Fakultät für Physik - Digitale Hochschulschriften der LMU - Teil 02/05 Archiv

In this thesis two different aspects of string theory compactifications are investigated. The first part deals with the issue of the huge amount of possible string vacua, known as the landscape. Concretely we investigate a specific well defined subset of type II orientifold compactifications. We develop the necessary tools to construct a very large set of consistent models and investigate their gauge sector on a statistical basis. In particular we analyse the frequency distributions of gauge groups and the possible amount of chiral matter for compactifications to six and four dimensions. In the phenomenologically relevant case of four-dimensional compactifications, special attention is paid to solutions with gauge groups that include those of the standard model, as well as Pati-Salam, SU(5) and flipped SU(5) models. Additionally we investigate the frequency distribution of coupling constants and correlations between the observables in the gauge sector. These results are compared with a recent study of Gepner models. Moreover, we elaborate on questions concerning the finiteness of the number of solutions and the computational complexity of the algorithm. In the second part of this thesis we consider a new mathematical framework, called generalised geometry, to describe the six-manifolds used in string theory compactifications. In particular, the formulation of T-duality and mirror symmetry for nonlinear topological sigma models is investigated. Therefore we provide a reformulation and extension of the known topological A- and B-models to the generalised framework. The action of mirror symmetry on topological D-branes in this setup is presented and the transformation of the boundary conditions is analysed. To extend the considerations to D-branes in type II string theory, we introduce the notion of generalised calibrations. We show that the known calibration conditions of supersymmetric branes in type IIA and IIB can be obtained as special cases. Finally we investigate the action of T-duality on the generalised calibrations.

The dynamics of single semiflexible polymers in solution under the influence of an external field are investigated with Brownian Dynamics simulations. Hydrodynamic interactions are included on the Rotne-Prager level and proof to be essential. Model equations are used to derive scaling laws. The work consists of five projects that are distinct but closely related to each other: In the first project, a neutral semiflexible particle is moved by centrifugal or gravitational forces relative to quiescent fluid. A coupling between hydrodynamic interactions and flexibility leads - depending on the elastic parameters - to a rod orientation perpendicular to the external field. This coupling is also investigated for a filament that is rotated at one end by some external torque (second project). Above a critical torque the filament folds itself around the rotational axis, with important consequences for the propulsion with a nano-machine. The third project deals with flexible polymers in an ultracentrifuge where a novel compactification and unfolding scenario is predicted: The established theories on sedimentation use the preaveraging approximation of the hydrodynamic interactions and cannot explain the polymer configurations at high fields consisting of a dense head and a long tail, which make a new efficient separation technique possible. In the forth project, the diffusion of charged semiflexible polymers under different salt conditions is treated. Ions are included explicitly and not on a mean-field level. The theory of electrolyte friction for spherical objects is qualitatively extended to semiflexible polymers. A heuristic formula for the diffusion constant over the whole range of persistence lengths is proposed. In the final project, the hydrodynamic orientation mechanism found in the first project is suggested as a possible source of anomalous electric birefringence which is observed for rod-like polymers. It is compared with the competing parallel induced dipole orientation. The dependence of the polarizability on rod length, salt and polymer concentration is clarified.

Mit den Mitteln der Infrarotspektroskopie wurde der Einfluss der organischen Hülle auf Struktur und Dynamik von CdSe Nanopartikeln untersucht. Zunächst wurde ein Verfahren entwickelt, das es ermöglicht, aus dem statischen Infrarotspektrum Informationen über die Qualität der organischen Hülle und das Bindungsverhalten der Liganden zu gewinnen. An qualitativ hochwertigen und gut charakterisierten Proben wurde anschließend die Dynamik des niederenergetischsten Elektronenniveaus 1S nach optischer Anregung im Sichtbaren zeitaufgelöst gemessen. Als Referenz diente CdSe TOPO, das durch Proben mit den Liganden Octanthiol, Octansäure, Octylamin, Naphthoquinon, Benzoquinon und Pyridin ergänzt wurde. Die untersuchten Nanopartikel hatten einen Durchmesser von 4.86 nm. Mit Hilfe des Anreg-Abtast- oder Pump-Probe-Verfahrens wurden zunächst Messungen im Pikosekundenbereich durchgeführt. Die Anregungswellenlängen wurden dabei spektral eingeschränkt und so gewählt, dass selektiv die Übergänge 1S-1S und 1P-1P, nicht aber der dazwischenliegende 2S-1S-Übergang, angeregt wurden. Die Anregungsintensitäten wurden bewusst so niedrig gehalten, dass die Anregung mehrerer Exzitonen in einem Kristall vermieden werden konnte. Die Abtastwellenlänge im Infraroten entsprach der Energiedifferenz zwischen den Elektronenniveaus 1S und 1P. Die Transienten im Pikosekundenbereich zeichnen sich durch einen steilen Anstieg des Signals aus, auf den ein multiexponentieller Zerfall folgt. Der Anstieg, der die Bevölkerung des angeregten Zustands widerspiegelt, ist unabhängig von der Wahl der Liganden. Der Einfluss der organischen Hülle wird erst in den unterschiedlichen Zerfallszeiten der angeregten Elektronenniveaus sichtbar. Der Zerfall des Messsignals von CdSe TOPO lässt sich näherungsweise mit drei Zeitkonstanten beschreiben: eine Zerfallszeit im frühen Pikosekundenbereich, eine Zeitkonstante um die hundert Pikosekunden und eine Zeitkonstante bei einigen Nanosekunden. Bei ansteigender Abtastwellenlänge werden die Zerfallszeiten länger. Durch gezielte Anregung des 1S-1S und des 1P-1P-Übergangs konnte der Zerfall des 1P-Zustands in den energetisch günstigeren 1S-Zustand beoachtet werden, der im verzögerten Anstieg des Messsignals bei Anregung des 1P-1P-Übergangs sichtbar wird. Dem Übergang zwischen den Elektronenniveaus 1P und 1S konnte eine Zeitkonstante von ca. 190 fs zugewiesen werden, die nicht von der Wahl der organischen Hülle beeinflusst wird. Nanopartikel mit den Liganden TOPO, Pyridin und Octanthiol zeigen auch nach 3 ns noch ein gut sichtbares Messsignal. An diesen Proben wurden Messungen im Nanosekundenbereich durchgeführt. Auch hier ist der Einfluss der organischen Hülle auf die Dynamik der Nanopartikelprobe deutlich zu erkennen. Mit der Kombination beider Messreihen konnte erstmals ein Zeitbereich abgedeckt werden, der sich von einigen hundert Femtosekunden bis in den Mikrosekundenbereich hinein erstreckt.

Entanglement is the key element for many experiments in quantum communication and information. Especially for future applications like quantum networks or the quantum repeater it is mandatory to achieve entanglement also between separated quantum processors. For this purpose, entanglement between different quantum objects like atoms and photons forms the interface between atomic quantum memories and photonic quantum communication channels, finally allowing the distribution of quantum information over arbitrary distances. Furthermore, atom-photon entanglement is also the key element to give the final answer to Einstein's question wether a local and realistic description of physical reality is possible or not. Until now, the results of many experiments testing Bell's inequality indicate that local realistic theories are not a valid description of nature. However, all these tests were subject to loopholes. In this context, atom-photon entanglement represents a crucial step towards the realization of entanglement between distant atoms that would allow a final loophole-free test of Bell's inequality. This thesis describes the generation and verification of an entangled state between a single neutral atom and a single photon at a wavelength suitable for long distance information transport. For this purpose we store a single Rb-87 atom in an optical dipole trap. The atom is prepared in an excited state, that together with its two decay channels forms a lambda-type transition. In the following spontaneous decay, conservation of angular momentum leads to the formation of an entangled state between the angular momentum of the atom and the polarization of the emitted photon. To verify the entanglement we introduce an atomic state-analysis, based on a state-selective adiabatic population transfer between atomic hyperfine levels. This allows the direct analysis of the internal state of the atom in arbitrary measurement bases without the necessity of additional state manipulations. Using this method together with a polarization measurement of the emitted photon, we performed correlation measurements as well as a full state tomography of the combined atom-photon system. From the experimental results we obtain an entanglement fidelity of 87%, which clearly shows that the generated state is entangled. The degree of entanglement observed in our experiment is high enough to allow the generation of entanglement between distant atoms via entanglement swapping, which would allow a final, loophole-free test of Bell's inequality. Furthermore, it opens up a variety of applications in quantum communication and information science.

Our current understanding of structure formation in the Universe seems to be well described by a hierarchical scenario, in which small units assemble first to produce more massive systems. In recent years, much observational evidence has been accumulated, indicating that star formation proceeded instead in an antihierarchical fashion. Constraining the age and chemical composition of the stellar populations in galaxies should help shed light on this apparent dichotomy between mass assembly and star formation activity. The integrated spectra of galaxies contain valuable clues about the ages and metallicities of the stars producing the light. However, at first order, they are affected in a similar way by age and metallicity. Studies of more refined spectral diagnostics, such as individual stellar absorption features, are thus needed to provide more stringent constraints on these parameters. This method has been limited so far to small samples of elliptical galaxies, using population synthesis models with limited spectral resolution and restricted coverage in stellar effective temperatures. The objective of this thesis is the interpretation of the optical spectra of large samples of nearby galaxies in terms of the light-weighted metallicity, age and mass of their stellar populations. I have developed a new method to simultaneously derive median-likelihood estimates of each physical parameter and the associated confidence intervals. The method, based on a recent highresolution population synthesis code with full temperature coverage, consists in comparing each observed spectrum with a comprehensive library of star formation histories. The constraints are set by the simultaneous fit of an optimally selected set of spectral absorption features. I have applied this method to a sample of 200,000 galaxies from the Sloan Digital Sky Survey, including galaxies with any star formation history, from quiescent early-type to actively star forming galaxies. Thanks to the unprecedented statistics, I could give an accurate description of the galaxy distribution in the full physical parameters space. The relation between stellar metallicity, age and stellar mass shows a rapid transition from low-mass, young, metal-poor to high-mass, old, metal-rich galaxies at a stellar mass of 3×10^10 solar masses, the same characteristic scale of several observed bi-modalities in galaxy properties. The stellar metallicity-mass relation is interpreted as a manifestation of galactic winds, which are more efficient in removing metals from the shallow potential well of low-mass galaxies. I then explored the implications of the above relations to re-assess the physical origin of observed scaling relations of elliptical galaxies, linking their luminous and dynamical mass to the properties of their stellar populations. The relations are driven by an increase in metallicity, age and element abundance ratios with galaxy mass. The scatter is contributed by a similar amount by both age and metallicity. The increasing spread towards younger ages at low stellar masses indicates that low-mass ellipticals either formed their stars later or have a more extended star formation history. This hints at a shift in stellar growth towards less massive galaxies in recent epochs. The large ranges in observational and physical properties covered by SDSS galaxies make it a representative sample of the local Universe. I could thus derive the total mass density of metals and baryons locked up in stars today. I have also studied how metals and stellar mass are distributed as a function of various galaxy properties. The galaxies containing the bulk of the total stellar mass (massive, bulge-dominated galaxies with old stellar populations) are also those that contribute the largest fraction of metals, as expected from the mass-metallicity relation. These quantities set the fundamental constraints at the present epoch of the cosmic star formation and chemical enrichment histories. The more detailed knowledge of the relations between galaxy physical parameters allows a more direct comparison with predictions from semi-analytic models of galaxy formation and evolution. Moreover, the more robust constraints represent an important calibration at redshift zero for similar studies at higher redshifts.

The aim of this thesis is to assess the effect of the metallicity on the Cepheid Period-Luminosity (PL) relation. The novelty of the approach adopted in this project consists in the homogeneous analysis of a large sample of Cepheids (72) observed in three galaxies (the Milky Way, the Large Magellanic Cloud and the Small Magellanic Cloud), spanning a factor of ten in metallicity. This allows us to explore the effect of the metallicity on the PL relation in a wide range and to study the gas enrichment histories of three different galaxies. To fulfil this goal, firstly, we have selected a sample of Cepheids for which distances and accurate photometry are available in the literature and we have collected high-resolution, high signal-to-noise spectra of these stars, using the highly advanced facilities of the European Southern Observatory in Chile. Secondly, we have directly measured iron and alpha-elements (O, Na, Mg, Al, Si, Ca, Ti) abundances of our sample from these spectra. We have compared our iron abundances with studies on Galactic and Magellanic Cepheids and found a good agreement for the average values and for the individual stars in common. We have then made a broader comparison with results for the Magellanic Clouds from the analysis of F and K non-variable supergiants (they have ages and temperatures similar to Cepheid stars) and of B stars, which are progenitors of Cepheids, and found a good agreement. Cepheids do not show any peculiar differences with these two other population of stars, this indicate that, during this evolutionary stage, there are no changes of the original iron content of the gas from which they were formed. We have then studied the trends of the individual alpha-elements abundance ratios relative to iron as a function of the iron content of our programme star. We can draw some preliminary conclusion considering oxygen, silicon and calcium as the most reliable indicators among the alpha-elements we have analysed. The trends of the abundance ratios of O, Si and Ca are in fairly good agreement with observational studies on Cepheids and on different kinds of stellar populations in the Galaxy and the Magellanic Clouds. The elemental abundances we have determined were used to investigate the effect of metallicity on the PL relation in the V and K bands, in order to check if there is a change of the effect as wavelength increases. We note different behaviours in the two bands. The metallicity has an effect in the V band in the sense that metal-rich Cepheids are fainter than metal-poor ones, while it does not have any effects in the K band. Thus, to safely measure the distances of galaxies, one can use the PL relation in the infrared bands (namely K), so as to minimise the effect of the metallicity. Using the K band has the additional advantage of reducing the effects of the interstellar extinction to the level of other systematic and random errors.

Diese Dissertation beschreibt die Ergebnisse des Wendelstein Calar Alto Pixellensing Project (WeCAPP), welches in Richtung der Andromeda Galaxie (M31) nach Dunkler Materie in Form von "Massiven Kompakten Halo Objekten" (Machos) sucht. Die neuesten wissenschaftlichen Befunde legen ein Universum mit flacher Geometrie nahe, zu dessen Dichteinhalt Dunkle Materie ca. 23% beitraegt. Weitere 4.5% werden baryonischer Materie zugeschrieben, wobei von diesem Anteil bei kleiner Rotverschiebung bisher nur ca. 10% nachgewiesen werden konnten. Die Kandidaten fuer Machos in den Halos von Galaxien umfassen eine baryonische Komponente (vergangene Sterne wie z.B. Weisse Zwerge oder Neutronensterne), sowie eine nicht-baryonische Komponente, zum Beispiel in Form von primordialen Schwarzen Loechern. Da diese Objekte nur sehr schwach leuchten, sind sie dem direkten Nachweis entzogen. Sie koennen jedoch indirekt ueber den Gravitationslinseneffekt nachgewiesen werden, den sie auf das Licht von Sternen im Hintergrund ausueben. Der beobachtbare Helligkeitsanstieg ist charakteristisch fuer solche sogenannten Mikrolinsenereignisse und laesst sich gut von der Helligkeitsaenderung Veraenderlicher Sterne unterscheiden. Die Seltenheit der Gravitationslinsenereignisse machte den Aufbau eines grossen Datensatzes mit entsprechender zeitlicher Ueberdeckung notwendig, was durch simultane Beobachtungen an zwei Standorten (Wendelstein und Calar Alto) erreicht werden konnte. Nach einer kurzen Einfuehrung gibt Kapitel 2 einen Ueberblick ueber das Experiment und die Beobachtungsstrategie und stellt die Teleskope und verwendeten Instrumente vor. Desweiteren behandelt Kapitel 2 die Eigenschaften des Datensatzes (1997 - 2005) und stellt die Algorithmen und Methoden vor, die zum Reduzieren der Daten angewandt wurden. Kapitel 3 praesentiert ein aktualisiertes Modell der Massen- und Lichtverteilung der Andromeda Galaxie, welches gut mit kinematischen Daten, als auch mit Vorhersagen von stellaren Populationsmodellen uebereinstimmt. In Kapitel 4 wird dieses Modell genutzt, um die erwartete Rate von Gravitationslinsenereignissen und deren raeumliche Verteilung fuer das WeCAPP Experiment zu berechnen. Kapitel 5 praesentiert die Kandidaten fuer Mikrolinsenereignisse, die im WeCAPP Datensatz identifiziert werden konnten. Sowohl die Anzahl der Ereignisse als auch ihre raeumliche Verteilung deuten darauf hin, dass sie durch stellare Linsen in M31 selbst verursacht wurden (self-lensing). Der Machoanteil ist demgegenueber als eher gering einzuschaetzen. Der aufgebaute Datensatz ist aufgrund seiner langen zeitlichen Ueberdeckung hervorragend geeignet, intrinsisch Veraenderliche Quellen in M31 zu studieren. In Kapitel 6 wird dieser Katalog von ueber 20 000 Veraenderlichen Quellen praesentiert. Die gemessene Anzahldichte der Quellen weist eine starke Asymmetrie auf, die auf den Einfluss erhoehter Extinktion in den Spiralarmen zurueckzufuehren ist. Die Veraenderlichen lassen sich in 3 Gruppen einteilen, wobei sich in Gruppe 1 die klassischen Cepheiden befinden. Gruppe 2 enthaelt unter anderem Klasse 2 Cepheiden und RV Tauri Veraenderliche, wohingegen sich Gruppe 3 aus Langperiodischen Veraenderlichen zusammensetzt. Die Parameter, die aus der Fourieranalyse der Lichtkurven klassischer Cepheiden extrahiert werden konnten, zeigen den bekannten Verlauf mit der Periode der stellaren Pulsation. Auch fuer die Klasse 2 Cepheiden und die RV Tauri Sterne konnte eine Korrelation bestimmter Phasenparameter gefunden werden, wobei die Relation der RV Tauri Sterne eine Fortfuehrung der Relation der Klasse 2 Cepheiden ist. Dieses Ergebnis unterstuetzt die enge Verbindung zwischen beiden Arten von Veraenderlichen. Neben pulsierenden Veraenderlichen wurden auch ueber 60 klassische Novae identifiziert, deren Helligkeitsverlauf einen eruptiven Charakter aufweist. Der daraus resultierende Novakatalog, der in Kapitel 7 praesentiert wird, ist einer der groessten und homogensten seiner Art. Eine Korrelation mit historischen Novae erbrachte 5 Kandidaten fuer wiederkehrende Novae. Fuer einige Novae gelang es, den Zeitpunkt des Ausbruchs genau zu bestimmen und damit zu zeigen, dass die Konstanz der Helligkeit 15 Tage nach Maximum fuer schnelle und moderat schnelle Novae zu gelten scheint. Sehr schnelle Novae scheinen jedoch davon abzuweichen. Mit Hilfe dieser Relation und den exponentiellen Angleichungen an die Lichtkurven konnte gezeigt werden, dass fuer mittlere Abfallszeitskalen t2 die maximale Helligkeit linear mit dem Logarithmus der Abfallszeit skaliert, fuer grosse t2 jedoch eine Abflachung dieser linearen Relation festzustellen ist.

Several lines of evidence suggest that the most active phase of galaxy evolution, especially in the most massive systems, was largely completed by $z\sim 1$. This results, e.g., from the observation that the most massive galaxies at low redshift have very old stellar populations ($\sim 10$ Gyr) and very little gas to fuel subsequent star formation. Similarly, active galactic nuclei (AGN) were more numerous and brighter in the early universe. Ultimately, the direct observation of high-redshift galaxies will be the only way to understand which processes shaped the universe we see today, in spite of the rich ``fossil'' data sets we have of the Milky Way and neighboring galaxies. Thanks to the new $8-10$ m telescope class and novel instrumentation, including SPIFFI/SINFONI on the VLT, individual galaxies at redshifts $z\sim 1-3$ ($2-6$ Gyr after the Big Bang) are now within the reach of astronomical spectrographs. Methodologically, this thesis focuses on the analysis of spectrally and spatially resolved optical emission lines, first of all \ha\ and [OIII]\lam5007, which are shifted into the near-infrared. {\sc Spiffi / Sinfoni} is very suited to such a programme, because it records the spectra of a contiguous field of view of up to 8\arcsec$\times$8\arcsec. The internal kinematic and chemical gradients within a galaxy can thus be measured in a single observation. Galaxies in the early universe had particularly high star-formation rates, so that many targets are bright optical line emitters. Internal kinematics are measured through the Doppler effect, line profiles and widths indicate the presence of an AGN, galactic ``superwinds'' and the relationship of chaotic to ordered motion. Star-formation rates are measured from the luminosity of the Balmer lines, especially \ha. Characteristic line ratios indicate the presence of an AGN, chemical composition, and electron densities in the ISM, and they allow to distinguish shocks and photoionization. This thesis is a pilot study: It comprises 9 galaxies that fulfill a variety of selection criteria: they are either bright UV or submillimeter emitters, or they are radio-loud. Perhaps the most fundamental result is that gravity (dominated by dark matter) is the main driver of early galaxy evolution, but it is not the only important process. Star formation and AGN cause hydrodynamical feedback processes, which might be a sign of self-regulated galaxy evolution. It is found that star-formation related feedback had similar properties at low and high redshift, but that AGN-driven gas expulsion might have played a major role in the high-redshift evolution of galaxies, that is without low-redshift equivalent. Another important result is the rotation curve we find in the central kiloparsec of a gravitationally lensed UV-selected galaxy. Velocity gradients of $\sim 100$ \kms\ have been observed in many high-redshift galaxies, but the interpretation as rotation curves is generally not unique. Given the relatively coarse spatial resolution of high-redshift galaxy data, two nearby galaxies, maybe interacting or undergoing a merger, might blend into one smooth velocity gradient. Galaxy mergers are an important ingredient of the ``hierarchical model'', the current paradigm of structure formation, and therefore nearby galaxy pairs were likely more common at high redshift than they are today. The large similarity of the lensed rotation curve with those of nearby galaxies might be a first sign that galaxies evolved inside-out.

During the last ten to fifteen years cosmology has turned from a data-starved to a data-driven science. Several key parameters of the Universe have now been measured with an accuracy better than 10%. Surprisingly, it has been found that instead of slowing down, the expansion of the Universe proceeds at an ever increasing rate. From this we infer the existence of a negative pressure component -- the so-called Dark Energy (DE) -- that makes up more than two thirds of the total matter-energy content of our Universe. It is generally agreed amongst cosmologists and high energy physicists that understanding the nature of the DE poses one of the biggest challenges for the modern theoretical physics. Future cosmological datasets, being superior in both quantity and quality to currently existing data, hold the promise for unveiling many of the properties of the mysterious DE component. With ever larger datasets, as the statistical errors decrease, one needs to have a very good control over the possible systematic uncertainties. To make progress, one has to concentrate the observational effort towards the phenomena that are theoretically best understood and also least ``contaminated'' by complex astrophysical processes or several intervening foregrounds. Currently by far the cleanest cosmological information has been obtained through measurements of the angular temperature fluctuations of the Cosmic Microwave Background (CMB). The typical angular size of the CMB temperature fluctuations is determined by the distance the sound waves in the tightly coupled baryon-photon fluid can have traveled since the Big Bang until the epoch of recombination. A similar scale is also expected to be imprinted in the large-scale matter distribution as traced by, for instance, galaxies or galaxy clusters. Measurements of the peaks in the CMB angular power spectrum fix the physical scale of the sound horizon with a high precision. By identifying the corresponding features in the low redshift matter power spectrum one is able to put constraints on several cosmological parameters. In this thesis we have investigated the prospects for the future wide-field SZ cluster surveys to detect the acoustic scale in the matter power spectrum, specifically concentrating on the possibilities for constraining the properties of the DE. The core part of the thesis is concerned with a power spectrum analysis of the SDSS Luminous Red Galaxy (LRG) sample. We have been able to detect acoustic features in the redshift-space power spectrum of LRGs down to scales of ~ 0.2 hMpc^{-1}, which approximately corresponds to the seventh peak in the CMB angular spectrum. Using this power spectrum measurement along with the measured size of the sound horizon, we have carried out the maximum likelihood cosmological parameter estimation using Markov chain Monte Carlo techniques. The precise measurement of the low redshift sound horizon in combination with the CMB data has enabled us to measure, under some simplifying assumptions, the Hubble constant with a high precision: H_0 = 70.8 {+1.9} {-1.8} km/s/Mpc. Also we have shown that a decelerating expansion of the Universe is ruled out at more than 5-sigma confidence level.

In this thesis gauge-field theories and gravity on noncommutative spaces are studied. We start with an introduction to the concepts underlying the construction of field theories on noncommutative spaces. By a noncommutative space we mean a noncommutative algebra, which replaces the algebra of functions on ordinary space. We construct derivatives and deformed symmetries ("Quantum Group" symmetries) acting on noncommutative spaces. Consistency requires us to change the action on a product of representations ("deformed coproducts"); this gives rise in particular to deformed Leibniz rules. We also show how a noncommutative space and the generators of deformed symmetries acting on it can be represented on the ordinary algebra of functions; the commutative, point-wise product is substituted by a noncommutative one ("star-product"). One possible way to define gauge-field theories on noncommutative spaces is to construct "Seiberg--Witten maps". In this approach it is possible to express all noncommutative quantities in terms of their commutative counterparts. We illustrate this by two examples, the two-dimensional q -deformed Euclidean plane and the \kappa -deformed Minkowski space-time. In addition gauge-field theory on "fuzzy" S^{2}\times S^{2} is discussed as a multi-matrix model. We show that this model reduces in an appropriate limit to gauge-field theory on noncommutative \mathbb{R}^{4} . We also present a new approach to deformed gauge theories, which is based on "twisted" gauge transformations. In this setting new fields occur in addition to the usual gauge fields. Consistent equations of motion and conserved currents are obtained. This is the first time that conservation laws have been derived from a generalized, Quantum Group symmetry. We discuss in detail how to construct deformed infinitesimal diffeomorphisms by deformations via generic "twists". Then we construct gravity as a theory, which is covariant with respect to these diffeomorphisms. This leads to a deformation of Einstein's equations. For canonically deformed spaces, a deformed Einstein--Hilbert action can be even defined. It reduces to the usual Einstein--Hilbert action in the commutative limit. All relevant quantities are expanded in terms of the usual, commutative fields up to second order in the deformation parameter.

Intracellular transport phenomena, such as kinesins and myosins moving along cytoskeletal filaments or ribosomes along messenger RNA, can be modeled by one-dimensional driven lattice gases. Among these, the Totally Asymmetric Simple Exclusion Process (TASEP), has been extensively used. It describes a system of particles hopping in a preferred direction with hard core interaction. The goal of this thesis is to explore the relevance of some features that are missed by this simple model, such as the exchange of particles between molecular track and the cytoplasm, the extended molecular structure of each motor, and the interaction of motors with imperfections on the track acting as road blocks for intracellular traffic. Recent studies have taken into account particle exchange between the track and bulk solution (Langmuir kinetics). It was found that this violation of current conservation along the track leads to phase coexistence regions in the phase diagram not present in the TASEP. We have extended these studies in two ways. First, motivated by the fact that many molecular motors are dimers, we study how the stationary properties of the system (density profile and phase behavior) change upon replacing monomers with extended particles. Analytical refined and generalized mean field theory, supported by numerical Monte Carlo simulations, give a detailed description of the phase diagram. Our study proves that the extension gives quantitative but not qualitative changes in the phase diagram, showing that the picture obtained in the case of monomers is robust upon considering extended particles. Second, motivated by the presence of structural imperfections of the track that act as road blocks, we study the influence of an isolated defect characterized by a reduced hopping rate on the non-equilibrium steady state. We explore the phase behavior in the full parameter range and find that the phase diagram changes qualitatively as compared to the case without defects, showing new phase coexistence regions. In particular above a certain threshold strength of the defect, its presence induces a macroscopic change in the density profile. The regions where the defect is relevant (called bottleneck phases) are identified and studied. In the second part of the thesis we investigate the dynamical features of these models. First we concentrate on the dynamics of the simple TASEP, for which a complete analysis was missing. We use a technique borrowed from solid state physics, the Boltzmann-Langevin method, to give a full description of the correlation function in the whole parameter space. Finally we study the dynamics of a tracer particle in a TASEP with on-off kinetics. We observe that it is possible to reconstruct the density profile from the velocity of the tracer particle and we propose to perform single molecule experiments with fluorescently labelled molecular motors to explore the density profile and ultimately test the phase behavior predicted in this thesis.

Air traffic impacts cirrus cloud cover and consequently the radiation budget of the earth. Additionally air traffic may change the optical properties of already existent cirrus clouds and hence the radiation budget of the atmosphere. For the first time the impact of air traffic was investigated over Europe, North-Atlantic and North-Africa for a period of 11 months of 2004 with a high temporal-resolution satellite sensor. A significant correlation between cirrus cloud cover and air traffic density was shown for the region of interest. The air traffic induced cirrus cloud cover has been estimated with 0.6±0.2% for this region. Global extrapolation yields 0.17± 0.06%. Based on this value an air traffic induced radiative forcing of 34 mW/m2 follows. The direct investigation of the impact of air traffic on outgoing fluxes yields a warming effect of 1.1 W/m2 for the region of interest. This value has been calculated from the difference between outgoing fluxes of air traffic free regions and the whole region. The global extrapolation yields a warming of 290 mW/m2. However this value is very uncertain. Additionally further aspects have been investigated. As a result, a strong dependency of the impact of air traffic on the geographic location and daytime could be shown.

In dieser Arbeit werden Präzisionsrechnungen für die Prozesse gamma gamma -> 4 Fermionen und H -> WW/ZZ -> 4 Fermionen vorgestellt. An einem gamma-gamma-Collider werden wegen des großen Wirkungsquerschnitts genaue theoretische Vorhersagen für die Prozesse gamma gamma -> WW -> 4f benötigt. Mittels dieser Prozesse lassen sich unter anderem die Eichboson-Kopplungen gamma-W-W und gamma-gamma-W-W messen. Außerdem wird über virtuelle geladene, massive Teilchen die Reaktion gamma gamma -> H -> WW/ZZ -> 4f ermöglicht. Auf diese Weise läßt sich die Kopplung gamma-gamma-H messen, und relativ schwere Higgs-Bosonen könnten erzeugt werden. Für Massen MH > 135 GeV zerfällt das Higgs-Boson hauptsächlich über W- und Z-Bosonen in vier Fermionen. Bei der kinematischen Rekonstruktion dieser Zerfälle spielen Quanten-Korrekturen, insbesondere Photon-Bremsstrahlung, eine wichtige Rolle. Die Einbeziehung der Zerfälle der Eichbosonen in Fermionen ist zum einen wichtig, weil unterhalb von MH ≈ 2MW/MZ „off-shell“-Effekte der Eichbosonen berücksichtigt werden müssen. Zum anderen lassen sich mit Hilfe von Winkel- und Energie-Verteilungen der Fermionen der Spin und die CP-Eigenschaften des Higgs-Bosons bestimmen. Besonders geeignet für den Vergleich theoretischer Vorhersagen mit experimentellen Daten sind Monte-Carlo-Generatoren. Für die Prozesse gamma gamma -> 4f und H -> WW/ZZ -> 4f werden solche Programme konstruiert. Sie liefern zum einen die kompletten Vorhersagen in niedrigster Ordnung der Störungstheorie. Zum anderen enthalten sie Quanten-Korrekturen, die sich unterteilen lassen in reelle Korrekturen, welche durch Photon-Bremsstrahlung gegeben sind, und virtuelle Korrekturen. Während die virtuellen Quanten-Korrekturen zu gamma gamma -> WW -> 4f in der Doppel-Pol-Näherung berechnet werden, in der nur die doppelt resonanten Beiträge berücksichtigt werden, werden zu den Prozessen H -> WW/ZZ -> 4f die kompletten Quantenkorrekturen der Ordnung O(alpha) berechnet. Für die Behandlung der in den virtuellen und reellen Korrekturen auftretenden infraroten Divergenzen („soft“ und „collinear“) wird wahlweise die Dipol-Subtraktions-Methode oder die Phase-Space-Slicing-Methode verwendet. Nicht bei allen Observablen müssen sich die bei kollinearer Photon-Abstrahlung auftretenden Massen-Singularitäten gegenseitig aufheben. Um auch solche nicht-kollinear-sichere Observablen untersuchen zu können, wird die Dipol-Subtraktions-Methode diesbezüglich erweitert. Die Diskussion der numerischen Ergebnisse umfasst den Einfluss eines realistischen Photon-Spektrums auf die Wirkungsquerschnitte, das Potential eines gamma-gamma-Colliders, Grenzen an anomale Eichboson-Kopplungen zu setzen, sowie verschiedene Verteilungen in der Invarianten Masse, in der Energie und in Winkeln, die für eine Rekonstruktion der Eichbosonen und die Bestimmung der Eigenschaften des Higgs-Bosons genutzt werden können.

Galaxy clusters are the largest gravitationally bound systems in the universe. Clusters consist of three components: galaxies, gas, and dark matter. The galaxies themselves contribute the least, at most a few percent, to the total mass. The remainder consists of diffuse, hot gas (the intracluster medium, or ICM) and an unseen component which is needed to explain the gravitational stability of clusters (the dark matter). The two most obvious means of studying clusters of galaxies are by observing the optical light emitted from the constituent galaxies or the X-ray emission from the ICM. Clusters of galaxies, bound ensambles of hundreds of galaxies, are an ideal environment to study galaxy evolution and to learn how this is affected by different physical processes: gravity, starbursts and star formation, interactions with the intergalactic medium and galaxy-galaxy encounters. Since the very early works of Hubble in the thirties, it has been recognized that galaxies in dense environments differ systematically from those in low-density regions in their morphological types, stellar populations and gaseous content. When during the history of the Universe and why such environmental differences were established is currently one of the subjects of most intensive investigation in the international astrophysical community. On the other hand, clusters can teach us a great deal about cosmology. The distributions of galaxies on the sky shows a net-like structure in which thin walls and filaments surround large voids. The galaxy clusters are the nodes of this network. Therefore, they trace out the Large-Scale Structure (LSS) of the universe and can be used to study the LSS formation. Moreover, if clusters provide a 'fair sample' of the universe, then the fraction of their mass in baryons should equal the universal baryon fraction, known as $\Omega_b/\Omega_m$. Moreover, the evolution of cluster number density with redshift can determine the mass density parameter, known as $\Omega_M$, and possibly determine the equation of state (and nature) of the dark energy believed to be causing the expansion of the universe to accelerate. Thus, galaxy clusters have a twofold importance: first as laboratories of galaxy formation and evolution, and second as cosmological tool. The aim of this project is to study galaxy clusters from these two perspectives. For this purpose we use the largest optical and X-ray surveys ever realized, the Sloan Digital Sky Survey (SDSS) and the Rosat All Sky Survey (RASS), respectively, to conduct a multiwavelenght study of the properties of galaxy clusters. The project is called RASS-SDSS Galaxy Cluster Survey reflecting the name of the two big surveys used for this work. All the analyses are performed on two cluster samples specially created for the survey: the X-ray selected RASS-SDSS galaxy cluster catalog and a subsample of optically selected, isolated and spectroscopically confirmed Abell clusters. The project consists of two parts. The aim of the first part is to understand which role play the gravitational processes, galaxy mergers and collisions and the interaction with ICM in the process of galaxy formation and evolution. For this purpose, we study the variations of several properties of the cluster galaxy population such as the luminosity and spatial distribution, the morphological type mix, the Star Formation Rate (SFR) and stellar mass as a function of the environmental conditions and the cluster global properties. Our detailed analysis of the cluster individual and composite luminosity functions reveals that the LF clearly shows a bimodal behavior with an upturn and a evident steepening in the faint magnitude range in any SDSS band. The LF is well fitted by the sum of two Schechter functions. The bright end of the LF is found to be universal in all the clusters. The faint end of the LF is much steeper and varies significantly from system to system, when calculated within a fixed metric aperture. The variations are not ramdom however. The more massive a cluster, the lower its fraction of dwarf galaxies. This effect disappears when the cluster LF is calculated within the physical size of the system, as the virial radius ($r_{200}$). This indicates that the previously observed variations are due to aperture effects caused by the observed increase of the fraction of dwarf galaxies with the clustercentric distance. Our conclusion is that the shape of the cluster LF is universal in all the magnitude ranges when the LF is calculated within the virial region. Moreover, the analysis of the composite cluster LF per morphological type, shows that the upturn and the steepening at the faint end of the LF is caused by dwarf early type galaxies. These systems are quite rare in low density regions and appear to be a typical cluster population. We provide evidence that the process responsible for creating the excess population of dwarf early type galaxies in clusters is a threshold process that occurs when the density exceeds $\sim 500$ times the critical density of the Universe. We interpret our results in the context of the 'harassment' scenario, where faint early-type cluster galaxies are predicted to be the descendants of tidally-stripped late-type galaxies. In the same context, we investigate whether the cluster total star formation rate ($\Sigma SFR$) depends on the cluster global properties for a sample of 90 very nearby clusters. The total cluster SFR is given by the sum of the SFR of all the cluster members within the virial region. It is found to be proportional to the number of cluster galaxies involved ($N_{gal}$). The best relation between the total SFR and the cluster mass reflects the $N_{gal}-M$ relation, which is a power law with exponent smaller than 1. As a consequence, the more massive a cluster, the lower its number of cluster galaxies and total SFR per unit mass. The mean SFR per cluster galaxy ($\Sigma SFR/N_{gal}$) is constant troughout our cluster sample and does not depend on the global properties of the system. Moreover, in order to account for projection effects, we study the galaxy surface number density profile in our cluster sample. We find that clusters of different mass exibit different profiles. In the low and intermediate mass systems the best fit is provided by a core King profile, with the core radius decreasing with cluster mass, until, at the highest cluster masses, the profile is better represented by a cuspy Navarro, Frenk \& White profile. All these different analysis converge to the conclusion that the global properties of the cluster galaxy population, such as the luminosity distribution, the galaxy type mix, the mean and total cluster SFR are only weakly dependent on the cluster mass and X-ray luminosity. This suggests that the gravitational processes and the interaction galaxy-ICM are not likely to affect those properties of the cluster galaxy population. Only the spatial distribution of the cluster galaxies depends on the cluster mass, probably reflecting the different relaxation status of systems of different masses. Instead, the variations of the LF and the galaxy type mix with the clustercentric distance reflect a link between the galaxy formation process and the galaxy-galaxy encounters, as suggested by the 'harassment' scenario. In the second part of the thesis, galaxy clusters are used as cosmological tool. The aim of this work is to elucidate which component, galaxies or ICM, traces better the cluster mass in order to understand whether different selection methods select the same cluster population. This will clarify which bias is introduced by the different selection methods in the results of the cosmological tests. This will clarify which bias is introduced by the different selection methods in the results of the cosmological tests. For this porpuse, we analyse as a first step the relation between the optical ($L_{op}$) and the X-ray ($L_X$) luminosity, respectively, to the cluster mass in the X-ray selected RASS-SDSS cluster sample. The main motivation in deriving these dependences is to evaluate $L_{op}$ and $L_X$, as predictors of the cluster mass and to compare the quality of the two quantities as predictors. Our analysis reveals that $L_{op}$ is a key measure of the cluster mass. In this respect, the optical luminosity performs even better than the X-ray luminosity, which suggests that the mass distribution of a cluster is better traced by cluster galaxies rather than by intracluster gas. On the other hand, our conclusion is at odds with the generally accepted view that a cluster main physical properties are more easily revealed in the X-ray than in the optical. Such a view was established at an epoch when the lack of optical wide field surveys precluded a reliable determination of the optical luminosities of a large sample of clusters. With the advent of the Sloan Digital Sky survey, this problem is now overcome. The application of the same analysis to an optically selected cluster sample (the Abell subsample) confirms the result. Neverthless, the Abell sample comprises a subpopulation of systems which scatter significantly in the $L_X-M$ relation and appear to be extremely X-ray underluminous (on average one order of magnitude) with regard to their mass. On the other hand, these systems do follow the general scaling relation between optical luminosity and virial mass. Therefore, we call them 'Abell X-ray Underluminous clusters' or AXU clusters for short. To understand the particular nature of these systems, we examine the properties of their galaxy population. The velocity distribution of the AXU clusters is Gaussian within the virial region but is leptokurtic (more centrally concentrated than a Gaussian) in the outskirts, as expected for the systems in accretion. In addition, the AXU clusters have a higher fraction of blue galaxies in the external region and show a marginally significant paucity of galaxies at the center. Our results seem to support the interpretation suggested by Bower et al. (1997) that the AXU clusters are systems in formation undergoing a phase of mass accretion. Their low X-ray luminosity should be due to the still accreting Intracluster gas or to an ongoing merging process. Our results give supports to the conclusion of Donahue et al. (2002) concerning the biases inherent in the selection of galaxy clusters in different wavebands. While the optical selection is prone to substantial projection effects, also the X-ray selection is not perfect or not simple to characterize. The existence of X-ray underluminous clusters, even with large masses, makes it difficult to reach the needed completeness in mass for cosmological studies. Clearly, a multi-waveband approach is needed for optimizing the completeness and reliability of clusters samples. The 'RASS-SDSS Galaxy Clusters Survey' series comprises 7 scientific papers which are inserted as part of the thesis. Four of the papers are accepted for pubblication on a scientific Journal ('Astronomy & Astrophysics') and three are submitted.