08 Fakultät Mathematik und Physik
Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/9
Browse
106 results
Search Results
Item Open Access Berücksichtigung der Mondrotation beim Asteroideneinfang an Lagrangepunkten(2019) Zatsch, Jonas Christian JörgIn der vorliegenden Arbeit wird das Verhalten und die Stabilität von Asteroiden nahe des zweiten Sonne-Erde-Lagrangepunkts L2 und der Einfluss des Erdmonds hierauf untersucht. Dafür wird die Transition State Theory, die sich zur Beschreibung der Dynamik an Rang-1-Sätteln eignet, angewendet.Item Open Access Bose-Einstein condensates with balanced gain and loss beyond mean-field theory(2017) Dast, Dennis; Wunner, Günter (Prof. Dr.)Most of the work done in the field of Bose-Einstein condensates with balanced gain and loss has been performed in the mean-field approximation using the non-Hermitian PT-symmetric Gross-Pitaevskii equation. However, the exchange of particles with the environment plays a crucial role in such systems which in general leads to deviations from the mean-field behavior. Thus, it is not clear whether a mean-field approach is appropriate. It is the purpose of this work to formulate and study a many-particle description of a Bose-Einstein condensate with balanced gain and loss. This is achieved by using a quantum master equation describing a double well where the incoupling of particles in one well and the outcoupling from the other are implemented with Lindblad superoperators. The in- and outcoupling rates are adjusted in an appropriate manner such that balanced gain and loss is achieved. It is shown that the mean-field limit of this master equation yields a PT-symmetric Gross-Pitaevskii equation. Furthermore the master equation supports the characteristic dynamical properties of PT-symmetric systems. There are, however, fundamental differences compared with the mean-field description revealing a new generic feature of PT-symmetric Bose-Einstein condensates. It is shown that the purity of the condensate periodically drops to small values but then is nearly completely restored, when the particles oscillate in the double well. Since in the mean-field limit a completely pure condensate is assumed, this effect cannot be covered by the Gross-Pitaevskii equation. These purity oscillations have a direct impact on the average contrast in interference experiments. In particular it is found that the extrema of the purity can be precisely measured since the average contrast at these points is not reduced by an imbalance of the particle distribution. To gain a detailed understanding of the purity oscillations, analytic solutions for the dynamics in the non-interacting limit are presented and the Bogoliubov backreaction method is used to discuss the influence of the on-site interaction. A central result is that the strength of the purity revivals does neither depend on the amount of particles in the system nor the interaction strength, but is almost exclusively determined by the strength of the in- and outcoupling processes. However, the strong revivals are shifted towards longer times for larger particle numbers. Without interaction this would make the purity oscillations unobservable for a realistic particle number, but by adjusting the interaction strength the strong revivals again occur earlier.Item Open Access Macroscopic quantum tunneling in Bose-Einstein condensates(2013) Schwidder, Torsten; Main, Jörg (Prof. Dr.)The decay of Bose-Einstein condensates from a metastable ground state into collapse due to macroscopic quantum tunneling is investigated using a semiclassical approximation to Feynman’s path integral formalism. Applying a variational ansatz of a single Gaussian to the wave function determined by the Gross-Pitaevskii equation, a special choice of the Gaussian width parameters yields a mean-field energy functional in Hamiltonian form. The temporal spatial extension of the condensate then is described in the picture of a particle moving in an external potential. In this picture the decay of the condensate wave function is investigated using the bounce trajectory method, accounting for the action of the tunneling orbit in imaginary time and quadratic fluctuations around it, the latter described by the Gelfand-Yaglom differential equation. Additionally, the tunneling formalism is used for describing the condensate wave function by a trial function of a superposition of several Gaussians. Using this ansatz a Hamiltonian form of the mean-field energy does not exist and the formalism of describing the tunneling process has to be extended. The bounce trajectory is described in the parameter space of the Gaussian width parameters and the equations of motion for the imaginary time evolution are obtained by applying a time-dependent variational principle. The action of the bounce trajectory is investigated as a function of the number of Gaussians taken into account and the contribution of the fluctuations is evaluated using the monodromy matrix.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 Thermodynamic functionality of autonomous quantum networks(2010) Schröder, Heiko Christian; Mahler, Günter (Prof. Dr.)Thermodynamics is a theory of impressive success and a wide range of applicability. Nevertheless, it took about two hundred years after the basic formulation of phenomenological thermodynamics until Boltzmann and Maxwell gave a foundation in terms statistical mechanics based on classical mechanics. The invention of quantum mechanics has triggered various attempts to establish a theory of quantum thermodynamics, i.e., to explain and derive thermodynamics by quantum mechanics only. Recently, a new approach to this question has been developed by Gemmer et al. focusing on the role of the partitioning of the universe into "system" and "environment" and on how the entanglement between those parts and the properties of typical environments lead to a thermal state in the system for almost any instant in time. Within this approach, the emergence of thermodynamic behavior in subsystems of a wide class of autonomous quantum networks could be established although the state of the total system is a pure. This turns our understanding of the emergence of thermodynamics upside down: No longer the presence of ideal (infinitely large and always in equilibrium) makes the system thermodynamic, but thermodynamic behavior of the system itself induced by an appropriate embedding - which by itself does not need to be thermodynamic in any way - becomes the crucial ingredient. Moreover, it was found that not only macroscopic embeddings but also quantum networks as small as 10 spins may serve already as excellent thermal embeddings. In this context, this thesis approaches a number of questions: First, complementary to the emergence of relaxation (heat), how does mechanical control over a system (work) emerge in autonomous quantum systems? What types of embeddings allow for this control, and is there a lower limit of their size? The answer is discussed by making the connection between work, parametric control of a Hamiltonian, and classical driving with the help of the factorization approximation. Using this link, we propose the local effective measurement basis method to determine heat and work currents in arbitrary bipartite quantum systems, and discuss measures of how to assess the thermodynamic functionality of an arbitrary embedding. We then apply these concepts to a minimal model consisting of only a spin and a quantum harmonic oscillator (spin-oscillator model) to demonstrate that even a single oscillator may act as an ideal work reservoir. A slight variation of the model then illustrates the pros and cons of the proposed measures of thermodynamic functionality. Second, since thermodynamics is first and foremost a theory of processes, which need both, thermal and mechanical control, we ask if autonomous quantum networks can implement thermodynamic cycles. We do so by first reviewing some specialties of quantum thermodynamic processes in general and then presenting the autonomous dynamic three spin machine, an autonomous quantum network implementing a thermodynamic cycle, which is driven by a emergent quantum work reservoir as discussed in the first part. Finally, we discuss quantum thermodynamic pseudomachines, a class of models that exhibit machine-like functionality without use of a thermodynamic cycle. This gives an answer to the question how new forms of control that are only found in quantum systems lead to new thermodynamic functionalities. The presented models can all be understood as thermodynamic laser models. In particular, we discuss the extended dissipative Jaynes-Cummings model and its thermodynamic properties. We resolve a conflict between different interpretations of the model by a careful analysis of the model itself and the thermodynamic concepts used by different authors. It is found that the model is an intricate heat transport model and no machine and that its thermodynamic functionality relies on the transition-selective coupling of heat baths to a few-level quantum system.Item Open Access Measurements of effective quasiparticle recombination times and of densities of electronic states at the Fermi level in superconducting Al- and Pb-films(1979) Epperlein, Peter W.; Eisenmenger, WolfgangTemperature-dependent quasiparticle recombination lifetimes tau exp (T) and densities N 0 of electronic states at the Fermi level have been measured from time decay experiments of excess quasiparticle concentrations in evaporated, superconducting Al- and Pb-tunnel junctions. Current pulses were used to inject excess, nonthermal quasiparticles in a single junction acting simultaneously as generator and detector. The experimental lifetimes in "unperturbed" Al show satisfactory agreement with calculations based on the 2Delta-phonon trapping lifetime model. Tau exp decreases with increasing perturbations of the Al film structure by oxygen background evaporation. In Pb the measured times indicate 2Delta-phonon volume losses. The densities N 0 in Pb-films and "unperturbed" as well as oxygen-perturbed Al-films differ by less than 5% from the corresponding bulk material data. Therefore, in trying to explain the enhancement of the transition temperature from 1.23 K to 1.85 K in perturbed, granular Al-films a change of N 0 can be ruled out.Item Open Access Classical and semiclassical approaches to excitons in cuprous oxide(2024) Ertl, Jan; Main, Jörg (Prof. Dr.)When an electron is excited from the valence into the conduction band it leaves behind a positively charged hole in the valence band to which it can couple through the Coulomb interaction. Bound states of electrons and holes, the excitons, are the solid state analogue of the hydrogen atom. As such they follow a Rydberg series. T. Kazimierczuk et al. [Nature 514, 343 (2014)] were able to show the existence of Rydberg excitons in cuprous oxide up to principle quantum number n=25. These states then have extensions in the µm range and thus lie in a region where the correspondence principle is applicable and quantum mechanics turns into classical mechanics. A more precise study of experimental spectra reveals significant deviations from a purely hydrogen-like behavior. These deviations can be traced to the complex valence band structure of cuprous oxide which inherits the cubic symmetry of the system. A theoretical description of the band structure introduces new degrees of freedom, i.e., a quasispin I=1 describing the three-fold degenerate valence band. Due to the coupling of quasispin and hole spin the valence band splits resulting in a yellow exciton series and two green exciton series with light and heavy holes. In this thesis we provide a semiclassical interpretation for excitons in cuprous oxide beyond the hydrogen-like model. To this end we introduce an adiabatic approach diagonalizing the band structure part of the Hamiltonian in a basis for quasi- and hole spin. This leads to a description via energy surfaces in momentum space, which correspond to the different exciton series. Classical dynamics can be calculated by choosing the energy surface of the series under interest and integrating Hamilton's equations of motion. Due to the energy surfaces the symmetry is drastically reduced compared to the hydrogen-like problem now allowing for the existence of fully three-dimensional orbits as well as the possibility of chaotic dynamics. For the yellow exciton series we find mostly regular phase space regions with quasi-periodic motion on near-integrable tori and small chaotic phase space regions. To demonstrate the existence of classical exciton orbits in the quantum spectra we show that the quantum mechanical recurrence spectra exhibit peaks, which, by application of semiclassical theories and a scaling transformation, can be directly related to classical periodic exciton orbits. An analysis of the energy dependence reveals that the dynamics deviations' from a purely hydrogen-like behavior increase with decreasing energy. Starting from the full Hamiltonian we develop a spherical model from which we are able to derive the quantum defects of the yellow exciton series using a semiclassical torus quantization. A comparison with quantum mechanical calculations show good agreement with our semiclassical results, thus allowing to identify individual quantum states by a corresponding classical exciton orbit in analogy to Bohr's atomic model. Finally, we provide a comparison of yellow exciton series with the two distinct green exciton series. The phase space is analyzed by application of Poincaré surfaces of section and Lagrangian descriptors. In addition, we investigate the Lyapunov stability of individual orbits. The analysis reveals the existence of a classically chaotic exciton dynamics for both yellow and green excitons, however, the chaotic regions are more pronounced for the green than for the yellow excitons. Excitons in cuprous oxide thus provide an example of a two-particle system with chaos even without the application of external fields.Item Open Access Werner Eissner (1930-2022) : a pioneer in computational atomic physics(2023) Bhatia, Anand K.; Lynas-Gray, Anthony E.; Mendoza, Claudio; Nahar, Sultana; Nussbaumer, Harry; Pradhan, Anil K.; Seaton, Anthony M.; Wunner, Günter; Zeippen, Claude J.Item Open Access On the microscopic limit for the existence of local temperature(2005) Hartmann, Michael; Mahler, Günter (Prof. Dr.)Recent progress in the synthesis and processing of nano-structured materials and systems calls for an improved understanding of thermal properties on small length scales. In this context, the question whether thermodynamics and, in particular, the concept of temperature can apply on the nanoscale is of central interest. Here we consider a quantum system consisting of a regular chain of elementary subsystems with nearest neighbour interactions and assume that the total system is in a canonical state with temperature T. We analyse, under what condition the state factors into a product of canonical density matrices with respect to groups of n subsystems each, and when these groups have the same temperature T. In quantum systems the minimal group size depends on the temperature, contrary to the classical case. As examples, we apply our analysis to a harmonic chain and different types of Ising spin chains. For the harmonic chain, which successfully describes thermal properties of insulating solids, our approach gives a first quantitative estimate of the minimal length scale on which temperature can exist: This length scale is found to be constant for temperatures above the Debye temperature and proportional to 1/T^3 below. We finally apply the harmonic chain model to various materials of relevance for technical applications and discuss the results. These show that, indeed, high temperatures can exist quite locally, while low temperatures exist on larger scales only. The technique of the approach is based on a quantum central limit theorem, which should prove usefull in different settings, too.Item Open Access Predictions of a galactic outflow model for spectral mapping observations(2021) Schaible, Anna LenaGalactically scaled outfows are regarded as extremely important for many aspects and processes of galaxy evolution. This thesis focuses on galactic winds and enables the analysis of spatial resolved spherical galactic outflows. For the frst time, a method to calculate 3D datacubes for galactic outflows is presented. Spatially resolved spectra of outflows are predicted.