## Institut für Physik und Astronomie

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Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter systems. We here formulate a stochastic model based on a generalised Langevin equation in which non-Gaussian shapes of the probability density function and normal or anomalous diffusion have a common origin, namely a random parametrisation of the stochastic force. We perform a detailed analysis demonstrating how various types of parameter distributions for the memory kernel result in exponential, power law, or power-log law tails of the memory functions. The studied system is also shown to exhibit a further unusual property: the velocity has a Gaussian one point probability density but non-Gaussian joint distributions. This behaviour is reflected in the relaxation from a Gaussian to a non-Gaussian distribution observed for the position variable. We show that our theoretical results are in excellent agreement with stochastic simulations.

The Sun is a star, which due to its proximity has a tremendous influence on Earth. Since its very first days mankind tried to "understand the Sun", and especially in the 20th century science has uncovered many of the Sun's secrets by using high resolution observations and describing the Sun by means of models. As an active star the Sun's activity, as expressed in its magnetic cycle, is closely related to the sunspot numbers. Flares play a special role, because they release large energies on very short time scales. They are correlated with enhanced electromagnetic emissions all over the spectrum. Furthermore, flares are sources of energetic particles. Hard X-ray observations (e.g., by NASA's RHESSI spacecraft) reveal that a large fraction of the energy released during a flare is transferred into the kinetic energy of electrons. However the mechanism that accelerates a large number of electrons to high energies (beyond 20 keV) within fractions of a second is not understood yet. The thesis at hand presents a model for the generation of energetic electrons during flares that explains the electron acceleration based on real parameters obtained by real ground and space based observations. According to this model photospheric plasma flows build up electric potentials in the active regions in the photosphere. Usually these electric potentials are associated with electric currents closed within the photosphere. However as a result of magnetic reconnection, a magnetic connection between the regions of different magnetic polarity on the photosphere can establish through the corona. Due to the significantly higher electric conductivity in the corona, the photospheric electric power supply can be closed via the corona. Subsequently a high electric current is formed, which leads to the generation of hard X-ray radiation in the dense chromosphere. The previously described idea is modelled and investigated by means of electric circuits. For this the microscopic plasma parameters, the magnetic field geometry and hard X-ray observations are used to obtain parameters for modelling macroscopic electric components, such as electric resistors, which are connected with each other. This model demonstrates that such a coronal electric current is correlated with large scale electric fields, which can accelerate the electrons quickly up to relativistic energies. The results of these calculations are encouraging. The electron fluxes predicted by the model are in agreement with the electron fluxes deduced from the measured photon fluxes. Additionally the model developed in this thesis proposes a new way to understand the observed double footpoint hard X-ray sources.

We develop a method of finding analytical sotutions of the Bogolyubov-de Gennes equations for the excitations of a Bose condensate in the Thomas-Fermi regime in harmonic traps of any asymmetry and introduce a classification of eigenstates. In the case of cylindrical symmetry we emphasize the presence of an accidental degeneracy in the excitation spectrum at certain values of the projection of orbital angular momentum on the symmetry axis and discuss possible consequences of the degeneracy in the context of new signatures of Bose- Einstein condensation

Die vorliegende Arbeit beschäftigt sich mit der Charakterisierung von Seismizität anhand von Erdbebenkatalogen. Es werden neue Verfahren der Datenanalyse entwickelt, die Aufschluss darüber geben sollen, ob der seismischen Dynamik ein stochastischer oder ein deterministischer Prozess zugrunde liegt und was daraus für die Vorhersagbarkeit starker Erdbeben folgt. Es wird gezeigt, dass seismisch aktive Regionen häufig durch nichtlinearen Determinismus gekennzeichent sind. Dies schließt zumindest die Möglichkeit einer Kurzzeitvorhersage ein. Das Auftreten seismischer Ruhe wird häufig als Vorläuferphaenomen für starke Erdbeben gedeutet. Es wird eine neue Methode präsentiert, die eine systematische raumzeitliche Kartierung seismischer Ruhephasen ermöglicht. Die statistische Signifikanz wird mit Hilfe des Konzeptes der Ersatzdaten bestimmt. Als Resultat erhält man deutliche Korrelationen zwischen seismischen Ruheperioden und starken Erdbeben. Gleichwohl ist die Signifikanz dafür nicht hoch genug, um eine Vorhersage im Sinne einer Aussage über den Ort, die Zeit und die Stärke eines zu erwartenden Hauptbebens zu ermöglichen.

The occurrence of earthquakes is characterized by a high degree of spatiotemporal complexity. Although numerous patterns, e.g. fore- and aftershock sequences, are well-known, the underlying mechanisms are not observable and thus not understood. Because the recurrence times of large earthquakes are usually decades or centuries, the number of such events in corresponding data sets is too small to draw conclusions with reasonable statistical significance. Therefore, the present study combines both, numerical modeling and analysis of real data in order to unveil the relationships between physical mechanisms and observational quantities. The key hypothesis is the validity of the so-called "critical point concept" for earthquakes, which assumes large earthquakes to occur as phase transitions in a spatially extended many-particle system, similar to percolation models. New concepts are developed to detect critical states in simulated and in natural data sets. The results indicate that important features of seismicity like the frequency-size distribution and the temporal clustering of earthquakes depend on frictional and structural fault parameters. In particular, the degree of quenched spatial disorder (the "roughness") of a fault zone determines whether large earthquakes occur quasiperiodically or more clustered. This illustrates the power of numerical models in order to identify regions in parameter space, which are relevant for natural seismicity. The critical point concept is verified for both, synthetic and natural seismicity, in terms of a critical state which precedes a large earthquake: a gradual roughening of the (unobservable) stress field leads to a scale-free (observable) frequency-size distribution. Furthermore, the growth of the spatial correlation length and the acceleration of the seismic energy release prior to large events is found. The predictive power of these precursors is, however, limited. Instead of forecasting time, location, and magnitude of individual events, a contribution to a broad multiparameter approach is encouraging.

Hysteresis in the pinning-depinning transitions of spiral waves rotating around a hole in a circular shaped two- dimensional excitable medium is studied both by use of the continuation software AUTO and by direct numerical integration of the reaction-diffusion equations for the FitzHugh-Nagumo model. In order to clarify the role of different factors in this phenomenon, a kinematical description is applied. It is found that the hysteresis phenomenon computed for the reaction-diffusion model can be reproduced qualitatively only when a nonlinear eikonal equation (i.e. velocity- curvature relationship) is assumed. However, to obtain quantitative agreement, the dispersion relation has to be taken into account.

We present a theoretical framework for the analysis of the statistical properties of thermal fluctuations on a lossy transmission line. A quantization scheme of the electrical signals in the transmission line is formulated. We discuss two applications in detail. Noise spectra at finite temperature for voltage and current are shown to deviate significantly from the Johnson-Nyquist limit, and they depend on the position on the transmission line. We analyze the spontaneous emission, at low temperature, of a Rydberg atom and its resonant enhancement due to vacuum fluctuations in a capacitively coupled transmission line. The theory can also be applied to study the performance of microscale and nanoscale devices, including high-resolution sensors and quantum information processors

We present a momentum transfer mechanism mediated by electromagnetic fields that originates in a system of two nearby molecules: one excited (donor D*) and the other in ground state (acceptor A). An intermolecular force related to fluorescence resonant energy or Forster transfer (FRET) arises in the unstable D* A molecular system, which differs from the equilibrium van der Waals interaction. Due to the its finite lifetime, a mechanical impulse is imparted to the relative motion in the system. We analyze the FRET impulse when the molecules are embedded in free space and find that its magnitude can be much greater than the single recoil photon momentum, getting comparable with the thermal momentum (Maxwell-Boltzmann distribution) at room temperature. In addition, we propose that this FRET impulse can be exploited in the generation of acoustic waves inside a film containing layers of donor and acceptor molecules, when a picosecond laser pulse excites the donors. This acoustic transient is distinguishable from that produced by thermal stress due to laser absorption, and may therefore play a role in photoacoustic spectroscopy. The effect can be seen as exciting a vibrating system like a string or organ pipe with light; it may be used as an opto-mechanical transducer.