08 Fakultät Mathematik und Physik
Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/9
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Item Open Access Spin-orbit coupled states arising in the half-filled t2g shell(2023) Schönleber, MarcoStrongly 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.Item Open Access Collective variables in data-centric neural network training(2023) Nikolaou, KonstantinNeural 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.Item Open Access Thermodynamical stability analysis of a model quasicrystal(2022) Holzwarth, MoritzThe 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.Item Open Access Lasertreatment of Al-Cu materials(2023) Kümmel, SimonIn 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.Item Open Access Microwave properties of superconducting SrTiO3 at mK-temperatures(2022) Beydeda, CenkIn 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.Item Open Access Simulation studies of selective laser melting(2022) Gorgis, AzadThe 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.Item Open Access Übergangsraten eines getriebenen Spinsystems unter Berücksichtigung von Relaxation(2021) Maihöfer, MichaelDer 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.Item Open Access Semiclassical quantization for the states of cuprous oxide in consideration of the band structure(2021) Marquardt, MichaelExcitons 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.Item Open Access Preconditioning techniques for coupled Stokes Darcy systems(2020) Schmalfuß, JennyItem Open Access Wave functions and oscillator strengths in a two-band model for Rydberg excitons in cuprous oxide quantum wells(2024) Kühner, LeonRydberg physics is the study of systems involving highly excited states of atoms or molecules, known as Rydberg states. In these states, one or more electrons are far from the nucleus, giving the atom exaggerated properties such as large size, long lifetimes, and strong interactions with external fields and nearby particles. These unique features make Rydberg systems a valuable tool for exploring a range of phenomena in atomic physics, quantum optics, and condensed matter physics. They are particularly important for applications in quantum technologies, such as quantum simulation and computation and sensing. Another candidate for Rydberg physics are excitons. When an electron is excited from the valence band to the conduction band the electron in the conduction band and the positively charged hole in the valance band can form hydrogen-like states. Excitons in cuprous oxide, though with relatively low principal quantum numbers, have already been detected in the 1950s by Gross and Hayashi. In 2014 it was possible to measure exciton states with a principal quantum number up to n=25, since then the exciton Rydberg physics has attracted large attention. These states have radii in the range of microns. Rydberg excitons show a large variety of phenomena which do not occur in atomic physics, for example the structure of the valence band leads to a breaking of the spherical symmetry, the spin-orbit coupling leads to the occurrence of a green and yellow exciton series, and central-cell corrections have effects on even parity states. Other effects occur when Rydberg excitons are confined in quantum wells. Such effects have been experimentally observed in GaAs. Thin layers in cuprous oxide have already been produced. Therefore, the observation of excitons in cuprous oxide quantum wells is expected soon. Excitons in quantum wells allow one to investigate the dimensional crossover from three-dimensional systems with weak confinement to two-dimensional systems with strong confinement. For this system the energy spectra have already been computed and effects like overlapping Rydberg series and resonances have been discussed. The theoretical calculations have so far been restricted to the computation of eigenenergies in a hydrogen-like model ignoring the impact of the valence band. The aim of this thesis is to study the effects of Rydberg excitons which rely on the wave functions. Such effects are the behavior of wave functions from weak to strong confinement and the quenching behavior in these regions that are visualized in this thesis. Numerically the wave functions are expanded in a B-spline basis. Also resonances above the first scattering threshold as well as bound states in the continuum above this threshold are visualized. Further, wave functions that undergo an avoided crossing are investigated. Another aspect is the influence of electrostatic effects for exciton states in quantum wells. These lead to the appearance of surface excitons, which can be seen in the visualization of these states. Oscillator strengths are investigated and rely on the behavior of the wave function. In our system the oscillator strengths are no longer translational invariant. Ultimately, this work provides a comprehensive exploration of Rydberg exciton wave functions, which could be instrumental in advancing the use of these systems in emerging quantum applications.
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