Universität Stuttgart
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Item Open Access Lagrange-Deskriptor-Analyse der klassischen Dynamik von Satelliten in Sonne-Planet-Mond-Systemen(2023) Oguz, NihatMithilfe der Himmelsmechanik ist es möglich, das Verhalten von Himmelskörpern und Satelliten in ihren Gravitationsfeldern zu untersuchen. Bildet sich durch diese Körper ein Mehrkörperproblem, wird dieses durch mathematische Formulierungen der wirkenden Kräfte sowie Bewegungsgleichungen beschrieben und je nach Möglichkeit werden die Orbits analytisch oder numerisch berechnet und ausgewertet. Dabei ist zu beobachten, dass sich die Orbits unterscheiden und außergewöhnliche Eigenschaften besitzen können. Hierbei ist das Verständnis der Dynamik wichtig, um passende Orbits, unter anderem Transferorbits, für natürliche und künstliche Satelliten zu bestimmen, die sich in der Nähe der Lagrangepunkte befinden. In dieser Arbeit wird das System bestehend aus dem Stern, dem Planeten, dem Mond und dem Satelliten, der sich in der Nähe von den Lagrangepunkten befindet, untersucht. Dazu wird das Verhalten von Satelliten an diesen Orten untersucht und Trajektorien sowie Lagrangedeskriptoren an Positionen mit unterschiedlichen Anfangsbedingungen berechnet. Die Lagrangedeskriptoren werden hierbei genutzt, um Strukturen in Phasenräumen aufzudecken. Außerdem wird der Einfluss des Mondes auf die Dynamik betrachtet.Item Open Access Korrelationsfunktions-Quanten-Monte-Carlo-Methode zur Berechnung von angeregten Zuständen von Mehrelektronen-Atomen in Neutronensternmagnetfeldern(2012) Meyer, Dirk; Wunner, Günter (Prof. Dr.)Um beobachtete Absorptionsfeatures in Spektren isolierter Neutronensterne mit thermischen Emissionen durch atomare Übergänge erklären zu können, benötigt man atomare Daten von Mehrelektronen-Atomen in starken Magnetfeldern. Die in dieser Arbeit untersuchte Korrelationsfunktions-Quanten-Monte-Carlo-Methode (CFQMC-Methode) ist in der Lage, prinzipielle Fehler anderer Methoden (wie beim Hartree-Fock-Verfahren das Hartree-Fock-Limit) zu überwinden. Die CFQMC-Methode ist eine Quanten-Monte-Carlo-Methode, mit der man die Energien des Grundzustands und der niedrigsten m angeregten Zustände eines Symmetrieunterraumes für ein quantenmechanisches Mehrteilchensystem simultan berechnen kann. Diese Arbeit beschäftigt sich mit der präzisen Berechnung der Energien von Mehrelektronen-Atomen (speziell von Helium) in starken Magnetfeldern (2·10^5 – 2·10^7 Tesla), wie sie auf Neutronensternen vorkommen. Im Gegensatz zur Diffusions-Quanten-Monte-Carlo-Methode (DQMC-Methode) für Grundzustandsenergien, auf der die CFQMC-Methode basiert, benötigt sie keine Näherung der Schrödinger-Gleichung, um die in Magnetfeldern notwendigerweise komplexen Wellenfunktionen zu erfassen. Des Weiteren ist sie variationell auch für die Energien angeregter Zustände, im Gegensatz zur Fixed-Phase DQMC-Methode (FPDQMC-Methode) und der Hartree-Fock-Methode. Wie andere Quanten-Monte-Carlo-Verfahren ermöglicht die CFQMC-Methode eine Fehlerabschätzung der berechneten Ergebnisse. Die CFQMC-Methode benötigt bereits gute Näherungen in Form sogenannter Trial-Funktionen an die Zustände, deren Energien berechnet werden sollen. In dieser Arbeit wird dafür ein Hartree-Fock-Ansatz verwendet, bei dem die Einelektronen-Wellenfunktionen in der Richtung transversal zum Magnetfeld in einer Basis von Landau-Funktionen dargestellt werden. Dieser Ansatz ist den untersuchten hohen Magnetfeldstärken gut angepasst. In dieser Arbeit werden die Grundlagen und die Funktionsweise der CFQMC-Methode dargestellt, wie auch der DQMC-Methode für Magnetfelder in verschiedenen Varianten (Fixed-Phase DQMC und Released-Phase DQMC). Verschiedene Verfahren werden in Form eines modularen und erweiterbaren C++-Programms mit grafischer Benutzeroberfläche implementiert. Es werden exemplarische Rechnungen hauptsächlich für Helium in starken Magnetfeldern durchgeführt und diskutiert und die mit der Magnetfeldstärke ansteigende Varianz des CFQMC-Verfahrens untersucht. Es stellt sich heraus, dass das Verfahren für Helium über einer Magnetfeldstärke von etwa 2·10^6 T versagt. Davon ausgehend wird eine Variante des CFQMC-Verfahrens, das Fixed-Phase CFQMC-Verfahren, entwickelt, mit dessen Hilfe der dem Verfahren zugängliche Bereich der Magnetfeldstärke um eine Zehnerpotenz erweitert werden kann. Die Rechnungen wurden wegen der hohen Rechenzeit des CFQMC-Verfahrens parallelisiert auf dem Cluster des BWGrid durchgeführt.Item Open Access Fluctuations and correlations of quantum heat engines(2020) Denzler, Tobias; Lutz, Eric (Prof. Dr.)In this work we study the effect of quantum and thermal fluctuations on the statistics of quantum heat engine performance parameters, like efficiency and power. We begin by deriving an explicit solution for the characteristic function of the heat distribution of a thermal quantum harmonic oscillator. We then derive a general framework based on the standard two-point-measurement scheme to compute the efficiency distribution of a quantum Otto cycle. We analyze the generic properties of this distribution for scale-invariant driving Hamiltonians which describe a large class of single-particle, many-body, and nonlinear systems. We find that the efficiency is deterministic and that its mean is equal to the macroscopic efficiency for adiabatic driving. We continue our research by studying the efficiency large deviation function of two exemplary quantum heat engines, the harmonic oscillator and the two-level Otto cycles. While the efficiency statistics follow the ’universal’ theory of Verley et al. [Nature Commun. 5, 4721 (2014)] for nonadiabatic driving, we find that the latter framework does not apply in the adiabatic regime. We can relate this unusual property to the perfect anticorrelation between work output and heat input that suppresses thermal as well as quantum fluctuations. We then probe our findings in an experimental NMR setup using spin-1/2 systems and find them to agree rather well with our theoretical predictions. Afterward, we move on to the finite-time quantum Carnot cycle and investigate its power fluctuations. In particular, we consider how level degeneracy and level number, two commonly found properties in quantum systems, influence the relative work fluctuations. We find that their optimal performance may surpass those of nondegenerate two-level engines or harmonic oscillator motors. Our results highlight that these parameters can be employed to realize high-performance, high-stability cyclic quantum heat engines.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 List of parameters influencing the pedestrian movement and pedestrian database(2015) Dridi, Mohamed H.In this paper we present a list of factors influencing the pedestrian behaviour in different situations and conditions. In crowd simulation input we must consider at least two simulation conditions. The first is the normal condition and the second is the emergency condition or panic situation. In panic situations most parameters will be changed and the time factor becomes very important. Both emotion and personality clearly have a strong and considerable impact on individual behaviours in such situations. However, most existing approaches in their attempt to model the behaviour of individuals and for guiding an agent to interact with its environment and other agents, consider the individual as an autonomous agent or autonomous particle that obeys some human-like behaviour modules such as locomotion, perception, and decision making. Other models treat the crowd as a collection of homogeneous particles interacting through physical forces. Today with the enormous knowledge development in computer science, many models try to improve themselves. There seems to be an evolution in crowd simulation to model each individual as some kind of intelligent agent with attempts to incorporate more and more social and psychological factors into the agent behaviour model. However, to reproduce more realistic simulation behaviours many factors and attributes influencing pedestrians must be considered. The actual shortcoming of the existing models is the absence of modelling the social group process and its impact on human behaviour. One way to gain a better understanding of human behaviour in this area is to enrich the tools available for planning, such as pedestrian micro simulation in case of panic situations and emergency conditions. In this work a pedestrian database called PedGUI containing a lot of information about pedestrians is developed, this have a significant impact on the simulation input at least two mean pedestrian characteristics like age and gender can be considered.Item Open Access Polaritontransformation der gelben Magnetoexzitonen in Kupferoxydul(2017) Ertl, JanWird im Halbleiter ein Elektron aus dem Valenzband in das Leitungsband angeregt, so bleibt ein Loch im Valenzband zurück. Gebundene Elektronen-Loch-Paare, die sogenannten Exzitonen, können im Festkörper durch Absorption eines Photons angeregt werden. Trifft Licht auf den Festkörper so kann es mit den Exzitonen in Wechselwirkung treten. Diese Kopplung von Licht und Exzitonen wird durch ein neues Quasiteilchen, das Exziton-Polariton, beschrieben. Zur Beschreibung der Exziton-Polaritonen wird dann ein Basiswechsel, die Polaritontransformation, durchgeführt. In dieser Arbeit wird zur Beschreibung der Exzitonen ein wasserstoffartiges Modell angenommen. Damit wird die gelbe Exzitonenserie in Kupferoxydul für verschiedene Magnetfelder in der Coulomb-Sturm'schen Basis ausgewertet. Anschließend wird die Polaritontransformation durchgeführt und der Einfluss von verschiedenen Parametern auf die Polaritondispersion untersucht.Item Open Access Nonequilibrium aspects of quantum thermodynamics(2006) Michel, Mathias; Mahler, Günter (Prof. Dr.)Questions about the route from a nonequilibrium initial state to the final global equilibrium have played an important role since the early days of phenomenological thermodynamics and statistical mechanics. Nowadays, their implications reach from central technical devices of the contemporary human society, like heat engines, refrigerators and computers to recent physics at almost all length scales, from Bose-Einstein-condensation and superconductors to black holes. This work addresses the foundation of macroscopic laws concerning the decay to equilibrium, e.g. the celebrated Fourier's Law, on microscopic Schrödingerian quantum dynamics. Here, a proper treatment requires the usage of modern methods in theoretical physics such as the Theory of Open Quantum Systems, the Kubo Formula in Liouville Space and the novel Hilbert Space Average Method. It turns out that both the relaxation to equilibrium as well as the transport of heat is mainly determined by quantum effects comparable to the role of entanglement in considerations of the global equilibrium within Quantum Thermodynamics. Finally, the foundation of phenomenological thermodynamics on a microscopic theory will hopefully improve our understanding of those most impressive and far-reaching theories and their background and will possibly open the way to overcoming their nanoscopic limits.Item Open Access Realisierung von Balanced Gain and Loss in einem Bose-Hubbard-Modell mit zeitabhängigen Potentialen(2016) Dizdarevic, DanielItem Open Access Contraction dynamics of biological muscles : mechanical and thermodynamical prediction, and experimental verification(2013) Häufle, Daniel F. B.; Wunner, Günter (Prof. Dr.)Biological movement generation is a dynamical process involving not only biomechanical structures, e.g., muscles, bones, ligaments, etc. but also metabolic energy processing, physiological sensing, and neuronal control. In this thesis, a physics approach to study these complex interactions is presented. It builds upon the results of physiological experiments with isolated animal muscles over the course of which their distinct dynamic properties have been described in great detail. Derived from previous simulation studies, the hypotheses posed were that the dynamic properties of muscles strongly contribute to generation and control of movements, they allow very simple control strategies, and thus reduce control effort in comparison to (technical) systems whose actuators do not have similar dynamic properties. Hopping was used as a template model to study the relation of muscle properties, control strategies, and interaction with the environment. It was found that the typical non-linear force-velocity relation of the biological muscle is important for hopping stability. Additionally, stability could be improved by combining feed-forward and feedback control strategies. The results highlight the importance of the muscle properties, especially that of the force-velocity relation for the control of periodic movements. If an organism exploits the muscle properties, the control effort was expected to be less than in a (technical) system without these properties. To quantify control effort, a new measure based on information theory was developed. Applied to hopping models this method revealed that the required information to control hopping can be as low as I=34bit with a muscle vs. I=798bit with a DC-motor. Concerning the muscle, the control strategy was particularly designed to exploit the muscle properties. In case of the DC-motor, a typical engineering control approach was chosen, where a negative-feedback controller was used to enforce a predefined trajectory regardless of the actuator properties. This shows that the approach to control effort based on information theory is applicable to and comparable across completely different actuator designs and control approaches. So far, biomechanical muscle models incorporated the force-velocity relation as a phenomenological fit to experimental data, i.e. a hyperbolic function. Only microscopic muscle models proposed a physical origin of the hyperbolic force-velocity relation. However, microscopic muscle models can neither be used in simulation studies of complex human movements, nor as a blueprint for the construction of artificial muscles. A different macroscopic model predicted the hyperbolic force-velocity relation from an arrangement of three macroscopic physical components: a mechanical energy source (active element AE), a parallel damper element (PDE), and a serial element (SE) that exhibits operating points with hyperbolic force-velocity dependency. To verify the contraction dynamics of this model, the analytical model was compared to a numerical simulation and a hardware implementation. The analytical model only predicts the operating points at steady state, whereas the numerical model includes the dynamics of the contraction, and the hardware implementation is used to verify the real world functionality of the concept. The same experiments as usually performed with biological muscles were conducted, i.e. quick release experiments against different loads. A similar hyperbolic force-velocity relation was found in the numerical model and the hardware implementation. However, deviations from the analytical prediction were found. To resolve these discrepancies, two types of quick release experiments were performed. These experiments represent two extreme cases of the contraction dynamics, i.e. against a constant force (isotonic) and against an inertial mass. Both experiments revealed hyperbolic force-velocity relations. Interestingly, the analytical model not only predicts these extreme cases, but additionally all contraction states in between as well. It was possible to validate these predictions with the numerical model and the hardware experiment. These results prove that the origin of the hyperbolic force-velocity relation can be mechanically explained on a macroscopic level by the dynamical interaction of three mechanical elements. Thus, the concept can be seen as a starting point for the development of muscle-like bionic actuators. With these studies, this thesis contributes to the understanding of the role that muscles play in the control of periodic movements, and proposes a design concept allowing a transfer of their beneficial properties into technical systems. By using information theory to quantify the control effort, technical biological systems can be compared and key characteristics can be identified. These new insights and methods contribute to the integrated view of biological movement generation.Item Open Access Exceptional points in atomic spectra and Bose-Einstein condensates(2008) Cartarius, Holger; Main, Jörg (Prof. Dr.)Exceptional points are a special type of degeneracy which can appear for the resonances of parameter-dependent quantum spectra described by non-Hermitian Hamiltonians. They represent positions in the parameter space at which two or even more resonances pass through a branch point singularity. At the critical parameter values, the energies, the widths, and the wave functions describing the resonances are identical. The branching eigenstates show a geometric phase for a parameter space loop around the branch point. In this thesis exceptional points are investigated in two important quantum systems. The first system is the hydrogen atom in crossed external electric and magnetic fields. It is a representative for the class of atoms in static external fields, which are as fundamental quantum system accessible both with experimental and theoretical methods and are ideally suited to study the influence of exceptional points. The resonance spectra of the hydrogen atom are numerically calculated with the complex rotation method. A procedure to systematically search for exceptional points is elaborated and the existence of exceptional points is proven. The influence of the branch point singularities on the resonance energies, the wave functions, and the photoionization cross section is analyzed. In addition, a possibility for the observation of exceptional points in an experiment with atoms is proposed. The investigation of the resonances in spectra of the hydrogen atom in this thesis furthermore reveals structures which can provide an insight into the ionization mechanism. The ionization mechanism of the hydrogen atom in crossed electric and magnetic fields has been investigated, e.g., by application of the transition state theory. Here, calculations are performed which give clear evidence for an important influence of the classical transition state in the quantum spectrum. A second class of quantum systems in which exceptional points appear are the stationary states of Bose-Einstein condensates. They are described by the nonlinear Gross-Pitaevskii equation and it is known that by a variation of the system's parameters the ground state and a second stationary solution are born together in a tangent bifurcation. It is pointed out in this thesis that the mean field energies, the chemical potentials, and the wave functions show at the point of bifurcation the behavior of an exceptional point. The results allow for the extension of the concept of exceptional points to nonlinear quantum systems. Two types of condensates are investigated for this purpose. Bose-Einstein condensates with a laser-induced gravity-like 1/r interaction exhibit analytic solutions which directly prove the existence of exceptional points. The results obtained in this system are used to identify and describe exceptional points in the Bose-Einstein condensation of dipolar gases which is of high experimental interest and has already been realized.