiven Magnetfeld, welche eine bevorzugte Achse sowie eine Potentialbarriere darstellt, beschreibt Übergänge der Magnetisierung.
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    Semiclassical quantization for the states of cuprous oxide in consideration of the band structure
    (2021) Marquardt, Michael
    Excitons are atom-like states in semiconductors like cuprous oxide formed by an electron and a positively charged hole. They are created by exciting an electron from the valence band into the conduction band where the electron forms a bound hydrogen-like state with the hole remaining in the valence band. In this thesis we will focus on excitons of the yellow series which have excitation energies corresponding to wavelengths of about 590 nm. Excitons in cuprous oxide have been studied intensively in experiments and quantum mechanical calculations. Those investigations showed that there are similarities to the hydrogen atom but also deviations caused by the band structure of the crystal. For the hydrogen atom it was possible to connect the quantum mechanical energy spectrum to classical Keplerian orbits in the Bohr-Sommerfeld model. The question arises whether this is possible for excitons in cuprous oxide as well. Semiclassical trace formulas relate fluctuations of the density of states to classical periodic orbits where the frequencies are related to the action or period of the periodic orbits while the amplitude is related to stability properties of the orbits. In this thesis we want to apply semiclassical theories for the calculation and interpretation of exciton spectra. In order to take the band structure of cuprous oxide into account in classical calculations we treat the quasispin and hole spin degrees of freedom with an adiabatic approach. Thereby, we assume the spin dynamics to be much faster than the classical motion and calculate the spin-dependent part of the Hamiltonian quantum mechanically while the exciton dynamics is treated classically. Cuprous oxide has a cubic Oh symmetry. Therefore, it has distinct symmetry planes in which two-dimensional classical exciton orbits occur. In order to simplify the problem we limit ourselves to orbits in the plane orthogonal to the [001] axis. For investigating the classical exciton dynamics we show a Poincaré surface of section and search for periodic orbits in the plane. Furthermore, we calculate the action, period and stability properties of these orbits and use them for semiclassical calculations.
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    Quantum machine learning for time series prediction
    (2024) Fellner, Tobias
    Time series prediction is an essential task in various fields, such as meteorology, finance and healthcare. Traditional approaches to time series prediction have primarily relied on regression and moving average methods, but recent advancements have seen a growing interest in applying machine learning techniques. With the rise of quantum computing, it is of interest to explore whether quantum machine learning can offer advantages over classical methods for time series forecasting. This thesis presents the first large-scale systematic benchmark comparing classical and quantum models for time series prediction. A variety of quantum models are evaluated against classical counterparts on different datasets. A novel quantum reservoir computing architecture is proposed, demonstrating promising results in handling nonlinear prediction tasks. The findings suggest that, for simpler time series prediction tasks, quantum models achieve accuracy comparable to classical methods. However, for more complex tasks, such as long-term forecasting, certain quantum models show improved performance. While current quantum machine learning models do not consistently outperform classical approaches, the results point to specific contexts where quantum methods may be beneficial.
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    Application of machine learning to find exceptional points
    (2023) Egenlauf, Patrick
    In open quantum systems, resonances can occur. These are quasi-bound states which can decay. By introducing a complex scaling, e.g. according to Reinhardt, and thus non-Hermitian operators, the complex energy eigenvalues of the resonances can be calculated. Here, the real part represents their energy, while the imaginary part unveils their lifetime. Resonances can degenerate, where a special case is the so-called exceptional point (EP) at which not only the eigenvalues but also the eigenvectors degenerate. Thus, the two resonances coalesce at the EP. An isolated EP can be described by a two-dimensional matrix model. A property of such an EP is that the two associated eigenvalues exchange their positions after one adiabatic orbit in parameter space around the EP. In 2007 the existence of these EPs was proven for the hydrogen atom in electric and magnetic fields by Cartarius. Due to limitations especially in magnetic field strengths, EPs in the hydrogen atom are not experimentally accessible. In 2014, a remarkable discovery by Kazimierczuk et al. revealed a mesmerizing hydrogen-like spectrum within cuprous oxide. This revelation stemmed from the resemblance between an exciton, a quasi-particle in a semiconductor consisting of electron and hole, and their atomic counterpart, the hydrogen atom. However, the fact that the excitons are environed by cuprous oxide necessitated consideration of the band structure to precisely describe the observed spectrum. This discovery kindled excitement as it provided a rare opportunity to bridge the realms of experimental and theoretical physics, inviting an enthralling dialogue between theory and experiment. For cuprous oxide the field strengths to observe EPs of resonances with small quantum numbers are much lower compared to the field strengths for the hydrogen atom, which is why it is favorable to find EPs in this system. This was already done for a hydrogen-like model, but to obtain experimentally comparable results the above mentioned band structure terms need to be considered. However, this increases the computational cost drastically for each diagonalization of the Hamiltonian due to its complexity. The existing methods to find EPs are based on a Taylor expansion around the EP. Due to the computational expensive diagonalizations of the Hamiltonian, these methods are inefficient or even not applicable. Hence, a new method is required to accurately and efficiently identify EPs in cuprous oxide. Inspired by the remarkable advances in machine learning, especially within the realm of physics, a novel method on the foundation of Gaussian process regression (GPR) is developed. As a prominent member of the supervised machine learning family, GPR serves as a powerful and innovative approach to predict the positions of EPs in cuprous oxide. The used data to train a GPR model is obtained by simulations. Hence, the error is only due to numerical inaccuracies, which can be neglected. Unlike neural networks, GPR offers the advantage of precisely passing through the provided training points, which is a key motivation for its utilization. Yet, the optimization of the searching process goes beyond the new method. An efficient algorithm is devised to enhance the search for EPs in cuprous oxide, which contributes to the discovery of promising EPs and thus enables a possible experimental verification of these data.