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This thesis investigates the Casimir effect between plates made of normal and superconducting metals over a broad range of temperatures, as well as the Casimir-Polder interaction of an atom to such a surface. Numerical and asymptotical calculations have been the main tools in order to do so. The optical properties of the surfaces are described by dielectric functions or optical conductivities, which are reviewed for common models and have been analyzed with special weight on distributional properties and causality. The calculation of the Casimir energy between two normally conducting plates (cavity) is reviewed and previous work on the contribution to the Casimir energy due to the surface plasmons, present in all metallic cavities, has been generalized to finite temperatures for the first time. In the field of superconductivity, a new analytical continuation of the BCS conductivity to to purely imaginary frequencies has been obtained both inside and outside the extremely dirty limit of vanishing mean free path. The Casimir free energy calculated from this description was shown to coincide well with the values obtained from the two fluid model of superconductivity in certain regimes of the material parameters. The Casimir entropy in a superconducting cavity fulfills the third law of thermodynamics and features a characteristic discontinuity at the phase transition temperature. These effects were equally encountered in the Casimir-Polder interaction of an atom with a superconducting wall. The magnetic dipole coupling of an atom to a metal was shown to be highly sensible to dissipation and especially to the surface currents. This leads to a strong quenching of the magnetic Casimir-Polder energy at finite temperature. Violations of the third law of thermodynamics are encountered in special models, similar to phenomena in the Casimir-effect between two plates, that are debated controversely. None of these effects occurs in the analog electric dipole interaction. The results of this work suggest to reestablish the well-known plasma model as the low temperature limit of a superconductor as in London theory rather than use it for the description of normal metals. Superconductors offer the opportunity to control the dissipation of surface currents to a great extent. This could be used to access experimentally the low frequency optical response of metals, which is strongly connected to the thermal Casimir-effect. Here, differently from corresponding microwave experiments, energy and momentum are independent quantities. A measurement of the total Casimir-Polder interaction of atoms with superconductors seems to be in reach in today’s microchip-based atom-traps and the contribution due to magnetic coupling might be accessed by spectroscopic techniques
In this thesis, the properties of nonlinear disordered one dimensional lattices is investigated. Part I gives an introduction to the phenomenon of Anderson Localization, the Discrete Nonlinear Schroedinger Equation and its properties as well as the generalization of this model by introducing the nonlinear index α. In Part II, the spreading behavior of initially localized states in large, disordered chains due to nonlinearity is studied. Therefore, different methods to measure localization are discussed and the structural entropy as a measure for the peak structure of probability distributions is introduced. Finally, the spreading exponent for several nonlinear indices is determined numerically and compared with analytical approximations. Part III deals with the thermalization in short disordered chains. First, the term thermalization and its application to the system in use is explained. Then, results of numerical simulations on this topic are presented where the focus lies especially on the energy dependence of the thermalization properties. A connection with so-called breathers is drawn.
The acquisition of phonological alternations consists of many aspects as discussions in the relevant literature show. There are contrary findings about the role of naturalness. A natural process is grounded in phonetics; they are easy to learn, even in second language acquisition when adults have to learn certain processes that do not occur in their native language. There is also evidence that unnatural – arbitrary – rules can be learned. Current work on the acquisition of morphophonemic alternations suggests that their probability of occurrence is a crucial factor in acquisition. I have conducted an experiment to investigate the effects of naturalness as well as of probability of occurrence with 80 adult native speakers of German. It uses the Artificial Grammar paradigm: Two artificial languages were constructed, each with a particular alternation. In one language the alternation is natural (vowel harmony); in the other language the alternation is arbitrary (a vowel alternation depends on the sonorancy of the first consonant of the stem). The participants were divided in two groups, one group listened to the natural alternation and the other group listened to the unnatural alternation. Each group was divided into two subgroups. One subgroup then was presented with material in which the alternation occurred frequently and the other subgroup was presented with material in which the alternation occurred infrequently. After this exposure phase every participant was asked to produce new words during the test phase. Knowledge about the language-specific alternation pattern was needed to produce the forms correctly as the phonological contexts demanded certain alternants. The group performances have been compared with respect to the effects of naturalness and probability of occurrence. The natural rule was learned more easily than the unnatural one. Frequently presented rules were not learned more easily than the ones that were presented less frequently. Moreover, participants did not learn the unnatural rule at all, whether this rule was presented frequently or infrequently did not matter. There was a tendency that the natural rule was learned more easily if presented frequently than if presented infrequently, but it was not significant due to variability across participants.
Complex network theory provides an elegant and powerful framework to statistically investigate the topology of local and long range dynamical interrelationships, i.e., teleconnections, in the climate system. Employing a refined methodology relying on linear and nonlinear measures of time series analysis, the intricate correlation structure within a multivariate climatological data set is cast into network form. Within this graph theoretical framework, vertices are identified with grid points taken from the data set representing a region on the the Earth's surface, and edges correspond to strong statistical interrelationships between the dynamics on pairs of grid points. The resulting climate networks are neither perfectly regular nor completely random, but display the intriguing and nontrivial characteristics of complexity commonly found in real world networks such as the internet, citation and acquaintance networks, food webs and cortical networks in the mammalian brain. Among other interesting properties, climate networks exhibit the "small-world" effect and possess a broad degree distribution with dominating super-nodes as well as a pronounced community structure. We have performed an extensive and detailed graph theoretical analysis of climate networks on the global topological scale focussing on the flow and centrality measure betweenness which is locally defined at each vertex, but includes global topological information by relying on the distribution of shortest paths between all pairs of vertices in the network. The betweenness centrality field reveals a rich internal structure in complex climate networks constructed from reanalysis and atmosphere-ocean coupled general circulation model (AOGCM) surface air temperature data. Our novel approach uncovers an elaborately woven meta-network of highly localized channels of strong dynamical information flow, that we relate to global surface ocean currents and dub the backbone of the climate network in analogy to the homonymous data highways of the internet. This finding points to a major role of the oceanic surface circulation in coupling and stabilizing the global temperature field in the long term mean (140 years for the model run and 60 years for reanalysis data). Carefully comparing the backbone structures detected in climate networks constructed using linear Pearson correlation and nonlinear mutual information, we argue that the high sensitivity of betweenness with respect to small changes in network structure may allow to detect the footprints of strongly nonlinear physical interactions in the climate system. The results presented in this thesis are thoroughly founded and substantiated using a hierarchy of statistical significance tests on the level of time series and networks, i.e., by tests based on time series surrogates as well as network surrogates. This is particularly relevant when working with real world data. Specifically, we developed new types of network surrogates to include the additional constraints imposed by the spatial embedding of vertices in a climate network. Our methodology is of potential interest for a broad audience within the physics community and various applied fields, because it is universal in the sense of being valid for any spatially extended dynamical system. It can help to understand the localized flow of dynamical information in any such system by combining multivariate time series analysis, a complex network approach and the information flow measure betweenness centrality. Possible fields of application include fluid dynamics (turbulence), plasma physics and biological physics (population models, neural networks, cell models). Furthermore, the climate network approach is equally relevant for experimental data as well as model simulations and hence introduces a novel perspective on model evaluation and data driven model building. Our work is timely in the context of the current debate on climate change within the scientific community, since it allows to assess from a new perspective the regional vulnerability and stability of the climate system while relying on global and not only on regional knowledge. The methodology developed in this thesis hence has the potential to substantially contribute to the understanding of the local effect of extreme events and tipping points in the earth system within a holistic global framework.