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

Solar energy takes a leading role amongst renewable energies. For the planning of new solar power plants

the ISIS data set (Irradiance at the Surface derived from ISCCP cloud data) has been generated in

this study. For the first time a data set contains global and direct normal irradiance and is therefore

applicable for all kinds of solar power plants. The ISIS data set consists of 21 years of three-hourly

irradiances (1984-2004), which have been derived from International Satellite Cloud Climatology

Project (ISCCP) cloud data with the method that has been developed for this study. On the basis of the ISIS

data set long-term variability of global and direct normal irradiance has been investigated. The average

year to year variability of global irradiance within an ISIS grid box of 280 km x 280 km is 3%,

the variability of direct normal irradiance of 7% is more than twice as high. Through volcano eruptions

yearly averages of direct normal irradiance are reduced by 19% on average, yearly averages of global

irradiance are only reduced by 3%. Global irradiance shows no trend within the analysed time span, but

direct normal irradiance increases on average by 0.63% per year. As cause of these trends stratospheric

aerosol and changes in cloud amount and optical thickness of clouds could be identified.

In this thesis we study two quantum aspects of black holes, their entropy and the Hawking effect. First, we present a model for the statistical interpretation of black hole entropy and show that this entropy emerges as a result of missing information about the exact state of the matter from which the black hole was formed. We demonstrate that this idea can be applied to black holes made from both ultra-relativistic and nonrelativistic particles.

In the second part we focus our attention on several features of black hole evaporation. We discuss the dependence of the Hawking radiation on the vacuum definition of different observers. It becomes evident that in certain cases the choice of observer has an influence on the particle spectrum. In particular, we study the meaning of the Kruskal vacuum on the horizon. After that we determine the Hawking flux for nonstationary black holes. We find approximate coordinates which are regular on the time dependent horizon and calculate the particle density measured by an observer at infinity.

Finally, we derive the response of a particle detector in curved background. In our approach we use the Unruh detector to quantify the spectrum of radiation seen by general observers in Minkowski, Schwarzschild and Vaidya space-times. We find that an arbitrarily accelerated detector in flat space-time registers a particle flux with a temperature proportional to a time dependent acceleration parameter. A detector moving in Schwarzschild space-time will register a predominantly thermal spectrum with the exact temperature depending on the observer's trajectory. If the detector is located at constant distance from the black hole it measures a shifted temperature which diverges on the horizon. On the other hand, a detector in free fall towards the black hole does not register a thermal particle flux when it crosses the horizon. In this framework corrections to the temperature measured by a detector moving in Vaidya space-time are obtained as well. We argue that our result also clarifies the role of horizons in black hole radiation.

As of now, string theory is the best candidate for a theory of quantum gravity. Since it is anomaly–free only in ten space-time dimensions, the six surplus spatial dimensions must be compactified.

This thesis is concerned with the geometry of toroidal orbifolds and their applications in string theory. An orbifold is the quotient of a smooth manifold by a discrete

group. In the present thesis, we restrict ourselves to orbifolds of the form T^6 /Z_N or T^6 /Z_N × Z_M . These so–called toroidal orbifolds are particularly popular as compactification manifolds in string theory. They present a good compromise between a trivial compactification manifold, such as the T^6 and one which is so complicated that explicit calculations are nearly impossible, which unfortunately is the case for many if not most Calabi–Yau manifolds. At the fixed points of the discrete group which is divided out, the orbifold develops quotient singularities. By resolving these singularities via blow–ups, one arrives at a smooth Calabi–Yau manifold. The systematic method to do so is explained in detail. Also the transition to the Orientifold quotient is explained.

In string theory, toroidal orbifolds are popular because they combine the advantages of calculability and of incorporating many features of the standard model, such as non-Abelian gauge groups, chiral fermions and family repetition.

In the second part of this thesis, applications in string phenomenology are discussed. The applications belong to the framework of compactifications with fluxes in type

IIB string theory. Flux compactifications on the one hand provide a mechanism for supersymmetry breaking. One the other hand, they generically stabilize at least part

of the geometric moduli. The geometric moduli, i.e. the deformation parameters of the compactification manifold correspond to massless scalar fields in the low energy

effective theory. Since such massless fields are in conflict with experiment, mechanisms which generate a potential for them and like this fix the moduli to specific values

must be investigated. After some preliminaries, two main examples are discussed. The first belongs to the category of model building, where concrete models with realistic

properties are investigated. A brane model compactified on T^6 /Z_2 × Z_2 is discussed.

The flux-induced soft supersymmetry breakingparameters are worked out explicitly.

The second example belongs to the sub ject of moduli stabilization along the lines of the proposal of Kachru, Kallosh, Linde and Trivedi (KKLT). Here, in addition to the

background fluxes, non-perturbative effects serve to stabilize all moduli. In a second step, a meta-stable vacuum with a small positive cosmological constant is achieved.

Orientifold models which result from resolutions of toroidal orbifolds are discussed as possible candidate models for an explicit realization of the KKLT proposal.

The appendix collects the technical details for all commonly used toroidal orbifolds

and constitutes a reference book for these models.

In this thesis we investigate a large new class of four-dimensional supersymmetric string vacua defined as compactifications of the $E_8 \times E_8$ and the $SO(32)$ heterotic string on smooth Calabi-Yau threefolds with unitary gauge bundles and heterotic five-branes. This opens up the way for phenomenologically interesting string compactifications on simply connected manifolds in that the conventional gauge symmetry breaking via Wilson lines is replaced by the embedding of non-flat line bundles into the ten-dimensional gauge group.

The first part of the thesis discusses the implementation of this idea into the $E_8 \times E_8$ heterotic string. After specifying a large class of group theoretic embeddings featuring unitary bundles, we analyse the effective four-dimensional ${\cal N}=1$ supergravity upon compactification. The simultaneous presence of five-branes and abelian gauge groups requires the introduction of new anomaly cancelling counter terms into the effective action. These are also derived by an M-theory computation. The full set of Green-Schwarz terms allows for the extraction of the threshold corrections. From the gauge invariant K\"ahler potential for the moduli fields we derive a modification of the Fayet-Iliopoulos D-terms arising at one-loop in string perturbation theory. From this we conjecture a one-loop deformation of the Hermitian Yang-Mills equation and introduce the idea of $\lambda$-stability as the perturbatively correct stability concept generalising the notion of Mumford stability valid at tree-level.

We then proceed to a definition of $SO(32)$ heterotic vacua with unitary gauge bundles in the presence of heterotic five-branes and find agreement of the resulting spectrum with the S-dual framework of Type I/Type IIB orientifolds. A similar analysis of the effective four-dimensional supergravity is performed. Further evidence for the proposed one-loop correction to the stability condition is found by identifying the heterotic corrections as the S-dual of the perturbative part of $\Pi$-stability as the correct stability concept in Type IIB theory.

After reviewing the construction of holomorphic stable vector bundles on elliptically fibered Calabi-Yau manifolds via spectral covers, we provide semi-realistic examples for $SO(32)$ heterotic vacua with Pati-Salam and MSSM-like gauge sectors. These can be viewed, by S-duality, as the generalisation of toroidal magnetized $D9$-branes to non-abelian braneworlds on genuine Calabi-Yau manifolds.

We finally discuss the construction of realistic vacua with flipped $SU(5)$ GUT and MSSM gauge group within the $E_8 \times E_8$ framework, based on the embedding of line bundles into both $E_8$ factors. Some of the appealing phenomenological properties of this stringy realisation of flipped $SU(5)$ models, in particular stability of the proton, are discussed. MSSM-like gauge coupling unification is possible for the threshold corrected gauge couplings. We explicitly construct a couple of supersymmetric string vacua in both setups with precisely the three observed chiral matter generations and without any exotic chiral states.

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 deta