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Based on state of the art literature, broad introductions to the concepts of discretized free Dirac fermions in 1+1 d, their topological static and dynamical entanglement, as well as their holographic duals are given. We depict these fields systematically and undertake new investigations, connecting them to current literature. We focus on a specific model lying in the BDI class of the Altland–Zirnbauer class of symmetry protected topological insulators. In particular we find that the entanglement structure of the ground state manifold possesses hyperbolic symmetry (invariance under Lorentz boosts) for the trivial and single winding phase. Furthermore, we find an analytical expression for the evolution after a dynamical topological phase transition (performing a quantum quench) between flattened Hamiltonians. These transitions show spatially and temporally confined dynamics, which leads us to suggest and study edge states located on a compact space-time manifold as a possible dynamical topological invariant to classify them. Finally, we give an accessible introduction to the holographic principle and depict its discrete realization "Exact Holographic Mapping" (EHM) introduced by Qi. We demonstrate its translational symmetry breaking and suggest to sum over all possible tensor network configurations to solve this problem. With EHM at hand, we investigate a holographic quench and find that certain higher topological phase transitions possess dual descriptions of several disconnected AdS spaces., author: Simon Graf, Masterarbeit Universität Innsbruck 2021

Based on state of the art literature, broad introductions to the concepts of discretized free Dirac fermions in 1+1 d, their topological static and dynamical entanglement, as well as their holographic duals are given. We depict these fields systematically and undertake new investigations, connecting them to current literature. We focus on a specific model lying in the BDI class of the Altland–Zirnbauer class of symmetry protected topological insulators. In particular we find that the entanglement structure of the ground state manifold possesses hyperbolic symmetry (invariance under Lorentz boosts) for the trivial and single winding phase. Furthermore, we find an analytical expression for the evolution after a dynamical topological phase transition (performing a quantum quench) between flattened Hamiltonians. These transitions show spatially and temporally confined dynamics, which leads us to suggest and study edge states located on a compact space-time manifold as a possible dynamical topological invariant to classify them. Finally, we give an accessible introduction to the holographic principle and depict its discrete realization "Exact Holographic Mapping" (EHM) introduced by Qi. We demonstrate its translational symmetry breaking and suggest to sum over all possible tensor network configurations to solve this problem. With EHM at hand, we investigate a holographic quench and find that certain higher topological phase transitions possess dual descriptions of several disconnected AdS spaces., author: Simon Graf, Masterarbeit Universität Innsbruck 2021

Die vorliegende Arbeit betrachtet die Eigenschaften eines tribologischen Kontaktes bei elektrischem Stromdurchgang. Diese unerwünschten Stromdurchgänge entstehen etwa durch die Kombination von unvermeidbaren parasitären Kapazitäten in einem Elektromotor unter dem Einsatz von schnellschaltenden Frequenzumrichtern mit steilen Spannungsflanken. Folge dieser Stromdurchgänge sind Schäden an den Kontaktpartnern als auch an dem dazwischen befindlichen Schmiermittel. Zur Vorhersage der Gefährdung eines Antriebsstrangs hinsichtlich parasitärem Stromdurchgang werden elektro-mechanische Simulationen eingesetzt. Diese erlauben eine Beurteilung des tribologisch-elektrischen Kontaktes hin auf seine Gefährdung gegen Stromdurchgang. Basierend hierauf können dann geeignete Abhilfemaßnahmen getroffen werden. Zur weiteren Verbesserung solcher elektro-mechanischen Simulationen werden im ersten Teil der Arbeit experimentell die Durchschlagspannung als auch der Widerstand des Entladekanals ermittelt. Hierbei zeigt sich ein ausgeprägtes nichtlineares Verhalten des Entladewiderstands, welches in dieser Form nicht vollumfänglich mit den Kenntnissen aus der Hochspannungstechnik erklärt werden kann. Hierauf aufbauend werden die langzeitlichen Auswirkungen des parasitären Stromdurchgangs im definierten tribologischen Zustand der Mischreibung betrachtet. Zur Ermittlung von Wechselwirkungen werden umfangreiche Messgrößen aufgezeichnet und analysiert. Im abschließenden Teil der Arbeit werden die Auswirkungen des elektrischen Stromdurchgangs auf die Oberflächenrauheiten simulativ ermittelt., The present work researched the properties of a tribological contact during an electric current passage. For example, these current crossings occur due to the combination of unavoidable parasitic capacitances in an electric motor by using fast-switching frequency converters with high voltage edges. The consequence of these current crossings is damage to the contact partners as well as to the used lubricant. Electro-mechanical simulations are used to predict the hazard of a drive train with respect to parasitic current passage. These allow the tribological electrical contact to be assessed in terms of its vulnerability to the passage of current. Based on this, suitable remedial measures can then be taken. To further improve such electro-mechanical simulations, the breakdown voltage and the resistance of the discharge channel are determined experimentally in the first part of the work.This showed a pronounced nonlinear behavior of the discharge resistance, which cannot be fully explained with the knowledge from high-voltage engineering. Based on this, the long-term effects of the parasitic current passage in the defined tribological state of mixed friction are considered. Extensive measured variables are recorded and analyzed to determine interactions. In the final part of the work, the effects of the electric current passage on the surface roughnesses are determined simulatively.