Classical limit of the Nelson model

Since the development of quantum mechanics it has been natural to analyze the connection between classical and quantum mechanical descriptions of physical systems. In particular one should expect that in some sense when quantum mechanical effects becomes negligible the system will behave like it is dictated by classical mechanics. One famous relation between classical and quantum theory is due to Ehrenfest. This result was later developed and put on firm mathematical foundations by Hepp. He proved that matrix elements of bounded functions of quantum observables between suitable coherents states (that depend on Planck's constant h) converge to classical values evolving according to the expected classical equations when h goes to zero. His results were later generalized by Ginibre and Velo to bosonic systems with infinite degrees of freedom and scattering theory. In this thesis we study the classical limit of Nelson model, that describes non relativistic particles, whose evolution is dictated by Schrödinger equation, interacting with a scalar relativistic field, whose evolution is dictated by Klein-Gordon equation, by means of a Yukawa-type potential. The classical limit is a mean field and weak coupling limit. We proved that the transition amplitude of a creation or annihilation operator, between suitable coherent states, converges in the classical limit to the solution of the system of differential equations that describes the classical evolution of the theory. The quantum evolution operator converges to the evolution operator of fluctuations around the classical solution. Transition amplitudes of normal ordered products of creation and annihilation operators between coherent states converge to suitable products of the classical solutions. Transition amplitudes of normal ordered products of creation and annihilation operators between fixed particle states converge to an average of products of classical solutions, corresponding to different initial conditions.

Development of empirical potentials for amorphous silica

Development of empirical potentials for amorphous silica Amorphous silica (SiO2) is of great importance in geoscience and mineralogy as well as a raw material in glass industry. Its structure is characterized as a disordered continuous network of SiO4 tetrahedra. Many efforts have been undertaken to understand the microscopic properties of silica by classical molecular dynamics (MD) simulations. In this method the interatomic interactions are modeled by an effective potential that does not take explicitely into account the electronic degrees of freedom. In this work, we propose a new methodology to parameterize such a potential for silica using ab initio simulations, namely Car-Parrinello (CP) method [Phys. Rev. Lett. 55, 2471 (1985)]. The new potential proposed is compared to the BKS potential [Phys. Rev. Lett. 64, 1955 (1990)] that is considered as the benchmark potential for silica. First, CP simulations have been performed on a liquid silica sample at 3600 K. The structural features so obtained have been compared to the ones predicted by the classical BKS potential. Regarding the bond lengths the BKS tends to underestimate the Si-O bond whereas the Si-Si bond is overestimated. The inter-tetrahedral angular distribution functions are also not well described by the BKS potential. The corresponding mean value of theSiOSi angle is found to be ≃ 147◦, while the CP yields to aSiOSi angle centered around 135◦. Our aim is to fit a classical Born-Mayer/Coulomb pair potential using ab initio calculations. To this end, we use the force-matching method proposed by Ercolessi and Adams [Europhys. Lett. 26, 583 (1994)]. The CP configurations and their corresponding interatomic forces have been considered for a least square fitting procedure. The classical MD simulations with the resulting potential have lead to a structure that is very different from the CP one. Therefore, a different fitting criterion based on the CP partial pair correlation functions was applied. Using this approach the resulting potential shows a better agreement with the CP data than the BKS ones: pair correlation functions, angular distribution functions, structure factors, density of states and pressure/density were improved. At low temperature, the diffusion coefficients appear to be three times higher than those predicted by the BKS model, however showing a similar temperature dependence. Calculations have also been carried out on crystalline samples in order to check the transferability of the potential. The equilibrium geometry as well as the elastic constants of α-quartz at 0 K are well described by our new potential although the crystalline phases have not been considered for the parameterization. We have developed a new potential for silica which represents an improvement over the pair potentials class proposed so far. Furthermore, the fitting methodology that has been developed in this work can be applied to other network forming systems such as germania as well as mixtures of SiO2 with other oxides (e.g. Al2O3, K2O, Na2O).

Quantum gravity effects in rotating black hole spacetimes

The aim of this work is to explore, within the framework of the presumably asymptotically safe Quantum Einstein Gravity, quantum corrections to black hole spacetimes, in particular in the case of rotating black holes. We have analysed this problem by exploiting the scale dependent Newton s constant implied by the renormalization group equation for the effective average action, and introducing an appropriate "cutoff identification" which relates the renormalization scale to the geometry of the spacetime manifold. We used these two ingredients in order to "renormalization group improve" the classical Kerr metric that describes the spacetime generated by a rotating black hole. We have focused our investigation on four basic subjects of black hole physics. The main results related to these topics can be summarized as follows. Concerning the critical surfaces, i.e. horizons and static limit surfaces, the improvement leads to a smooth deformation of the classical critical surfaces. Their number remains unchanged. In relation to the Penrose process for energy extraction from black holes, we have found that there exists a non-trivial correlation between regions of negative energy states in the phase space of rotating test particles and configurations of critical surfaces of the black hole. As for the vacuum energy-momentum tensor and the energy conditions we have shown that no model with "normal" matter, in the sense of matter fulfilling the usual energy conditions, can simulate the quantum fluctuations described by the improved Kerr spacetime that we have derived. Finally, in the context of black hole thermodynamics, we have performed calculations of the mass and angular momentum of the improved Kerr black hole, applying the standard Komar integrals. The results reflect the antiscreening character of the quantum fluctuations of the gravitational field. Furthermore we calculated approximations to the entropy and the temperature of the improved Kerr black hole to leading order in the angular momentum. More generally we have proven that the temperature can no longer be proportional to the surface gravity if an entropy-like state function is to exist.

Finite-element discretization of 3D energy-transport equations for semiconductors

In this thesis a mathematical model was derived that describes the charge and energy transport in semiconductor devices like transistors. Moreover, numerical simulations of these physical processes are performed. In order to accomplish this, methods of theoretical physics, functional analysis, numerical mathematics and computer programming are applied. After an introduction to the status quo of semiconductor device simulation methods and a brief review of historical facts up to now, the attention is shifted to the construction of a model, which serves as the basis of the subsequent derivations in the thesis. Thereby the starting point is an important equation of the theory of dilute gases. From this equation the model equations are derived and specified by means of a series expansion method. This is done in a multi-stage derivation process, which is mainly taken from a scientific paper and which does not constitute the focus of this thesis. In the following phase we specify the mathematical setting and make precise the model assumptions. Thereby we make use of methods of functional analysis. Since the equations we deal with are coupled, we are concerned with a nonstandard problem. In contrary, the theory of scalar elliptic equations is established meanwhile. Subsequently, we are preoccupied with the numerical discretization of the equations. A special finite-element method is used for the discretization. This special approach has to be done in order to make the numerical results appropriate for practical application. By a series of transformations from the discrete model we derive a system of algebraic equations that are eligible for numerical evaluation. Using self-made computer programs we solve the equations to get approximate solutions. These programs are based on new and specialized iteration procedures that are developed and thoroughly tested within the frame of this research work. Due to their importance and their novel status, they are explained and demonstrated in detail. We compare these new iterations with a standard method that is complemented by a feature to fit in the current context. A further innovation is the computation of solutions in three-dimensional domains, which are still rare. Special attention is paid to applicability of the 3D simulation tools. The programs are designed to have justifiable working complexity. The simulation results of some models of contemporary semiconductor devices are shown and detailed comments on the results are given. Eventually, we make a prospect on future development and enhancements of the models and of the algorithms that we used.

Virtual Compton scattering in baryon chiral perturbation theory

This thesis is concerned with the calculation of virtual Compton scattering (VCS) in manifestly Lorentz-invariant baryon chiral perturbation theory to fourth order in the momentum and quark-mass expansion. In the one-photon-exchange approximation, the VCS process is experimentally accessible in photon electro-production and has been measured at the MAMI facility in Mainz, at MIT-Bates, and at Jefferson Lab. Through VCS one gains new information on the nucleon structure beyond its static properties, such as charge, magnetic moments, or form factors. The nucleon response to an incident electromagnetic field is parameterized in terms of 2 spin-independent (scalar) and 4 spin-dependent (vector) generalized polarizabilities (GP). In analogy to classical electrodynamics the two scalar GPs represent the induced electric and magnetic dipole polarizability of a medium. For the vector GPs, a classical interpretation is less straightforward. They are derived from a multipole expansion of the VCS amplitude. This thesis describes the first calculation of all GPs within the framework of manifestly Lorentz-invariant baryon chiral perturbation theory. Because of the comparatively large number of diagrams - 100 one-loop diagrams need to be calculated - several computer programs were developed dealing with different aspects of Feynman diagram calculations. One can distinguish between two areas of development, the first concerning the algebraic manipulations of large expressions, and the second dealing with numerical instabilities in the calculation of one-loop integrals. In this thesis we describe our approach using Mathematica and FORM for algebraic tasks, and C for the numerical evaluations. We use our results for real Compton scattering to fix the two unknown low-energy constants emerging at fourth order. Furthermore, we present the results for the differential cross sections and the generalized polarizabilities of VCS off the proton.

Statistical Physics and Modeling of Human Mobility

In this thesis, we extend some ideas of statistical physics to describe the properties of human mobility. By using a database containing GPS measures of individual paths (position, velocity and covered space at a spatial scale of 2 Km or a time scale of 30 sec), which includes the 2% of the private vehicles in Italy, we succeed in determining some statistical empirical laws pointing out "universal" characteristics of human mobility. Developing simple stochastic models suggesting possible explanations of the empirical observations, we are able to indicate what are the key quantities and cognitive features that are ruling individuals' mobility. To understand the features of individual dynamics, we have studied different aspects of urban mobility from a physical point of view. We discuss the implications of the Benford's law emerging from the distribution of times elapsed between successive trips. We observe how the daily travel-time budget is related with many aspects of the urban environment, and describe how the daily mobility budget is then spent. We link the scaling properties of individual mobility networks to the inhomogeneous average durations of the activities that are performed, and those of the networks describing people's common use of space with the fractional dimension of the urban territory. We study entropy measures of individual mobility patterns, showing that they carry almost the same information of the related mobility networks, but are also influenced by a hierarchy among the activities performed. We discover that Wardrop's principles are violated as drivers have only incomplete information on traffic state and therefore rely on knowledge on the average travel-times. We propose an assimilation model to solve the intrinsic scattering of GPS data on the street network, permitting the real-time reconstruction of traffic state at a urban scale.

Fluorescence close to dielectric interfaces

The aim of the work was to study the correlation between the orientation and excited-state lifetimes of organic dyes close to dielectric interfaces. For this purpose, an experimental setup was designed and built, guiding the light through a prism in total internal reflection geometry. Fluorescence intensities and lifetimes for an ensemble of dye molecules were analyzed as a function of the excitation and detection polarizations. Working close to the total internal reflection angle, the differences between polarization combinations were enhanced. A classical electromagnetic model that assumes a chromophore as a couple of point-like electrical dipoles was developed. A numerical method to calculate the excitation and emission of dye molecules embedded in a multilayer system was implemented, by which full simulation of the time resolved fluorescence experiments was achieved. Free organic dyes and organic dyes covalently bound to polyelectrolyte chains were used. The polymer functionalization process avoided aggregation and provided control over the dyes position, within a few nanometers to the interface. Moreover, by varying the pH, the polymer chains could be deposited on different substrates with different conformations and the resulting fluorescence characteristics analyzed. Initially the fluorescence of organic dyes embedded in a polymer matrix was studied as a function of the distance between the fluorophores and the polymer-air interface. The non-radiative decay rate, vacuum decay rate and the relative angle between the excitation and emission dipoles of the chromophores could be determined. Different free organic dyes were deposited onto different dielectric spacers, as close as possible to the air-dielectric interface. Surprisingly, the fluorescence characteristics of dyes deposited onto polyelectrolyte layer were in good agreement with theoretical predictions of dyes in a polymer matrix, even when the layer was only 2 nm thick. When functionalized chains were deposited at low pH, on top of a polyelectrolyte spacer, the fluorescence had the characteristics of emitters embedded in a polymer matrix as well. Surface deposition at high pH showed an intermediate behaviour between emitters embedded in polymer and on top of the surface, in air. In general, for low pH values, the chains are deposited on a substrate in a train-like conformation. For high pH values, the chains are deposited in a loop-like conformation. As a consequence at low pH the functionalized polymer strongly interdigitates with the polyelectrolyte chains of the spacer, bringing most of the dyes inside the polymer. Thus, the fluorophores may experience the polymer as surrounding environment. On the other hand, for high pH values the dye-loaded chains adsorbed have a conformational arrangement of dense loops that extend away from the surface. Therefore many fluorophores experience the air as surrounding environment. Changing the spacer from polyelectrolyte to negatively charged silane produced contradictory results for lifetimes and intensities. The fluorescence intensities indicated the behaviour of emitters embedded in a polymer matrix, regardless of the pH value. On the other hand, for low pH values, the excited-state lifetimes showed that the emitters behaved as in air. For higher pH values, an intermediate behaviour between fluorophores located within and above of a dielectric film was observed. The poor agreement between theoretical and experimental data may be due to the simplified model utilized, by which the dipoles are assumed either in one side or in the other with respect to a geometrical air-dielectric interface. In the case when the dielectric film is constituted by the functionalized polymer chains themselves, reality is more complex and a different model may apply. Nevertheless, possible applications of the technique arise from a qualitative analysis.

Exploring physical processes related to past climate proxies: lake sediments and stable water isotopes

Proxy data are essential for the investigation of climate variability on time scales larger than the historical meteorological observation period. The potential value of a proxy depends on our ability to understand and quantify the physical processes that relate the corresponding climate parameter and the signal in the proxy archive. These processes can be explored under present-day conditions. In this thesis, both statistical and physical models are applied for their analysis, focusing on two specific types of proxies, lake sediment data and stable water isotopes.rnIn the first part of this work, the basis is established for statistically calibrating new proxies from lake sediments in western Germany. A comprehensive meteorological and hydrological data set is compiled and statistically analyzed. In this way, meteorological times series are identified that can be applied for the calibration of various climate proxies. A particular focus is laid on the investigation of extreme weather events, which have rarely been the objective of paleoclimate reconstructions so far. Subsequently, a concrete example of a proxy calibration is presented. Maxima in the quartz grain concentration from a lake sediment core are compared to recent windstorms. The latter are identified from the meteorological data with the help of a newly developed windstorm index, combining local measurements and reanalysis data. The statistical significance of the correlation between extreme windstorms and signals in the sediment is verified with the help of a Monte Carlo method. This correlation is fundamental for employing lake sediment data as a new proxy to reconstruct windstorm records of the geological past.rnThe second part of this thesis deals with the analysis and simulation of stable water isotopes in atmospheric vapor on daily time scales. In this way, a better understanding of the physical processes determining these isotope ratios can be obtained, which is an important prerequisite for the interpretation of isotope data from ice cores and the reconstruction of past temperature. In particular, the focus here is on the deuterium excess and its relation to the environmental conditions during evaporation of water from the ocean. As a basis for the diagnostic analysis and for evaluating the simulations, isotope measurements from Rehovot (Israel) are used, provided by the Weizmann Institute of Science. First, a Lagrangian moisture source diagnostic is employed in order to establish quantitative linkages between the measurements and the evaporation conditions of the vapor (and thus to calibrate the isotope signal). A strong negative correlation between relative humidity in the source regions and measured deuterium excess is found. On the contrary, sea surface temperature in the evaporation regions does not correlate well with deuterium excess. Although requiring confirmation by isotope data from different regions and longer time scales, this weak correlation might be of major importance for the reconstruction of moisture source temperatures from ice core data. Second, the Lagrangian source diagnostic is combined with a Craig-Gordon fractionation parameterization for the identified evaporation events in order to simulate the isotope ratios at Rehovot. In this way, the Craig-Gordon model can be directly evaluated with atmospheric isotope data, and better constraints for uncertain model parameters can be obtained. A comparison of the simulated deuterium excess with the measurements reveals that a much better agreement can be achieved using a wind speed independent formulation of the non-equilibrium fractionation factor instead of the classical parameterization introduced by Merlivat and Jouzel, which is widely applied in isotope GCMs. Finally, the first steps of the implementation of water isotope physics in the limited-area COSMO model are described, and an approach is outlined that allows to compare simulated isotope ratios to measurements in an event-based manner by using a water tagging technique. The good agreement between model results from several case studies and measurements at Rehovot demonstrates the applicability of the approach. Because the model can be run with high, potentially cloud-resolving spatial resolution, and because it contains sophisticated parameterizations of many atmospheric processes, a complete implementation of isotope physics will allow detailed, process-oriented studies of the complex variability of stable isotopes in atmospheric waters in future research.rn

Simulations of charge transport in organic compounds

To aid the design of organic semiconductors, we study the charge transport properties of organic liquid crystals, i.e. hexabenzocoronene and carbazole macrocycle, and single crystals, i.e. rubrene, indolocarbazole and benzothiophene derivatives (BTBT, BBBT). The aim is to find structure-property relationships linking the chemical structure as well as the morphology with the bulk charge carrier mobility of the compounds. To this end, molecular dynamics (MD) simulations are performed yielding realistic equilibrated morphologies. Partial charges and molecular orbitals are calculated based on single molecules in vacuum using quantum chemical methods. The molecular orbitals are then mapped onto the molecular positions and orientations, which allows calculation of the transfer integrals between nearest neighbors using the molecular orbital overlap method. Thus we obtain realistic transfer integral distributions and their autocorrelations. In case of organic crystals the differences between two descriptions of charge transport, namely semi-classical dynamics (SCD) in the small polaron limit and kinetic Monte Carlo (KMC) based on Marcus rates, are studied. The liquid crystals are investigated solely in the hopping limit. To simulate the charge dynamics using KMC, the centers of mass of the molecules are mapped onto lattice sites and the transfer integrals are used to compute the hopping rates. In the small polaron limit, where the electronic wave function is spread over a limited number of neighboring molecules, the Schroedinger equation is solved numerically using a semi-classical approach. The results are compared for the different compounds and methods and, where available, with experimental data. The carbazole macrocycles form columnar structures arranged on a hexagonal lattice with side chains facing inwards, so columns can closely approach each other allowing inter-columnar and thus three-dimensional transport. When taking only intra-columnar transport into account, the mobility is orders of magnitude lower than in the three-dimensional case. BTBT is a promising material for solution-processed organic field-effect transistors. We are able to show that, on the time-scales of charge transport, static disorder due to slow side chain motions is the main factor determining the mobility. The resulting broad transfer integral distributions modify the connectivity of the system but sufficiently many fast percolation paths remain for the charges. Rubrene, indolocarbazole and BBBT are examples of crystals without significant static disorder. The high mobility of rubrene is explained by two main features: first, the shifted cofacial alignment of its molecules, and second, the high center of mass vibrational frequency. In comparsion to SCD, only KMC based on Marcus rates is capable of describing neighbors with low coupling and of taking static disorder into account three-dimensionally. Thus it is the method of choice for crystalline systems dominated by static disorder. However, it is inappropriate for the case of strong coupling and underestimates the mobility of well-ordered crystals. SCD, despite its one-dimensionality, is valuable for crystals with strong coupling and little disorder. It also allows correct treatment of dynamical effects, such as intermolecular vibrations of the molecules. Rate equations are incapable of this, because simulations are performed on static snapshots. We have thus shown strengths and weaknesses of two state of the art models used to study charge transport in organic compounds, partially developed a program to compute and visualize transfer integral distributions and other charge transport properties, and found structure-mobility relations for several promising organic semiconductors.

Construction and commissioning of a collinear laser spectroscopy setup at TRIGA Mainz and laser spectroscopy of magnesium isotopes at ISOLDE (CERN)

Collinear laser spectroscopy has been used as a tool for nuclear physics for more than 30 years. The unique possibility to extract nuclear properties like spins, radii and nuclear moments in a model-independent manner leads to important physics results to test the predictive power of existing nuclear models. rnThis work presents the construction and the commissioning of a new collinear laser spectroscopy experiment TRIGA-LASER as a part of the TRIGA-SPEC facility at the TRIGA research reactor at the University of Mainz. The goal of the experiment is to study the nuclear structure of radioactive isotopes which will be produced by neutron-induced fission near the reactor core and transported to an ion source by a gas jet system. rnThe versatility of the collinear laser spectroscopy technique will be exploited in the second part of this thesis. The nuclear spin and the magnetic moment of the neutron-deficient isotope Mg-21 will be presented, which were measured by the detection of the beta-decay asymmetry induced by nuclear polarization after optical pumping. A combination of this detection method with the classical fluorescence detection is then used to determine the isotope shifts of the neutron-rich magnesium isotopes from Mg-24 through Mg-32 to study the transition to the ''island of inversion''.

Merkmalsbezogene Verifikation hochaufgelöster Niederschlagsvorhersagen für Deutschland

Die Verifikation bewertet die Güte von quantitativen Niederschlagsvorhersagen(QNV) gegenüber Beobachtungen und liefert Hinweise auf systematische Modellfehler. Mit Hilfe der merkmals-bezogenen Technik SAL werden simulierte Niederschlagsverteilungen hinsichtlich (S)truktur, (A)mplitude und (L)ocation analysiert. Seit einigen Jahren werden numerische Wettervorhersagemodelle benutzt, mit Gitterpunktabständen, die es erlauben, hochreichende Konvektion ohne Parametrisierung zu simulieren. Es stellt sich jetzt die Frage, ob diese Modelle bessere Vorhersagen liefern. Der hoch aufgelöste stündliche Beobachtungsdatensatz, der in dieser Arbeit verwendet wird, ist eine Kombination von Radar- und Stationsmessungen. Zum einem wird damit am Beispiel der deutschen COSMO-Modelle gezeigt, dass die Modelle der neuesten Generation eine bessere Simulation des mittleren Tagesgangs aufweisen, wenn auch mit zu geringen Maximum und etwas zu spätem Auftreten. Im Gegensatz dazu liefern die Modelle der alten Generation ein zu starkes Maximum, welches erheblich zu früh auftritt. Zum anderen wird mit dem neuartigen Modell eine bessere Simulation der räumlichen Verteilung des Niederschlags, durch eine deutliche Minimierung der Luv-/Lee Proble-matik, erreicht. Um diese subjektiven Bewertungen zu quantifizieren, wurden tägliche QNVs von vier Modellen für Deutschland in einem Achtjahreszeitraum durch SAL sowie klassischen Maßen untersucht. Die höher aufgelösten Modelle simulieren realistischere Niederschlagsverteilungen(besser in S), aber bei den anderen Komponenten tritt kaum ein Unterschied auf. Ein weiterer Aspekt ist, dass das Modell mit der gröbsten Auf-lösung(ECMWF) durch den RMSE deutlich am besten bewertet wird. Darin zeigt sich das Problem des ‚Double Penalty’. Die Zusammenfassung der drei Komponenten von SAL liefert das Resultat, dass vor allem im Sommer das am feinsten aufgelöste Modell (COSMO-DE) am besten abschneidet. Hauptsächlich kommt das durch eine realistischere Struktur zustande, so dass SAL hilfreiche Informationen liefert und die subjektive Bewertung bestätigt. rnIm Jahr 2007 fanden die Projekte COPS und MAP D-PHASE statt und boten die Möglich-keit, 19 Modelle aus drei Modellkategorien hinsichtlich ihrer Vorhersageleistung in Südwestdeutschland für Akkumulationszeiträume von 6 und 12 Stunden miteinander zu vergleichen. Als Ergebnisse besonders hervorzuheben sind, dass (i) je kleiner der Gitter-punktabstand der Modelle ist, desto realistischer sind die simulierten Niederschlags-verteilungen; (ii) bei der Niederschlagsmenge wird in den hoch aufgelösten Modellen weniger Niederschlag, d.h. meist zu wenig, simuliert und (iii) die Ortskomponente wird von allen Modellen am schlechtesten simuliert. Die Analyse der Vorhersageleistung dieser Modelltypen für konvektive Situationen zeigt deutliche Unterschiede. Bei Hochdrucklagen sind die Modelle ohne Konvektionsparametrisierung nicht in der Lage diese zu simulieren, wohingegen die Modelle mit Konvektionsparametrisierung die richtige Menge, aber zu flächige Strukturen realisieren. Für konvektive Ereignisse im Zusammenhang mit Fronten sind beide Modelltypen in der Lage die Niederschlagsverteilung zu simulieren, wobei die hoch aufgelösten Modelle realistischere Felder liefern. Diese wetterlagenbezogene Unter-suchung wird noch systematischer unter Verwendung der konvektiven Zeitskala durchge-führt. Eine erstmalig für Deutschland erstellte Klimatologie zeigt einen einer Potenzfunktion folgenden Abfall der Häufigkeit dieser Zeitskala zu größeren Werten hin auf. Die SAL Ergebnisse sind für beide Bereiche dramatisch unterschiedlich. Für kleine Werte der konvektiven Zeitskala sind sie gut, dagegen werden bei großen Werten die Struktur sowie die Amplitude deutlich überschätzt. rnFür zeitlich sehr hoch aufgelöste Niederschlagsvorhersagen gewinnt der Einfluss der zeitlichen Fehler immer mehr an Bedeutung. Durch die Optimierung/Minimierung der L Komponente von SAL innerhalb eines Zeitfensters(+/-3h) mit dem Beobachtungszeit-punkt im Zentrum ist es möglich diese zu bestimmen. Es wird gezeigt, dass bei optimalem Zeitversatz die Struktur und Amplitude der QNVs für das COSMO-DE besser werden und damit die grundsätzliche Fähigkeit des Modells die Niederschlagsverteilung realistischer zu simulieren, besser gezeigt werden kann.

Konstruktion und Analyse einer funktionalen Renormierungsgruppengleichung für Gravitation im Einstein-Cartan-Zugang

Während das Standardmodell der Elementarteilchenphysik eine konsistente, renormierbare Quantenfeldtheorie dreier der vier bekannten Wechselwirkungen darstellt, bleibt die Quantisierung der Gravitation ein bislang ungelöstes Problem. In den letzten Jahren haben sich jedoch Hinweise ergeben, nach denen metrische Gravitation asymptotisch sicher ist. Das bedeutet, daß sich auch für diese Wechselwirkung eine Quantenfeldtheorie konstruieren läßt. Diese ist dann in einem verallgemeinerten Sinne renormierbar, der nicht mehr explizit Bezug auf die Störungstheorie nimmt. Zudem sagt dieser Zugang, der auf der Wilsonschen Renormierungsgruppe beruht, die korrekte mikroskopische Wirkung der Theorie voraus. Klassisch ist metrische Gravitation auf dem Niveau der Vakuumfeldgleichungen äquivalent zur Einstein-Cartan-Theorie, die das Vielbein und den Spinzusammenhang als fundamentale Variablen verwendet. Diese Theorie besitzt allerdings mehr Freiheitsgrade, eine größere Eichgruppe, und die zugrundeliegende Wirkung ist von erster Ordnung. Alle diese Eigenschaften erschweren eine zur metrischen Gravitation analoge Behandlung.rnrnIm Rahmen dieser Arbeit wird eine dreidimensionale Trunkierung von der Art einer verallgemeinerten Hilbert-Palatini-Wirkung untersucht, die neben dem Laufen der Newton-Konstante und der kosmologischen Konstante auch die Renormierung des Immirzi-Parameters erfaßt. Trotz der angedeuteten Schwierigkeiten war es möglich, das Spektrum des freien Hilbert-Palatini-Propagators analytisch zu berechnen. Auf dessen Grundlage wird eine Flußgleichung vom Propertime-Typ konstruiert. Zudem werden geeignete Eichbedingungen gewählt und detailliert analysiert. Dabei macht die Struktur der Eichgruppe eine Kovariantisierung der Eichtransformationen erforderlich. Der resultierende Fluß wird für verschiedene Regularisierungsschemata und Eichparameter untersucht. Dies liefert auch im Einstein-Cartan-Zugang berzeugende Hinweise auf asymptotische Sicherheit und damit auf die mögliche Existenz einer mathematisch konsistenten und prädiktiven fundamentalen Quantentheorie der Gravitation. Insbesondere findet man ein Paar nicht-Gaußscher Fixpunkte, das Anti-Screening aufweist. An diesen sind die Newton-Konstante und die kosmologische Konstante jeweils relevante Kopplungen, wohingegen der Immirzi-Parameter an einem Fixpunkt irrelevant und an dem anderen relevant ist. Zudem ist die Beta-Funktion des Immirzi-Parameters von bemerkenswert einfacher Form. Die Resultate sind robust gegenüber Variationen des Regularisierungsschemas. Allerdings sollten zukünftige Untersuchungen die bestehenden Eichabhängigkeiten reduzieren.

Electron spectroscopy of novel charge transfer systems based on polycyclic aromatic hydrocarbons

Organische Ladungstransfersysteme weisen eine Vielfalt von konkurrierenden Wechselwirkungen zwischen Ladungs-, Spin- und Gitterfreiheitsgraden auf. Dies führt zu interessanten physikalischen Eigenschaften, wie metallische Leitfähigkeit, Supraleitung und Magnetismus. Diese Dissertation beschäftigt sich mit der elektronischen Struktur von organischen Ladungstransfersalzen aus drei Material-Familien. Dabei kamen unterschiedliche Photoemissions- und Röntgenspektroskopietechniken zum Einsatz. Die untersuchten Moleküle wurden z.T. im MPI für Polymerforschung synthetisiert. Sie stammen aus der Familie der Coronene (Donor Hexamethoxycoronen HMC und Akzeptor Coronen-hexaon COHON) und Pyrene (Donor Tetra- und Hexamethoxypyren TMP und HMP) im Komplex mit dem klassischen starken Akzeptor Tetracyanoquinodimethan (TCNQ). Als dritte Familie wurden Ladungstransfersalze der k-(BEDT-TTF)2X Familie (X ist ein monovalentes Anion) untersucht. Diese Materialien liegen nahe bei einem Bandbreite-kontrollierten Mottübergang im Phasendiagramm.rnFür Untersuchungen mittels Ultraviolett-Photoelektronenspektroskopie (UPS) wurden UHV-deponierte dünne Filme erzeugt. Dabei kam ein neuer Doppelverdampfer zum Einsatz, welcher speziell für Milligramm-Materialmengen entwickelt wurde. Diese Methode wies im Ladungstransferkomplex im Vergleich mit der reinen Donor- und Akzeptorspezies energetische Verschiebungen von Valenzzuständen im Bereich weniger 100meV nach. Ein wichtiger Aspekt der UPS-Messungen lag im direkten Vergleich mit ab-initio Rechnungen.rnDas Problem der unvermeidbaren Oberflächenverunreinigungen von lösungsgezüchteten 3D-Kristallen wurde durch die Methode Hard-X-ray Photoelectron Spectroscopy (HAXPES) bei Photonenenergien um 6 keV (am Elektronenspeicherring PETRA III in Hamburg) überwunden. Die große mittlere freie Weglänge der Photoelektronen im Bereich von 15 nm resultiert in echter Volumensensitivität. Die ersten HAXPES Experimente an Ladungstransferkomplexen weltweit zeigten große chemische Verschiebungen (mehrere eV). In der Verbindung HMPx-TCNQy ist die N1s-Linie ein Fingerabdruck der Cyanogruppe im TCNQ und zeigt eine Aufspaltung und einen Shift zu höheren Bindungsenergien von bis zu 6 eV mit zunehmendem HMP-Gehalt. Umgekehrt ist die O1s-Linie ein Fingerabdruck der Methoxygruppe in HMP und zeigt eine markante Aufspaltung und eine Verschiebung zu geringeren Bindungsenergien (bis zu etwa 2,5eV chemischer Verschiebung), d.h. eine Größenordnung größer als die im Valenzbereich.rnAls weitere synchrotronstrahlungsbasierte Technik wurde Near-Edge-X-ray-Absorption Fine Structure (NEXAFS) Spektroskopie am Speicherring ANKA Karlsruhe intensiv genutzt. Die mittlere freie Weglänge der niederenergetischen Sekundärelektronen (um 5 nm). Starke Intensitätsvariationen von bestimmten Vorkanten-Resonanzen (als Signatur der unbesetzte Zustandsdichte) zeigen unmittelbar die Änderung der Besetzungszahlen der beteiligten Orbitale in der unmittelbaren Umgebung des angeregten Atoms. Damit war es möglich, präzise die Beteiligung spezifischer Orbitale im Ladungstransfermechanismus nachzuweisen. Im genannten Komplex wird Ladung von den Methoxy-Orbitalen 2e(Pi*) und 6a1(σ*) zu den Cyano-Orbitalen b3g und au(Pi*) und – in geringerem Maße – zum b1g und b2u(σ*) der Cyanogruppe transferiert. Zusätzlich treten kleine energetische Shifts mit unterschiedlichem Vorzeichen für die Donor- und Akzeptor-Resonanzen auf, vergleichbar mit den in UPS beobachteten Shifts.rn

Interacting fermionic atoms in optical lattices - A quantum simulator for condensed matter physics

This thesis reports on the creation and analysis of many-body states of interacting fermionic atoms in optical lattices. The realized system can be described by the Fermi-Hubbard hamiltonian, which is an important model for correlated electrons in modern condensed matter physics. In this way, ultra-cold atoms can be utilized as a quantum simulator to study solid state phenomena. The use of a Feshbach resonance in combination with a blue-detuned optical lattice and a red-detuned dipole trap enables an independent control over all relevant parameters in the many-body hamiltonian. By measuring the in-situ density distribution and doublon fraction it has been possible to identify both metallic and insulating phases in the repulsive Hubbard model, including the experimental observation of the fermionic Mott insulator. In the attractive case, the appearance of strong correlations has been detected via an anomalous expansion of the cloud that is caused by the formation of non-condensed pairs. By monitoring the in-situ density distribution of initially localized atoms during the free expansion in a homogeneous optical lattice, a strong influence of interactions on the out-of-equilibrium dynamics within the Hubbard model has been found. The reported experiments pave the way for future studies on magnetic order and fermionic superfluidity in a clean and well-controlled experimental system.

Warped extra dimensions: flavor, precision tests and Higgs physics

In this thesis, the phenomenology of the Randall-Sundrum setup is investigated. In this context models with and without an enlarged SU(2)_L x SU(2)_R x U(1)_X x P_{LR} gauge symmetry, which removes corrections to the T parameter and to the Z b_L \bar b_L coupling, are compared with each other. The Kaluza-Klein decomposition is formulated within the mass basis, which allows for a clear understanding of various model-specific features. A complete discussion of tree-level flavor-changing effects is presented. Exact expressions for five dimensional propagators are derived, including Yukawa interactions that mediate flavor-off-diagonal transitions. The symmetry that reduces the corrections to the left-handed Z b \bar b coupling is analyzed in detail. In the literature, Randall-Sundrum models have been used to address the measured anomaly in the t \bar t forward-backward asymmetry. However, it will be shown that this is not possible within a natural approach to flavor. The rare decays t \to cZ and t \to ch are investigated, where in particular the latter could be observed at the LHC. A calculation of \Gamma_{12}^{B_s} in the presence of new physics is presented. It is shown that the Randall-Sundrum setup allows for an improved agreement with measurements of A_{SL}^s, S_{\psi\phi}, and \Delta\Gamma_s. For the first time, a complete one-loop calculation of all relevant Higgs-boson production and decay channels in the custodial Randall-Sundrum setup is performed, revealing a sensitivity to large new-physics scales at the LHC.