Fakultät für Physik - Digitale Hochschulschriften der LMU - Teil 04/05 Archiv

This thesis treats the classical simulation of strongly-interacting many-body quantum-mechanical systems in more than one dimension using matrix product states and the more general tensor product states. Contrary to classical systems, quantum many-body systems possess an exponentially larger number of degrees of freedom, thereby significantly complicating their numerical treatment on a classical computer. For this thesis two different representations of quantum many-body states were employed. The first, the so-called matrix product states (MPS) form the basis for the extremely successful density matrix renormalization group (DMRG) algorithm. While originally conceived for one-dimensional systems, MPS are in principle capable of describing arbitrary quantum many-body states. Using concepts from quantum information theory it is possible to show that MPS provide a representation of one-dimensional quantum systems that scales polynomially in the number of particles, therefore allowing an efficient simulation of one-dimensional systems on a classical computer. One of the key results of this thesis is that MPS representations are indeed efficient enough to describe even large systems in two dimensions, thereby enabling the simulation of such systems using DMRG. As a demonstration of the power of the DMRG algorithm, it is applied to the Heisenberg antiferromagnet with spin $S = 1/2$ on the kagome lattice. This model's ground state has long been under debate, with proposals ranging from static spin configurations to so-called quantum spin liquids, states where quantum fluctuations destroy conventional order and give rise to exotic quantum orders. Using a fully $SU(2)$-symmetric implementation allowed us to handle the exponential growth of entanglement and to perform a large-scale study of this system, finding the ground state for cylinders of up to 700 sites. Despite employing a one-dimensional algorithm for a two-dimensional system, we were able to compute the spin gap (i.e. the energy gap to the first spinful excitation) and study the ground state properties, such as the decay of correlation functions, the static spin structure factors, and the structure and distribution of the nearest-neighbor spin-spin correlations. Additionally, by applying a new tool from quantum information theory, the topological entanglement entropy, we could also with high confidence demonstrate the ground state of this model to be the elusive gapped $Z_2$ quantum spin liquid with topological order. To complement this study, we also considered the extension of MPS to higher dimensions, known as tensor product states (TPS). We implemented an optimization algorithm exploiting symmetries for this class of states and applied it to the bilinear-biquadratic-bicubic Heisenberg model with spin $S=3/2$ on the $z=3$ Bethe lattice. By carefully analyzing the simulation data we were able to determine the presence of both conventional and symmetry-protected topological order in this model, thereby demonstrating the analytically predicted existence of the Haldane phase in higher dimensions within an extended region of the phase diagram. Key properties of this symmetry-protected topological order include a doubling of the levels in the entanglement spectrum and the presence of edge spins, both of which were confirmed in our simulations. This finding simultaneously validated the applicability of the novel TPS algorithms to the search for exotic order.

Die Forschungsergebnisse der letzten Jahre haben gezeigt, dass das Universum bei weitem nicht nur aus baryonischer Materie besteht. Tatsächlich scheinen 72% aus sogenannter Dunkler Energie zu bestehen, während selbst vom verbleibenden Teil nur etwa ein Fünftel baryonischer Materie zugeordnet werden kann. Der Rest besteht aus Dunkler Materie, deren Beschaffenheit bis heute nicht mit Sicherheit geklärt ist. Ursprünglich in den Rotationskurven von Spiralgalaxien beobachtet, wurde die Notwendigkeit ihrer Existenz inzwischen auch in elliptischen Galaxien und Galaxienhaufen nachgewiesen. Tatsächlich scheint Dunkle Materie eine entscheidende Rolle in der Strukturbildung im Universum gespielt zu haben. In der Frühzeit des Universums, als die Materieverteilung im Weltraum noch äußerst gleichmäßig war und nur sehr geringe Inhomogenitäten aufwies, bildeten sie die Kondensationskeime für den gravitativen Kollaps der Materie. Numerische Simulationen haben gezeigt, dass der heute beobachtbare Entwicklungszustand des Universums erst durch die zusätzliche Masse Dunkler Materie ermöglicht wurde, die den strukturellen Kollaps erheblich beschleunigte und nur dadurch zur heute beobachtbaren Komplexität der Strukturen führen konnte. Da Dunkle Materie nicht elektromagnetisch wechselwirkt, sondern sich nur durch ihre Schwerkraft bemerkbar macht, stellt der Gravitationslinseneffekt eine ausgezeichnete Methode dar, die Existenz und Menge an Dunkler Materie nachzuweisen. Der schwache Gravitationslinseneffekt macht sich zu Nutzen, dass die intrinsischen Orientierungen der Galaxien im Weltraum keine Vorzugsrichtung haben, gleichbedeutend mit ihrer statistischen Gleichverteilung. Die gravitationsbedingte kohärente Verzerrung der Hintergrundobjekte führt zu einer Abweichung von dieser Gleichverteilung, die von den Eigenschaften der Gravitationslinsen abhängt und daher zu deren Analyse genutzt werden kann. Diese Dissertation beschreibt die Galaxy-Galaxy-Lensing-Analyse von insgesamt 89 deg^2 optischer Daten, die im Rahmen des CFHTLS-WIDE-Surveys beobachtet wurden und aus denen im Rahmen dieser Arbeit photometrische Rotverschiebungs- und Elliptizitätskataloge erzeugt wurden. Das Galaxiensample besteht aus insgesamt 5×10^6 Linsen mit Rotverschiebungen von 0.05 < z_phot ≤ 1 und einem zugehörigen Hintergrund von insgesamt 1.7×10^6 Quellen mit erfolgreich gemessenen Elliptizitäten in einem Rotverschiebungsintervall von 0.05 < z_phot ≤ 2. Unter Annahme analytischer Galaxienhaloprofile wurden für die Galaxien die Masse, das Masse-zu-Leuchtkraft-Verhältnis und die entsprechenden Halomodellprofilparameter sowie ihre Skalenrelationen bezüglich der absoluten Leuchtkraft untersucht. Dies geschah sowohl für das gesamte Linsensample als auch für Linsensamples in Abhängigkeit des SED-Typs und der Umgebungsdichte. Die ermittelten Skalenrelationen wurden genutzt, um die durchschnittlichen Werte für die Galaxienhaloparameter und eine mittlere Masse für die Galaxien in Abhängigkeit ihres SED-Typs zu bestimmen. Es ergibt sich eine Gesamtmasse von M_total = 23.2+2.8−2.5×10^11 h^{−1} M_⊙ für eine durchschnittliche Galaxie mit einer Referenzleuchtkraft von L∗ = 1.6×10^10 h^{−2} L_⊙. Die Gesamtmasse roter Galaxien bei gleicher Leuchtkraft überschreitet diejenige des entsprechenden gemischten Samples um ca. 130%, während die mittlere Masse einer blauen Galaxie ca. 65% unterhalb des Durchschnitts liegt. Die Gesamtmasse der Galaxien steigt stark mit der Umgebungsdichte an, betrachtet man die Geschwindigkeitsdispersion ist dies jedoch nicht der Fall. Dies bedeutet, dass die zentrale Galaxienmateriedichte kaum von der Umgebung sondern fast nur von der Leuchtkraft abhängt. Die Belastbarkeit der Ergebnisse wurde von zu diesem Zweck erzeugten Simulationen bestätigt. Es hat sich dabei gezeigt, dass der Effekt mehrfacher gravitativer Ablenkung an verschiedenen Galaxien angemessen berücksichtigt werden muss, um systematische Abweichungen zu vermeiden.

This work is focused on the search for intermediate-mass black holes (IMBHs) in the centers of globular clusters. It has been demonstrated that supermassive black holes (SMBHs) at the centers of galaxies show a tight correlation between their mass (M•) and the velocity dispersion (σ) of the galaxy. Investigating this M• − σ and similar correlations is crucial to constrain scenarios of galaxy formation and evolution. If they formed by runaway collisions of massive stars in young and dense stellar clusters, IMBHs could still be present in the centers of globular clusters, today. We measured the inner kinematic profiles for a sample of 9 galactic globular clusters using integral-field spectroscopy and combined them with existing outer kinematics and photom- etry obtained form HST archive images. In order to constrain the mass of a possible black hole we applied analytical Jeans models in combinations with varying M/LV profiles to each of the clusters. The results of these fits range from strong hints towards an IMBH (e.g. NGC 6388) to globular clusters which do not show any indications of a rising velocity dis- persion profile in their center (e.g. NGC 2808). Furthermore, the discovery of two high velocity stars in NGC 2808 opened another opportunity to study the internal kinematics of this particular cluster and indicates a high number of stellar-mass black holes in NGC 2808. We finally combined our results with measurements from the literature and investigated known scaling relations for SMBHs in galaxies (e.g. M• − σ) at the low-mass end by plac- ing the results and upper limits of IMBH measurements on these correlations. We found that IMBHs follow similar, but more shallow correlations of their mass and the properties of their host systems. This might be caused with the severe mass-loss the cluster suffers during its life time. In addition we ran numerical N-body simulations and compared globular clusters with dif- ferent black-hole retention fractions, IMBH masses and binary fractions. We found that IMBHs lead to a higher ejection rate of massive stars so that clusters with less depleted mass functions might therefore be good candidates to host IMBHs at their centers. In the future more N-body simulations will be performed in order to reproduce our observations in a more sophisticated way and perform crucial tests to our observing and analysis methods. The search for IMBHs requires both high spatial and spectral resolution and will remain at the edge of feasibility. However, it is crucial to continue the investigations in order to shed light on black-hole formation and growth.

This work focuses on the interaction of few-cycle laser pulses with nanosystems. Special emphasis is placed on the spatio-temporal evolution of the induced near-fields. Measurements on carrier-envelope-phase (CEP) controlled photoemission from isolated SiO2 nanospheres are taken by single-shot velocity map imaging (VMI) combined with CEP tagging. The obtained photoelectron spectra show a pronounced dependence on the CEP and extend to unexpectedly high energies. Comparison with numerical simulations identify the additional Coulomb forces of the liberated electron cloud as an effective additional acceleration mechanism for distinct trajectories. For larger spheres, an asymmetry in the field distribution is classically predicted. This asymmetry is also observed in the photoelectron momentum distributions. The mapping between position and momentum space in the VMI approach are investigated by analyzing the correlation of the photoelectron's birth and detection position. In a second set of experiments, photoemission at intensities exceeding 10^14 W/cm^2 from isolated nanospheres of different composition (SiO2, ZrO2, TiO2, Si, Au) is examined by stereo time-of-flight spectroscopy. It is found that the measured cutoff energies scale non-linearly with laser intensity depending on the material properties of the nanosystem. A trend towards a unified behavior for high intensities is observed indicating a drastic change in optical properties within the duration of the few-cycle laser pulse. The charge carrier generation mechanisms that could lead to such a transient effect are discussed. For a better understanding of the interaction of few-cycle fields with nanosystems, a direct access to the temporal evolution of (plasmonic) near-fields is highly desirable. The efforts on the realization of nanoplasmonic attosecond streaking spectroscopy are presented. Numerical simulations are used to identify the influence of the inhomogeneous near-field distributions on the streaking process. First experimental results obtained from Au nanotips show clear streaking features of sub-micron localized near-fields. The near-field oscillations are found to be phase offset as compared to reference measurements. The exact origin of the streaking features of the Au tip and possible improvements of the experimental approach are discussed.

Ein bedeutender Teilbereich der Nanomechanik beschäftigt sich mit der Erforschung kleiner, schwingender Systeme, welche aufgrund ihrer geringen Massen auf minimale Umgebungseinflüsse reagieren. Dies macht derartige nanoskalige Resonatoren zu äußerst empfindlichen Sensoren. Die fortschreitende Miniaturisierung nanomechanischer Systeme erfordert nun einerseits die Weiterentwicklung von Antriebs- und Detektionsmechanismen, andererseits spielt die Verbesserung der mechanischen Güte eine zentrale Rolle für die Erhöhung der Empfindlichkeit möglicher sensorischer Anwendungen. Hierfür ist die Untersuchung der Mechanismen, welche die mechanische Dämpfung der Resonatoren verursachen, erforderlich. Um das Dämpfungsverhalten eines beidseitig eingespannten nanomechanischen Siliziumnitridresonators zu untersuchen und zu kontrollieren wird in dieser Arbeit ein Rasterkraftmikroskop (AFM) eingesetzt. Dessen Spitze wird mit dem Resonator in Kontakt gebracht und beeinflusst als lokale Störung kontrolliert das nanomechanische System. Das AFM bildet hierbei einen mechanischen Punktkontakt mit der Aufhängung des Resonators aus, wodurch Schwingungsenergie vom Resonator in die AFM-Spitze abgeleitet wird. Aufgrund der hervorragenden räumlichen Auflösung des Rasterkraftmikroskops ist es somit möglich den ortsaufgelösten Energiefluss zwischen den beiden Systemen zu untersuchen. Hierfür wird die mechanische Resonanz der Siliziumnitridsaite im Radiofrequenzbereich mittels eines heterodynen Überlagerungsverfahrens elektrisch ausgelesen. Die Bewegung des zwischen zwei Goldelektroden platzierten Resonators ruft eine Kapazitätsänderung des durch die Elektroden gebildeten Kondensators hervor. Durch Kopplung an einen Mikrowellenschwingkreis kann diese Kapazitätsänderung ausgelesen werden. Zudem können Gleich- und Wechselspannungen an die Elektroden angelegt werden, wodurch einerseits die Resonanzfrequenz des Resonators verstimmt und andererseits die mechanische Bewegung angetrieben werden kann. Das derart angetriebene nanomechanische System kann nun unter Einfluss der lokalen Störung durch das AFM in positions- und kraftabhängigen Messungen untersucht werden. Es zeigt sich, dass der Energietransfer durch den mechanischen Punktkontakt einen äußerst starken Einfluss auf die mechanische Güte des Siliziumnitridbalkens hat, seine Resonanzfrequenz jedoch nur geringfügig beeinflusst wird. Dies kann durch eine Änderung der mechanischen Impedanzanpassung des Resonators an seine Umgebung erklärt werden. Die Impedanzänderung durch den mechanischen Punktkontakt ermöglicht den Übergang eines stark fehlangepassten nanomechanischen Systems hoher Güte zu einem angepassten System niedriger Güte auf einem einzigen Resonator. Hierbei bleibt die intrinsische Dämpfung des Resonators unverändert und die zusätzlich induzierte Dämpfung kann der Abstrahlung von Vibrationsenergie in die Umgebung zugeschrieben werden. Resonatoren hoher Güte ergeben sich somit als Systeme mit möglichst großer Fehlanpassung der mechanischen Impedanz. Desweiteren kann mit dieser Methode das in den Aufhängepunkt des Resonators hineinreichende Verzerrungsfeld abgebildet werden. Dies ermöglicht die Untersuchung gekoppelter Moden des Resonators sowie deren Modenform.

Birds fly, cells crawl and bacteria swim. Each of these individuals has their own propulsion mechanism leading to a persistent motion, hence they all belong to the class referred to as propelled particle systems. Propelled particles in large number typically exhibit impressive self-organization processes such as the flocking motion of birds, the coherent motion of cell colonies and the swarming of bacteria. The emergence of collective motion in these non-equilibrium systems constitutes a ubiquitous phenomenon in nature—and perhaps one of the most fascinating. One reason for this might be the emergence of highly dynamic, coherently moving spatial patterns such as clusters, swirls or waves, and the fact that the patterns commonly extend over length scales much larger than the size of the individuals. To elucidate the physical principles underlying the collective motion of these particles, numerous theoretical studies have been devoted to model propelled particle systems by approaching the problem on all levels of description. These range from particle-based simulations to kinetic theory and hydrodynamic models. However, these models were typically inspired by the idea of universality and tended to analyze the generic non-equilibrium phenomena in propelled particle systems, thereby obscuring a one-to-one relation to experimental studies. This thesis focusses on theoretical modeling approaches for propelled particle systems that are either in qualitative or quantitative agreement with recent observations and mea- surements in experimental propelled particle systems. Two experimental systems are specifically considered: The actin gliding assay, where molecular motors, immobilized on a substrate, propel actin filaments, and the polar vibrated disk assay, where disk-like gran- ular particles with a built-in polar asymmetry are driven by vertical vibrations. By means of various theoretical tools including rule-based automaton models, numerical solution of Newtonian equations of motion, and kinetic theory, the following central new findings and insights within the field of propelled particle systems were discovered: Anomalously strong curvature fluctuations of single actin filaments moving in the glid- ing assay arise from two different interactions with the molecular motors. The motors either “Push” or “Hold” locally, giving rise to persistent movement or localized jams, which, in turn, lead to pronounced curvature kinks. Interestingly, both excitation and relaxation of curvature originates from these interactions, and it is shown that the impact of thermal fluctuations on the curvature distribution is negligible compared to these active fluctua- tions. At high densities, filaments in the gliding assay form beautiful patterns of coherent motion such as clusters, swirls and waves. These patterns were shown to be triggered by local “ferromagnetic”-like alignment interactions between the filaments. In the later stages of pattern formation, hydrodynamic interactions become relevant. Coherently moving clus- ters induce a back-flow in the overlying fluid, mediating a ‘repulsive’ cluster–cluster or cluster–boundary interaction. With the addition of crosslinking molecules to the gliding assay at high filament densities, an absorbing state comprised of open and closed rings can form. The assembly dynamics is fully understood in terms of a competition between merging events of filaments and filament growth that freezes the curvature. Specifically, by means of an appropriate particle-based model, the statistical properties of the system, such as the characteristics of the ring radii distribution and the ratio of open to closed rings as a function of the system’s noise level, was qualitatively reproduced. The vibrated polar disk assay has a size of only about 20 particle diameters —a fact which precludes definitive conclusions on the nature of the underlying phase transition to a polarized state of coherent motion. By means of a microscopic model, the experimental single particle motion, the details of binary collisions and the collective dynamics in the confined geometry were quantitatively reproduced. Specifically, we matched all properties of the persistent random walk such as average speed, amplitude and spectrum of orien- tational and velocity fluctuations. Agreement between the characteristics of the collisions described by the model and those measured in the experiment, were verified by comparing the probability distributions for collision extension and time. Finally, collective properties were studied and likened by considering the average polarization within some restricted area, again confirming a very good agreement between model and experiment. The quan- titive match of all details of the experimental dynamics allowed us to use our models to scale up the vibrated polar disk assay in-silico, proving that a long-range polar ordered state would develop in the vibrated disk assay in the absence of boundaries. Moreover, a generic automaton model for propelled particles was employed to analyze the onset of collective motion in time. The central finding is that collective motion close to the transition is induced by nucleation of a cluster of sufficiently large mass, and not by a wide-spread coarsening process of polarized domains. In particle-conserving, propelled particle systems wave-like patterns generically emerge close to the phase boundary. Considering kinetic theory, there are clear indications that wave-like patterns cannot exist in the absence of particle conservation. Moreover, kinetic theory for propelled particle systems is found to be restricted to weak aligning systems, whereby post-collision angles are only slightly reduced with respect to pre-collision orientations. This conclusion was obtained by extending kinetic theory for propelled particle systems with respect to significant qualitative features of collisions ob- served in experimental propelled particle systems. Since kinetic theory predicts disorder for regimes in which real (experimental) systems exhibit order, the inherent restrictions of kinetic theory to weak aligning systems could be elucidated. Furthermore, using a set of Newtonian equations of motion for propelled, dissipative col- loids, we found that near the phase boundary, the microscopic states from which collective motion develops are not free of orientational correlations, i.e. the assumption of molecular chaos that is commonly applied in kinetic theory is not valid for propelled particle sys- tems at the onset of collective motion. Most importantly, the ensuing correlations at the onset are —for the aforementioned system— a qualitative prerequisite for kinetic theory to predict a phase transition to collective motion at all. This conclusion was made pos- sible by quantitatively connecting the details of the microscopic collision process with the mesoscopic kinetic description, in turn allowing for a quantitative test of the predictions of kinetic theory. If the aforementioned correlations are implemented into the kinetic ap- proach, the prediction of kinetic theory for the phase boundary quantitatively coincides with the one obtained from the underlying microscopic Newtonian particle dynamics in the regime of low packing fractions. Finally, an appropriate particle-based model for propelled particle systems at large packing fractions was analyzed in detail. Upon characterizing the degree of bond orienta- tional and translational order, the following generic states were identified: An unpolarized active crystal state with long-ranged orientational and translational order, and a polycrys- talline state, which coherently flows and is composed of hexagonal domains. It was shown that the underlying ordering transitions are defect–mediated. Most of the results of this thesis exemplify the importance of a one-to-one comparison between theoretical models and experimental studies in order to advance our understanding of propelled particle systems. Rather than adopting a generic approach, the central goal of this thesis is to develop both a bottom-up modeling framework as well as an experiment- specific one. This formulation advances our understanding of the physics of two specific experimental propelled particle systems and hopefully will serve as a starting point for investigations of the dynamics in other active systems such as moving cells and bacteria.

The petawatt field synthesizer (PFS) is a high-power optical parametric chirped-pulse amplification (OPCPA) system under development, which aims at generating fewcycle pulses with high energies of several Joule. The availability of light pulses with these unique parameters will enable an efficient generation of even shorter attosecond pulses with significantly higher photon flux than achievable today [1]. Not only the real-time observation, but also the control of charge transfer in molecular systems will become feasible for the first time [2]. The technique for realizing the ambitious PFS specifications is short-pulse pumped OPCPA in mm-thin crystals. The reduced crystal thickness allows for ultra-broadband amplification. The pump-pulse duration is reduced to a picosecond—compared to 100 ps to nanosecond pump-pulse duration in conventional high power OPCPA systems. The shortened pulse duration facilitates higher pump intensities whereby an efficient amplification in the mm-thin crystals is achieved. The demonstration of this novel scheme in the PFS project will allow its use in the extreme light infrastructure (ELI)[3]—a pan-European high-power laser project. Based on the PFS technology for the front end, the ELI will generate exawatt peakpower pulses and therefore facilitate the study of laser-matter interaction in an unprecedented intensity range [4]. This work describes the CPA-aspects of a suitable chirped pulse amplification (CPA) pump laser for the PFS OPCPA system. The diode-pumped Yb:YAG amplifiers up to an energy of 300 mJ (at 1030 nm) are presented in combination with the dispersion management. The application of spectral-amplitude shaping in conjunction with an Yb:glass amplifier with broader bandwidth than Yb:YAG enables an unprecedented bandwidth of 3.5nm in the Yb:YAG amplifier at this energy level. Simulations show that a similar bandwidth can be maintained for the full amplifier system. The pulses with 200 mJ could be compressed to 900 fs, close to the transform limit. Later changes in the stretcher increase the bandwidth more and compression down to 740 fs is demonstrated. To date, these are the highest peak power pulses generated in Yb:YAG. For the application as OPCPA pump, the so generated pulses are frequency doubled in a DKDP crystal. Another key aspect of this work is the synchronization of the OPCPA pump and signal pulses. In spite of optical synchronization of both pulses, a large timing fluctuation between these pulses is measured at the first OPCPA stage. The high accuracy jitter measurement setup and a series of measurements, which showed that the stretcher/compressor setup is the main source of jitter, are presented. Theoretical investigations yield that the optical delay in a compressor is orders of magnitude more sensitive to angle changes compared to free space propagation. This makes the stretcher and compressor extremely sensitive for timing jitter caused by turbulent air or mechanical instabilities. This novel insight helped us to significantly reduce the jitter to 100 fs and to demonstrate the feasibility of the PFS concept with first broad-band OPCPA experiments.

Massive gravity is a particular theoretical model that modifies gravity on cosmological scales and therefore could provide a dynamical explanation for the observed accelerated expansion of our Universe. In this thesis we investigate various theoretical problems of massive gravity, important for its consistency and phenomenological viability. It is known that the predictions from the linearized massive gravity contradict the predictions of General Relativity. It is, however, an artifact due to the breakdown of the perturbative expansion in the massless limit. In our work we investigate this problem in the diffeomorphism invariant formulation of massive gravity in which the graviton mass term is written in terms of four scalar fields. We determine the so-called Vainshtein scale below which the scalar modes of the massive graviton enter the non-perturbative regime for a wide class of non-linear mass terms. We find the asymptotic solutions of the spherically symmetric gravitational field below and above the Vainshtein radius, and show that massive gravity goes smoothly to the General Relativity below this scale. We also determine the corresponding corrections to the Newton potential. In general, any non-linear extension of the quadratic graviton mass term propagates the Boulware-Deser ghost. The only theory in which the ghost is not propagating in the high energy decoupling limit, is the de Rham-Gabadadze-Tolley theory. Here we show that the ghost arises in the fourth order of perturbations in this theory away from the decoupling limit. However, we further argue that the ghost can be avoided in the full non-linear theory if not all four scalar fields propagate independent degrees of freedom. In particular, we investigate the simple example of (1+1)-dimensional massive gravity and find that the theory exhibits a gauge symmetry, which reduces the number of degrees of freedom. We also generalize the diffeomorphism invariant formalism of massive gravity to arbitrary curved backgrounds. We find that, given a specific background metric, the resulting generally covariant massive gravity exhibits an internal symmetry in the configuration space of the scalar fields. The symmetry transformations of the scalar fields are given by the isometries of the reference metric. In particular, we investigate massive gravity on de Sitter space in this formalism. We confirm the known result that, in the case when the graviton mass is related to the cosmological constant as m^2=2\Lambda/3, the theory is partially massless and propagates only four degrees of freedom.

In der vorliegenden Arbeit wird mit Hilfe der verallgemeinerten Eichtheorie/Gravitations-Dualität, welche stark gekoppelte Eichtheorien mit schwach gekrümmten gravitativen Theorien verbindet, stark korrelierte Quantenzustände der Materie untersucht. Der Schwerpunkt liegt dabei in Anwendungen auf Systeme der kondensierten Materie, insbesondere Hochtemperatur-Supraleitung und kritische Quantenzustände bei verschwindender Temperatur. Die Eichtheorie/Gravitations-Dualität entstammt der Stringtheorie und erlaubt eine Umsetzung des holographischen Prinzips. Aus diesem Grund wird eine kurze Einführung in die Konzepte der Stringtheorie und ihre Auswirkungen auf das holographische Prinzip gegeben. Für das tiefere Verständnis der effektiven Niederenergie-Feldtheorien wird zusätzlich die Supersymmetrie benötigt. Ausgestattet mit einem robusten Stringtheorie-Hintergrund wird die unterschiedliche Interpretation der Dirichlet- oder D-Branen, ausgedehnte Objekte auf denen offene Strings/Fäden enden können, diskutiert: Zum einen als massive solitonische Lösungen der Typ II Supergravitation und auf der anderen Seite, ihre Rolle als Quelle für supersymmetrische Yang-Mills Theorien. Die Verbindung dieser unterschiedlichen Betrachtungsweise der D-Branen liefert eine explizite Konstruktion der Eichtheorie/Gravitations-Dualität, genauer der AdS_5/CFT_4 Korrespondenz zwischen der N=4 supersymmetrischen SU(N_c) Yang-Mills Theorie in vier Dimensionen mit verschwindender beta-Funktion in allen Ordnungen, also eine echte konforme Theorie, und Type IIB Supergravitation in der zehn dimensionalen AdS_5 X S^5 Raumzeit. Darüber hinaus wird das Wörterbuch, das zwischen den Operatoren der konformen Feldtheorie und den gravitativen Feldern übersetzt, im Detail eingeführt. Genauer gesagt, die Zustandssumme der stark gekoppelten N=4 supersymmetrischen Yang-Mills Theorie im Grenzwert großer N_c, ist identisch mit der Zustandssumme der Supergravitation unter Berücksichtigung der zugehörigen Lösungen der Bewegungsgleichungen, ausgewertet am Rand des AdS-Raumes. Die Anwendung der perturbativen Quantenfeldtheorie und die Verbindungen zur quantenstatistischen Zustandssumme erlaubt die Erweiterung des holographischen Wörterbuchs auf Systeme mit endlichen Dichten und endlicher Temperatur. Aus diesem Grund werden alle Aspekte der Quantenfeldtheorie behandelt, die für die Anwendung der ``Linear-Response''-Theorie, der Berechnung von Korrelationsfunktionen und die Beschreibung von kritischen Phänomenen benötigt werden, wobei die Betonung auf allgemeine Zusammenhänge zwischen Thermodynamik, statistischer Physik bzw. statistischer Feldtheorie und Quantenfeldtheorie liegt. Des Weiteren wird der Renormierungsgruppen-Formalismus zur Beschreibung von effektiven Feldtheorien und kritischen Phänomene im Kontext der verallgemeinerten Eichtheorie/Gravitations-Dualität ausführlich dargelegt. Folgende Hauptthemen werden in dieser Arbeit behandelt: Die Untersuchung der optischen Eigenschaften von holographischen Metallen und ihre Beschreibung durch das Drude-Sommerfeld Modell, ein Versuch das Homes'sche Gesetz in Hochtemperatur-Supraleitern holographisch zu beschreiben indem verschiedene Diffusionskonstanten und zugehörige Zeitskalen berechnet werden, das mesonische Spektrum bei verschwindender Temperatur und schlussendlich holographische Quantenzustände bei endlichen Dichten. Entscheidend für die Anwendung dieses Rahmenprogramms auf stark korrelierte Systeme der kondensierten Materie ist die Renormierungsgruppenfluss-Interpretation der AdS_5/CFT_4 Korrespondenz und die daraus resultierenden emergenten, holographischen Duale, welche die meisten Beschränkungen der ursprünglichen Theorie aufheben. Diese sogenannten ``Bottom-Up'' Zugänge sind besonders geeignet für Anwendungen auf Fragestellungen in der Theorie der kondensierten Materie und der ``Linear-Response''-Theorie, mittels des holographischen Fluktuations-Dissipations-Theorem. Die Hauptergebnisse der vorliegenden Arbeit umfassen eine ausführliche Untersuchung der R-Ladungs-Diffusion und der Impulsdiffusion in holographischen s- und p-Wellen Supraleitern, welche durch die Einstein-Maxwell Theorie bzw. die Einstein-Yang-Mills Theorie beschrieben werden, und eine Vertiefung des Verständnisses der universellen Eigenschaften solcher Systeme. Als zweites wurde die Stabilität der kalten holographischen Quantenzustände der Materie untersucht, wobei eine zusätzliche Diffusions-Mode entdeckt wurde. Diese Mode kann als eine Art ``R-Spin-Diffusion'' aufgefasst werden, die der Spin-Diffusion in Systemen mit frei beweglichen ``itineranten'' Elektronen ähnelt, wobei die Entkopplung der Spin-Bahn Kopplung die Spin-Symmetrie in eine globale Symmetrie überführt. Das Fehlen der Instabilitäten und die Existenz einer ``Zero-Sound'' Mode, bekannt von Fermi-Flüssigkeiten, deuten eine Beschreibung der kalten holographischen Materie durch eine effektive hydrodynamische Theorie an.

Self-assembled InGaAs quantum dots are nano-objects embedded in the solid-state matrix of GaAs. They act as natural potential traps for charge carriers and feature a number of quantized states due to the quantum confinement. When incorporated in a field effect structure the quantum dot states can be conveniently manipulated with an electric field and probed by resonant laser spectroscopy. In this thesis self-assembled quantum dots were investigated with an emphasis on the study of interactions between localized quantum dot states and charge or spin reservoirs in the environment. Experimentally the quantum dots were addressed in distinct regimes where the quantum dot spectrum was sensitive to individual charge fluctuations or mesoscopic reservoirs. The fundamental transition of a neutral quantum dot was found to exhibit a number of discontinuities in the usually linear dispersion of the exciton energy in external electrostatic fields. The discontinuities were identified to arise from charge fluctuations in the surrounding crystalline matrix in which impurity atoms can capture or release electrons. At characteristic conditions charging and discharging events lead to discrete changes of the electrostatic environment which in turn gives rise to an energy shift of the optical resonance condition. An electrostatic model was developed for a quantitative analysis of charging events and their signatures. On the basis of the model a comprehensive study of nearby quantum dots allowed to map out the relative spatial positions of quantum dots and impurities. In contrast to previous reports our results provide evidence for bulk impurities as the main source of charge fluctuations. By means of resonant laser spectroscopy in the energy dispersion of the neutral exciton a kink with a continuous energy shift has been observed which only occurs close to the regime where an electron is tunneling between the quantum dot and a 2D electron reservoir. The tunneling induces a weak coupling between the localized electron state of the quantum dot and the continuum of states in the reservoir. The tunnel coupling between the interacting states leads to hybridization into a new superposition state. In consequence the energy of the transition is renormalized which explains the kink in the energy dispersion. The hybridization model based on an Anderson-Fano approach quantitatively agrees with the experimental data and allows to extract the coupling strength between the reservoir and the localized state. In addition to the neutral exciton hybridization effects were also ob-served on the charged exciton. To study optical signatures of many-body effects sub-K laser spectroscopy was established and the setup performance was characterized with optical studies of a quantum dot in the Pauli-blockade regime. The electron bath temperature was determined using experimental and calculated electron spin populations as a function of magnetic field and temperature. The experiment provided quantitative access to all parameters except the electron bath temperature. With the optical Bloch equations the electron spin populations were modeled taking into account all relevant external parameters. An analysis of the evolution of the spin population in magnetic fields with the electron bath temperature as the only free fitting parameter was performed. An electron bath temperature of 380 mK was derived being slightly offset to the nominal base temperature of 250 mK. This proves the successful implementation of the sub-K laser spectroscopy setup.

The centers of galaxies are their own ultimate gravitational sinks. Massive black holes and star clusters as well as gas are especially likely to fall into the centers of galaxies by dynamical friction or dissipation. Many galactic centers harbor supermassive black holes (SMBH) and dense nuclear (star) clusters which possibly arrived there by these processes. Nuclear clusters can be formed in situ from gas, or from smaller star clusters which fall to the center. Since the Milky Way harbors both an SMBH and a nuclear cluster, both can be studied best in the Galactic Center (GC), which is the closest galactic nucleus to us. In Chapter 1, I introduce the different components of the Milky Way, and put these into the context of the GC. I then give an overview of relevant properties (e.g. star content and distribution) of the GC. Afterwards, I report the results of four different studies about the GC. In Chapter 2, I analyze the limitations of astrometry, one of the most useful methods for the study of the GC. Thanks to the high density of stars and its relatively small distance from us it is possible to measure the motions of thousands of stars in the GC with images, separated by few years only. I find two main limitations to this method: (1) for bright stars the not perfectly correctable distortion of the camera limits the accuracy, and (2) for the majority of the fainter stars, the main limitation is crowding from the other stars in the GC. The position uncertainty of faint stars is mainly caused by the seeing halos of bright stars. In the very center faint unresolvable stars are also important for the position uncertainty. In Chapter 3, I evaluate the evidence for an intermediate mass black hole in the small candidate cluster IRS13E within the GC. Intermediate mass black holes (IMBHs) have a mass between the two types of confirmed black hole: the stellar remnants and the supermassive black holes in the centers of galaxies. One possibility for their formation is the collision of stars in a dense young star cluster. Such a cluster could sink to the GC by dynamical friction. There it would consist of few bright stars like IRS13E. Firstly, I analyze the SEDs of the objects in IRS13E. The SEDs of most objects can be explained by pure dust emission. Thus, most objects in IRS13E are pure dust clumps and only three young stars. This reduces the significance of the 'cluster' IRS13E compared to the stellar background. Secondly, I obtain acceleration limits for these three stars. The non-detection of accelerations makes an IMBH an unlikely scenario in IRS13E. However, since its three stars form a comoving association, which is unlikely to form by chance, the nature of IRS13E is not yet settled. In the third study (Chapter 4) I measure and analyze the extinction curve toward the GC. The extinction is a contaminant for GC observations and therefore it is necessary to know the extinction toward the GC to determine the luminosity properties of its stars. I obtain the extinction curve by measuring the flux of the HII region in the GC in several infrared HII lines and in the unextincted radio continuum. I compare these ratios with the ratios expected from recombination physics and obtain extinctions at 22 different lines between 1 and 19 micron. For the K-band I derive A_Ks=2.62+/-0.11. The extinction curve follows a power law with a steep slope of -2.11+/-0.06 shortward of 2.8 micron. At longer wavelengths the extinction is grayer and there are absorption features from ices. The extinction curve is a tool to constrain the properties of cosmic dust between the sun and the GC. The extinction curve cannot be explained by dust grains consisting of carbonaceous and silicate grains only. In addition composite particles, which also contain ices are necessary to fit the extinction curve. In the final part of this thesis (Chapter 5) I look at the properties of most of the stars in the GC. These are the old stars that form the nuclear cluster of the Milky Way. I obtain the mass distribution and the light distribution of these stars. I find that the flattening of the stellar distribution increases outside 70''. This indicates that inside a nearly spherical nuclear cluster dominates and that the surrounding light belongs mostly to the nuclear disk. I dissect the light in two components and obtain for the nuclear cluster L_Ks=2.7*10^7 L_sun. I obtain proper motions for more than 10000 stars and radial velocities for more than 2400 stars. Using Jeans modeling I combine velocities and the radial profile to obtain within 100'' (4 pc) a mass of 6.02*10^6 M_sun and a total nuclear cluster mass of 12.88*10^6 M_sun. The Jeans modeling and various other evidence weakly favor a core in the extended mass compared to a cusp. The old star light shows a similar core. The mass to light ratio of the old stars of the nuclear cluster is consistent with the usual initial mass function in the Galaxy. This suggests that most stars in GC formed in the usual way, in a mode different from the origin of the youngest stars there.