Fakultät für Physik - Digitale Hochschulschriften der LMU - Teil 03/05

This thesis is concerned with real mirror symmetry, that is, mirror symmetry for a Calabi-Yau 3-fold background with a D-brane on a special Lagrangian 3-cycle defined by the real locus of an anti-holomorphic involution. More specifically, we will study real mirror symmetry by means of compact 1-parameter Calabi-Yau hypersurfaces in weighted projective space (at tree-level) and non-compact local P2 (at higher genus).

For the compact models, we identify mirror pairs of D-brane configurations in weighted projective space, derive the corresponding inhomogeneous Picard-Fuchs equations, and solve for the domainwall tensions as analytic functions over moduli space, thereby collecting evidence for real mirror symmetry at tree-level. A major outcome of this part is the prediction of the number of disk instantons ending on the D-brane for these models.

Further, we study real mirror symmetry at higher genus using local P2. For that, we utilize the real topological string, that is, the topological string on a background with O-plane and D-brane on top. In detail, we calculate topological amplitudes using three complementary techniques. In the A-model, we refine localization on the moduli space of maps with respect to the torus action preserved by the anti-holomorphic involution. This leads to a computation of open and unoriented Gromov-Witten invariants that can be applied to any toric Calabi-Yau with involution. We then show that the full topological string amplitudes can be reproduced within the topological vertex formalism. Especially, we obtain the real topological vertex with trivial fixed leg. Finally, we verify that the same results arise in the B-model from the extended holomorphic anomaly equations, together with appropriate boundary conditions, thereby establishing local real mirror symmetry at higher genus. Significant outcomes of this part are the derivation of real Gopakumar-Vafa invariants at high Euler number and degree for local P2 and the discovery of a new kind of gap structure of the closed and unoriented topological amplitudes at the conifold point in moduli space.

Einige der spektakulärsten Beobachtungen unserer Milchstrasse zeigen die filamentären Strukturen in der Umgebung von heissen massereichen O-Sternen. Sobald diese Sterne beginnen zu leuchten, ionisiert ihre ultraviolette Strahlung das umgebende Gas und erzeugt eine heisse HII-Region. Das erhitzte Gas expandiert in die umgebende kalte Molekülwolke. Die dabei entstehende Schockwelle komprimiert das kalte Gas in die auffälligen Strukturen. An den Spitzen dieser Strukturen entstehen neue, masseärmere Sterne. Bis heute ist die präzise Entstehung dieser Regionen nicht vollständig verstanden.

Ziel dieser Arbeit ist die Simulation dieser Entwicklung anhand hydrodynamischer Methoden. Dazu wird ionisierende Strahlung in einen Smoothed Particle Hydrodynamics (SPH) Code namens VINE, der vollständig OpenMP-parallelisiert ist, implementiert. Für die Berechnung der Ionisation wird angenommen, dass die betrachtete Region so weit von dem Stern entfernt ist, dass die Strahlung näherungsweise plan-parallel eintrifft. Zunächst wird die Eintrittsfläche in gleich grosse Strahlen unterteilt. Dann wird die Ionisation entlang dieser Strahlen propagiert. Die neue Implementation ist vollständig parallelisiert und trägt den Namen iVINE.

Zuerst wird anhand mehrerer Tests die Übereinstimmung von iVINE mit bekannten analytischen Lösungen gezeigt. Danach wird der durch Ionisation induzierte gravitative Kollaps einer marginal stabilen Sphäre untersucht. In allen drei simulierten Fällen mit unterschiedlichem einfallenden ionisierenden Fluss kollabiert die Sphäre. Zusätzlich kann die beobachtete Tendenz, dass jüngere Sterne weiter entfernt von der Quelle der Ionisation entstehen, bestätigt werden.

Desweiteren werden Simulationen über den Einfluss ionisierender Strahlung auf turbulente Molekülwolken durchgeführt. Hier zeigt sich, dass die beobachteten, komplexen Strukturen durch die Kombination von Ionisation, Hydrodynamik und Gravitation reproduziert werden können. An den Spitzen der Strukturen wird das Gas stark komprimiert und kollabiert unter dem Einfluss seiner Eigengravitation, genau wie beobachtet. Gleichzeitig treibt die ionisierende Strahlung die Turbulenz im kalten Gas weit stärker als bisher angenommen. Anhand von einer Parameterstudie folgt, dass die entstehenden Strukturen kritisch von dem jeweiligen Anfangsstadium der Wolke zur Zeit der Zündung des O-Sterns abhängen. Dies ergibt die einmalige Gelegenheit, zusätzliche Informationen über Molekülwolken, die ansonsten schwierig zu beobachten sind, in den von O-Sternen stark illuminierten Regionen zu erhalten.

Die Implementation ionisierender Strahlung im Rahmen dieser

Doktorarbeit ermöglicht die Untersuchung der Einwirkung

massereicher Sterne auf ihre Umgebung in bislang Unerreichter Genauigkeit. Die durchgeführten Simulationen vertiefen unser Verständnis der Wechselwirkung von Turbulenz und Gravitation im Rahmen der Sternentstehung. Weitere erstrebenswerte Schritte wären die genauere Berücksichtigung der Kühlprozesse innerhalb der Molekülwolke und die Implementation der Winde massereicher O-Sterne.

Hurricanes are some of the most spectacular yet deadly natural disasters. Especially in times of the widely discussed anthropogenic climate change, public interest focusses on such extreme weather events. Nowadays, highly sophisticated numerical models are used for example for track prediction, but still there are many fundamental open

questions. Among these, the question how intense a tropical cyclone may become is of major interest.

In this work a study of the two most common types of models for the hurricane boundary layer is carried out. This study reveals major deficiencies of boundary layer models and finally leads to a reassessment of the established theory of potential intensity of hurricanes.

In chapter (2), a linear model for the hurricane boundary layer is derived from a detailed scale analysis of the full equations of motions. It is shown how analytic solutions for the model may be calculated and how these solutions may be used to appraise the integrity of the linear approximation. Some of the results of this chapter are published in Vogl and Smith (2009).

In chapter (3), a slab model is examined, which yields results for the main thermodynamic quantities. Depending on the chosen boundary layer depth and the imposed wind profile, two different types of solution behaviour found and interpreted. Other aspects of the dynamics and thermodynamics of the boundary layer are studied as for

example the influence of shallow convection. The limitations and strengths of the slab model are discussed at the end of chapter (3). The results are published in Smith and Vogl (2008).

The results of the detailed investigation of the linear and the slab model both point out an important deficiency of hurricane boundary layer models, namely the assumption

of gradient wind balance. In chapter (4) it is shown that indeed the major deficiency of the established hurricane (P)otential (I)ntensity theory is the tacit assumption of

gradient wind balance in the boundary layer. The results of chapter (4) show a fundamental problem of the established PI theory and then point to an improved conceptual model of the hurricane inner core region. Thus this work suggests a way forward to an urgently needed more consistent theory for the hurricane potential intensity. It is published in Smith, Montgomery and Vogl (2008).

The study of the interplay between interaction-induced correlations and nonequilibrium initial conditions in many-body systems has recently attracted a lot of attention. New experimental techniques provide high control over many-body systems and systematic access to their nonequilibrium regime. In many systems the nonequilibrium properties of a Fermi liquid can be relevant. A first approach to their understanding is the main content of this thesis.

At the beginning, nonequilibrium phenomena, Landau's theory of a

Fermi liquid, the Hubbard model, time evolution in quantum mechanics, related experiments, and the flow equation method are reviewed.

The key observation of this thesis, namely a characteristic mismatch of expectation values in equilibrium and nonequilibrium, is first illustrated for the squeezed oscillator. For this one-particle model Hamiltonian the perturbative approach can be compared with the exact

solution and it is shown that the mismatch holds even beyond perturbation theory. Afterwards these observations are generalized to a larger class of one-particle models.

Then the nonequilibrium behavior of a Fermi liquid is examined by analyzing the Fermi liquid phase of the Hubbard model in more than one dimension. After a sudden switch-on of a weak two-particle interaction to the noninteracting Fermi gas the relaxation of the many-body system is observed. For this purpose, the flow equation transformation is implemented for the Hubbard Hamiltonian. Then the discussion of the momentum distribution function and of the kinetic energy displays a three-step relaxation behavior of the Fermi liquid from the initial perturbation until thermalization is reached. Firstly, the sudden switch inserts

excitation energy into the system which drives the following dynamics. Then a rapid initial build-up of correlations is caused by initial dephasing and leads to the establishment of a quasiparticle picture. By that the system enters into a quasi-stationary state which can be long-lasting for weak interaction. This state shows prethermalization of the kinetic energy

which already has relaxed to its final values. However, the momentum distribution still resembles a zero temperature Fermi liquid. Its later relaxation on a second time scale is caused by a residual two-particle interaction which allows for scattering processes and can be

described by a quantum Boltzmann equation. The physical origin of this delayed relaxation can be traced back to an interplay of translational invariance of the Hubbard model and the Pauli principle for fermions; together they restrict the phase space for scattering events.

Comparing with similar work I conjecture on the generic nature of the findings made for the quenched Fermi liquid in other many-body systems.

Finally I point out to the potential relevance of the delayed relaxation for the observation of further nonequilibrium phenomena, for instance in BCS systems. In order to extend the study of sudden switching to arbitrary switching processes the calculation is repeated using the Keldysh perturbation theory. First evaluations for a linear increase of the interaction strength are given. Extensions of this work are suggested and may motivate further research.

Our desire to observe electron dynamics in atoms and molecules on their natural timescale with the tools of attosecond physics demands ever shorter laser pulse durations. The reliance of this young eld on laser pulses is understandable: both the generation and the characterization of attosecond pulses, as well as time-resolved measurements directly use the electrical field that lasts only for a few oscillations of the wave.

This also means that exerting control over the evolution of the waveform on a sub-cycle scale can modify the characteristics of attosecond pulses and possibly in a favorable way. In this thesis we introduce a laser system that provides near single-cycle laser pulses and generate through their interaction with gases coherent XUV radiation. Our measurements indicate that the thus produced XUV spectrum supports the potential compressibility to an isolated attosecond pulse of a sub-100 as duration. Considering our already broadband fundamental laser spectrum, we demonstrate moreover a technique to further enhance our spectral intensity in the blue. By frequency-doubling a part of the original spectrum, and controlling the time-delay between the two harmonic laser pulses we show that we can induce a change in the waveform on an attosecond time-scale, suppress or increase some half-cycles or change the effective wavelength of the laser light. Our method's influence on the generation of XUV light is tested via spectral characterization, and we found that broad tunability of the central XUV-energy is possible by a change of the time-delay between the fundamental and the second-harmonic laser pulses. Our results furthermore give strong evidence that waveform-dependent interference of two quantum-paths was observed, which effect comes from two electron-trajectories that are inside one half-cycle of the laser field.

It is also of utmost importance to know the level of control over the waveform. To characterize the waveform, we demonstrate here the first single-shot measurement of the carrier-envelope phase (CEP) of a lightpulse. We measured with no phase-ambiguity the CEP of high repetition-rate (3 kHz) non-phase-stabilized and phase-stabilized laser pulses consecutively with an unprecedented measurement precision. Our method uniquely requires no prior phase-stabilization. It opens the door to CEP-tagging with non-phase-stabilized pulses using emerging few-cycle laser systems with relativistic peak intensities.

In this work, gold and semiconductor nanoparticles are used as building blocks for nanostructures, in which energy transfer is investigated. Nanoparticles have size-dependent controllable optical properties. Therefore, they are interesting objects to study different aspects and applications of energy transfer.

Fluorescence quenching by gold nanoparticles is investigated and used to develop novel immunoassays for medically relevant molecules. The range of fluorescence quenching by gold nanoparticles is effective over longer distances than for dye molecules. The reason for this is the large absorption cross-section of gold nanoparticles and the radiative rate suppression of dyes caused by gold nanoparticles. The influence of gold nanoparticles on radiative and non-radiative rates of Cy3 and Cy3B dyes is studied here.

A competitive, homogeneous immunoassay for digoxigenin and digoxin, a drug used to cure heart diseases, is developed. Dye-labeled digoxigenin is bound to the gold nanoparticles functionalized with anti-digoxigenin antibodies, quenching the dye fluorescence. Unlabeled digoxigenin partially replaces the dye-labeled digoxigenin leading to an increase of fluorescence. The assay has a limit of detection of 0.5 nM in buffer and 50 nM in serum. Time resolved spectroscopy reveals that the quenching is due to energy transfer with an efficiency of 70%.

A homogeneous sandwich immunoassay for cardiac troponin T, an indicator of damage to the heart muscle, is developed. Gold nanoparticles and fluorophores are functionalized with anti-troponin T antibodies. In the presence of troponin T the nanoparticles and fluorophores form a sandwich structure, in which the dye fluorescence is quenched by a gold nanoparticle. The limit of detection of the immunoassay in buffer is 0.02 nM and 0.11 nM in serum. Energy transfer, with up to 95% efficiency, is responsible for the fluorescence quenching, as found through time resolved spectroscopy.

Energy transfer is demonstrated in clusters of CdTe nanocrystals assembled using three methods. In the first method, clusters of differently-sized water soluble CdTe nanocrystals capped by negatively charged mercaptoacid stabilizers are produced through electrostatic interactions with positively charged Ca(II) cations. The two other methods employ covalent binding through dithiols and thiolated DNA as linkers between nanocrystals. Energy transfer from smaller nanocrystals to larger nanocrystals in aggregates is demonstrated by means of steady-state and time-resolved photoluminescence spectroscopy, paving the way for nanocrystal-based light harvesting structures in solution.

Multi-shell onion-like CdSe/ZnS/CdSe/ZnS nanocrystals are presented. In these structures the CdSe core and the CdSe shell produce two emission peaks upon UV light excitation. When the emission peaks are well matched, the resulting emission appears as pure white light. The shade of the white light can be controlled by annealing the particles. Evidence for intra-nanocrystal energy transfer is presented.