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 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.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 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 Realisierung von Balanced Gain and Loss in einem Bose-Hubbard-Modell mit zeitabhängigen Potentialen(2016) Dizdarevic, DanielItem 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 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.