08 Fakultät Mathematik und Physik
Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/9
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Item Open Access Item Open Access Adiabatic approximation for the dynamics of magnetoexcitons in Cu2O(2019) Ertl, JanWhen exciting an electron in a semiconductor from the valence to the conduction band, the missing electron in the valence band can be treated as a positively charged quasi particle, the hole. As a bound state of electron and hole the exciton is the solid state analogon to the hydrogen atom. The most important difference when comparing exctions to hydrogen-like systems is the influence of the band structure in the solid state system. The band structure breaks the full rotational symmetry of the hydrogen-like system leading to additional features in the absorption spectra of cuprous oxide. Absorption spectra for magnetoexcitons in cuprous oxide can be calculated in a quantum mechanical framework with good accordance to the experimental spectra. However those calculations are limited to low principal quantum numbers. On the other hand experimental data is available for higher energies. In the range of the gap energy one can observe quasi-Landau resonances. In atomic physics these features can be explained within a semiclassical theory. This connects properties of classical orbits to the observed absorption spectra. This thesis aims to lay down the foundations for the calculation of classical orbits for magentoexcitons in cuprous oxide as well as their parameters to provide the tools to apply semiclassical theory.Item Open Access Application of machine learning to find exceptional points(2023) Egenlauf, PatrickIn 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.Item Open Access Item Open Access Basic representation theory of crossed modules(2018) Truong, MonikaA group corresponds to a topological space with one nontrivial homotopy group. A crossed module corresponds to a topological space with two nontrivial homotopy groups. In classical group theory, Cayley's Theorem constructs for every group G an injective group morphism to the symmetric group S_G. For a crossed module V, we have a similar statement. For every category C, we have the symmetric crossed module S_C. For every crossed module V, we construct an injective crossed module morphism to the symmetric crossed module S_VCat. Suppose given an R-linear category M. On the one hand, we obtain the invertible monoidal category Aut_R(M) by means of category theory. On the other hand, we have the symmetric crossed module S_M as in the Cayley context. In S_M, we have the crossed submodule Aut^CM_R(M) containing only the R-linear elements of S_M. We consider the corresponding invertible monoidal category (Aut^CM_R(M))Cat. We show that there exists a monoidal isofunctor Real_M : (Aut^CM_R(M))Cat -~-> Aut_R(M). This means that starting with M, we obtain essentially the same object via crossed module theory as via category theory. A representation of a group G on an R-module N is given by a group morphism G -> Aut_R(N). Analogously, a representation of a crossed module V on an R-linear category M is given by a crossed module morphism V -> Aut^CM_R(M). We begin to study the representation theory of crossed modules.Item Open Access Berechnung hochangeregter Exzitonen in elektrischen und magnetischen Feldern mit der Methode der komplexen Koordinatenrotation(2018) Zielinski, PatrikDiese Arbeit befasst sich mit Exzitonen in äußeren elektrischen und magnetischen Feldern. Dabei liegt der Fokus auf das Ermitteln von Resonanzen in Kupferoxydul. Diese wurden mit Hilfe der komplexen Koordinatenrotation bestimmt. Des Weiteren konnte mit den Resonanzen Spektren berechnet werden.Item Open Access Bosonic many-body systems with topologically nontrivial phases subject to gain and loss(2017) Dangel, FelixTopological properties of physical systems are preserved under large variations in the system parameters and hence interesting for applications in communication networks and quantum computing. This work investigates the impact of dissipation on a class of one-dimensional bosonic systems, described by superlattice Bose-Hubbard models, that exhibit topologically nontrivial phases in the absence of dissipation. Gains and losses are modeled in two different frameworks (non-Hermitian PT-symmetric Hamiltonians and master equations in Lindblad form) and numerically investigated with variants of density matrix renormalization group methods. Empirically, both dissipative extensions give rise to similar effects when compared on different dissipative patterns. In the presence of strong local gain and loss, dissipative sites act as system boundaries that can induce edge states in the Hermitian subsystems.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 Descriptions of some double Burnside rings(2017) Krauß, NoraThe double Burnside R-algebra B_R(G,G) of a finite group G with coefficients in a commutative ring R has been introduced by S. Bouc. It is R-linearly generated by finite (G,G)-bisets, modulo a relation identifying disjoint union and sum. Its multiplication is induced by the tensor product. It contains the bifree double Burnside R-algebra B_R^Delta(G,G) generated by bifree finite (G,G)-bisets. Let S_n denote the symmetric group on n letters. For R in {Q, Z, Z_(2), F_2, Z_(3), F_3}, we calculate B_R(S_3,S_3) and B_R^Delta(S_4,S_4).Item Open Access Dielectric measurements at GHz frequencies(2019) Wendel, LarsAmongst the many dielectric materials that are topic of present research, two examples might be mentioned: SrTiO3 and nano-confined water molecules in single crystals. In SrTiO3 a quantum paraelectric or incipient ferroelectric behavior can be observed [1]. For low temperatures SrTiO3 is in a paraelectric phase, and the dielectric constant as a function of temperature follows a Curie-Weiss behavior. However, a real phase transition is not fully reached, indicated by the absence of a divergence in the permittivity at lowest observable temperatures. Quantum fluctuations then start to come into play and stabilize the frequency of the soft mode which leads to a saturation of the permittivity [2]. The dielectric constant of SrTiO3 is strongly anisotropic and depends vastly on temperature and frequency range and can go up to around 20000 [3, 4]. To confine water molecules in single crystals and observe the (quantum) paraelectric behavior, suitable hosts are needed. Possible candidates are single crystals of beryl or cordierite belonging to the gemstone family, where the water molecules are confined in structural channels [5, 6]. These large open channels run parallel to the crystal c-axis. In beryl the channels consist of six SiO4 tetrahedral rings, while in cordierite they consist of four SiO4 and two AlO4 tetrahedral rings. The water molecules are trapped in the center of the channels during the growth process and can occur in two distinct orientations: Either the electric dipole is perpendicular (type I) or parallel (type II) to the c-axis. For type I paraelectric behavior of the water molecules can be observed. This is due to the prevented hydrogen bonding, while the dipole-dipole interactions are kept which results in incipient ferroelectricity. The dielectric permittivity follows a Curie-Weiss behavior and saturates for low temperatures due to quantum fluctuations [6]. Whereas the permittivity of SrTiO3 ranges up to very large values, the dielectric constant of confined water molecules only goes up to around 20. Measurements were performed up to THz frequencies, where especially the cordierite system lacks information about the microwave regime. The different frequency regimes require separate approaches to probe the sample under study [7–9]. Different high frequency dielectric measurement techniques can access the desired dielectric properties in the GHz range of the bulk material. The methods can be roughly classified in four categories: Transmission and reflection line techniques, free-space methods, open-ended coaxial-probe techniques and resonant techniques [10–14]. Each technique has advantages and limitations regarding sample material and shape and which frequencies are possible to probe. Generally, the measurement methods can be classified if discrete frequencies are measured or the measurement is of broadband type. In broadband approaches the electromagnetic wave passes the material and allows to access frequencies continuously over a wide range. An example is the transmission line method where frequencies from the MHz up to the GHz range can be accessed [15]. However, this method lacks heavily in accuracy due to the non-resonant fixture type. Furthermore, unwanted parasitic losses occur in the microwave regime, strongly 11. Motivation influencing the measurement. Since the accuracy is of major interest, resonant techniques are suited for bulk dielectric measurements [16–18]. The obtained results are of highest accuracy compared to the other mentioned techniques. However, one big disadvantages is the accessibility of only a single frequency. The different resonant approaches are directly fabricated for the sample under test and are therefore able to probe only a single frequency in the spectrum. Especially regarding frequency-dependent dielectric properties this is an enormous weakness. Microwave waveguide resonator utilize the cavity perturbation theory and are able to probe numerous discrete frequencies [19]. Most of all, planar microwave resonators provide a wide field of potential researches [20–24]. It is possible to probe higher harmonics of a fundamental resonance frequency and perform measurements at cryogenic temperatures, while remaining at highly accurate results. A further upside is the simple fabrication of the the planar resonators as well as an fast and straightforward sample preparation of the studied materials. However, planar waveguide resonators are used for studies on dielectric thin films [25], whereas probing bulk dielectrics with this method is a recent research area. In this thesis a new resonant approach for bulk dielectric samples is developed in the microwave regime up to 20 GHz. With simulations utilized, different possible approaches are firstly studied regarding their suitability and functionality. This is investigated with focusing on the challenges which occur by going from thin films under study to bulk dielectrics. The respective approaches are then tested within experiments to check the simulated predictions. Finally, a new method is established by measuring known dielectrics and comparing the results to the literature. This thesis begins with a short guide into fundamental theoretical principles required for characterizing resonators and the analysis of microwave resonator experiments. Afterwards, the state of art of high frequency dielectric measurements is presented including several exemplary methods. Following, simulation and experimental basics and the consistency between them are elucidated. The first approach where the bulk dielectric sample acts as perturbation to the waveguide is then discussed for two different planar resonator structures. The new method with the resonator directly shaped on the sample under study is subsequently analyzed and discussed in detail including model requirements, simulations and experiments on TiO2, MgO and LaAlO3. This work finishes with an outlook for possible future experiments for the established resonant approach.Item Open Access Item Open Access Dynamik und Trennflächen für getriebene Systeme mit zwei zeitabhängigen Sattelpunkten(2018) Reiff, JohannesDie Arbeit untersucht chemische Reaktionen in zeitlich getriebenen Systemen mit zwei Sattelpunkten mithilfe der Transition State Theory.Item Open Access Dynamik von PT-symmetrischen und symmetriebrechenden Zweimodenmodellen, eingebettet in ein zeitabhängiges Viermoden-Bose-Hubbard-System(2017) Mathea, TinaBose-Einstein-Kondensate mit ausgeglichenem Gewinn und Verlust in einer optischen Doppelmulde stellen einen möglichen Kandidaten für die experimentelle Realisierung von PT-Symmetrie dar. Dieses System kann im Mean-Field-Limit unter Verwendung komplexer Potentiale mithilfe einer Gross-Pitaevskii-Gleichung beschrieben werden, was einer nicht-hermiteschen Beschreibung entspricht. Durch Einbettung dieses Systems in ein optisches Viermuldenpotential mit zeitabhängigen Parametern können die PT-symmetrischen Zustände des nicht-hermiteschen Systems in den inneren Mulden des hermiteschen Viermuldensystems eingestellt werden. Somit stellt das zeitabhängige Viermuldensystem eine Möglichkeit der experimentellen Realisierung von PT-Symmetrie dar. Da in dem beschriebenen System Vielteilcheneffekte eine wichtige Rolle spielen, stellt sich die Frage, ob sich das Verhalten der PT-symmetrischen Zustände des offenen Quantensystems auch im Vielteilchensystem einstellen lässt. In der vorliegenden Arbeit wird gezeigt, dass es unter Verwendung entsprechender Zeitabhängigkeiten der Kontrollparameter und unreiner Anfangszustände (d.h. Zustände, die sich nicht als Produkt der Einteilchenzustände darstellen lassen) möglich ist, das Verhalten der PT-symmetrischen Zustände in der Einteilchendynamik des Vielteilchensystems zu realisieren. Dazu wird ein Verfahren entwickelt, wie sich passende Anfangszustände konstruieren lassen. Die Vielteilchenbeschreibung des Systems erfolgt dabei mit dem Bose-Hubbard-Modell und der Bogoliubov-Backreaction-Methode.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 MD simulations of 3D laser printing(2024) Schmid, JonasItem Open Access Microwave investigations on SrTiO3-based materials at mK temperatures(2018) Zinßer, MarioStrontiumtitanat (STO) ist ein Halbleiter, der unter einer bestimmten n-Dotierung bei Milli KelvinTemperaturen (mK) einen Phasenübergang in den supraleitenden Zustand aufweist. Es war damit einer der ersten ”supraleitenden Halbleiter” und zugleich der erste Oxid-Supraleiter, der unter anderem die mit dem Nobel-Preis 1987 ausgezeichnete Entdeckung von Hochtemperatur-Supraleitern vorantrieb. Darüber hinaus wurde zum ersten Mal ein sogenanntes dome-förmiges Verhalten als Funktion der Dotierung festgestellt, welches durch eine Reduktion an Sauerstoffatomen oder eine Ersetzung von Titanatomen durch Niobatome (Nb-STO) erzielt wird. Die hierfür benötigten Ladungsträgerdichten und die damit verbunden Energieskalen sind verhältnismäßig klein und schränken damit die Anzahl an möglichen Kopplungsmechanismen der Cooperpaare erheblich ein. Dies ist nicht in Einklang mit der BCS-Theorie zu bringen und bis zum heutigen Tag nicht vollständig verstanden, weshalb STO ein aktuelles Forschungsthema darstellt. An der Grenzschicht zu Lanthan Aluminiumoxid (LAO) weist STO ein zweidimensionales Elektronengas extrem mobiler, freier Ladungsträger auf, das ebenfalls einen supraleitenden Ubergang bei mK- Temperaturen zeigt. Wie auch in STO selbst ist die Supraleitung dort dome-förmig und entstammt mehreren elektronischen Bändern. Diese Arbeit soll unter anderem auch zum Verständnis der Supraleitung an der LAO-STO-Grenzschicht beitragen. Hierfür sollen die elektronischen Bandeigenschaften und mit besonderem Schwerpunkt die effektiven Massen der bei mK-Temperaturen zur Supraleitung beitragenden Elektronen untersucht werden. Zur direkten Messung dieser bietet sich die Methode der Zyklotronresonanz an, bei der durch ein extern angelegtes Magnetfeld Leitungselektronen in definierte Laundauniveaus gequantelt werden und deren Ubergang mit entsprechenden Energien im µeV-Bereich angeregt wird. Eine der Hauptherausforderungen dieser Messmethode liegt in der Notwendigkeit einer höheren Messfrequenz als die Streurate, was nur für sehr reine Metalle im genannten Energiebereich erreicht werden kann. Die hierzu nötige Mikrowellenstrahlung wird mittels koplanarer und streifenleitenden Wellenleitern übertragen und deren Transmissionssignal analysiert. Um ein entsprechendes, der Zyklotronresonanz zuzuschreibendes Messsignal vorzufinden, wurden mehrere Experimente durchgeführt. Eines von diesen beinhaltet Anzeichen eines Zyklotron-Messsignals. Obwohl dieses Ergebnis nicht reproduziert werden konnte und damit dessen Verlässlichkeit in Frage zu stellen ist, gingen Messwerte aus dieser hervor, die effektive Massen zwischen 3 und 4 Elektronenmassen und Streuraten zwischen 9 und 10 GHz ergaben, was mit publizierter Literatur in Einklang steht. Außerdem wurden Messungen der komplexen, optischen Leitfähigkeit innerhalb des supraleitenden domes von Nb-STO durchgeführt. Mit diesen ist es möglich, zwei zur effektive Masse korrelierte Kohärenzlängen zu bestimmen und dadurch das Verhältnis beider Massen der zur Supraleitung beitragenden Elektronen zu bestimmen. Darüber hinaus wurden diese Daten noch genutzt, um einige andere charakteristische Eigenschaften wie die mittlere, freie Wegl¨ange, die Fermigeschwindigkeit von beiden supraleitenden Bändern und die suprafluide Dichte zu bestimmen. Letztere wurde zur Berechnung der London’schen Eindringtiefe und des Ginzburg-Landau-Parameters genutzt, die die Zugehörigkeit zur Klasse der Typ-II-Supraleiter von Nb-STO bestätigen. Des Weiteren legt der Vergleich der Kohärenzlänge mit der mittleren freien Weglänge und die Einordnung von Nb-STO in das Home’sche Gesetz ein dirty limit-Verhalten für Supraleiter nahe. All diese Eigenschaften sind starke Anzeichen für ein Mehrband-Supraleiter mit lediglich einer Energielücke in Nb-STO.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 Microwave response of the heavy-fermion superconductor CeCu2Si2(2019) Haug, AndréThis thesis covers microwave experiments carried out on CeCu2Si2 as my master's project. Our data cover a range from 200 MHz to 20 GHz and 80 mK up to 25 K. Our measurements indicate that, in spite of the recent findings from specific-heat measurements, CeCu2Si2 is indeed a d-wave rather than an s-wave superconductor. This is supported by things like uncondensed spectral weight, and the general behavior of e. g. superfluid density.Item Open Access The minimal projective resolution of Z_(2) over Z_(2)S_4(2017) Nitsche, SebastianWe consider the trivial module Z_(2) over the group ring Z_(2)S_4. Using the Wedderburn image of Z_(2)S_4, a minimal projective resolution of Z_(2) over Z_(2)S_4 with regular behavior is constructed. We give a closed formula for the projective terms and the differentials. The minimal projective resolution is used to calculate the cohomology groups of S_4 over Z_(2). In 1974, Thomas gave a description of the cohomology ring of S_4 as a factor ring of a polynomial ring. As far as we were able to compare both using Magma, our calculation is in accordance with his result.Item Open Access Modell mit Mastergleichung zur Beschreibung der Exziton-Phonon-Wechselwirkung in Cu2O(2017) Rommel, PatricExzitonen in äußeren Feldern sind ein wertvolles Modellsystem, um theoretische Vorhersagen über eine Vielzahl verschiedener Effekte experimentell zugänglich zu machen und zu überprüfen. Wichtig ist hier in erster Linie der Einfluss der Bandstruktur, durch welchen sich wichtige Korrekturen im Vergleich zum wasserstoffartigen Modell ergeben. Sie bildet unter anderem die reduzierte Symmetrie im Kristallgitter ab. Andererseits gibt es im Festkörper neben den Exzitonen auch andere Quasiteilchen deren Effekte zu beachten sind. In dieser Arbeit soll es dabei um die Exziton-Phonon-Wechselwirkung und ihren Einfluss auf das Eigenwertspektrum der Exzitonen gehen.
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