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

Investigating X-ray luminous galaxy clusters at high redshift (z>~1) provides a challenging but fundamental constraint on evolutionary studies of the largest virialized structures in the Universe, the baryonic matter component in form of the hot intracluster medium (ICM), their galaxy populations, and the effects of the mysterious Dark Energy.

The main aim of this thesis work is to establish

the observational foundation for the XMM-Newton Distant Cluster Project (XDCP). This new generation serendipitous X-ray survey is focused on the most distant galaxy clusters at z>1, based on the selection of extended X-ray sources, their identification as clusters and redshift estimation via two-band imaging, and their final spectroscopic confirmation.

As a first step, I have analyzed 80 deg^2 (469 fields) of deep XMM-Newton archival X-ray data with a new pipeline processing system and selected almost 1000 extended sources as galaxy cluster candidates, 75% of which could be identified as clusters or groups at z<~0.6 using available optical data. This left about 250 candidates with typical 0.5-2.0keV X-ray fluxes of ~10^{-14} erg/s/cm^2

in need of confirmation as distant cluster sources.

Therefore, I have adopted a new strategy to efficiently establish the nature of these extended X-ray sources and estimate their redshifts, based on medium deep Z- and H-band photometry and the observed Z-H `red-sequence' color of early-type cluster galaxies. To fully exploit this technique, I have designed a new near-infrared data reduction code, which was applied to the data collected for 25% of the 250 distant cluster candidates in two imaging campaigns at the 3.5m telescope at the Calar Alto Observatory. As a first main result, more than 20 X-ray luminous clusters were discovered to lie at a photometric redshift of z>~0.9.

Furthermore, the new Z-H red sequence method has allowed a cluster sample study over an unprecedented redshift baseline of 0.2<~z<~1.5. From a comparison of the observed color evolution of the cluster red-sequence galaxies with model predictions, I could constrain the formation epoch

of the bulk of their stellar populations as z_f=4.2+-1.1.

This confirms the well-established old age of the stellar populations of early-type galaxies in clusters.

The preliminary investigation of the H-band luminosity evolution of 63 brightest cluster galaxies (BCGs) over the same redshift range provides for the first time direct observational indications that the most massive cluster galaxies in the local Universe have doubled their stellar mass since z~1.5. My tentative finding that nearby BCGs have old, passively evolving stellar populations and were assembled in the last 9Gyr is in qualitative agreement with predictions from the latest numerical simulations based on the standard cold dark matter scenario of galaxy formation and evolution via hierarchical merging. The confirmation and refinement of these preliminary results will contribute to the development of a consistent picture of the cosmic evolution of galaxy populations and the large-scale structure.

Entanglement lies at the heart of quantum mechanics and challenged the intuition of physicists ever since it was discovered. At the same time, it is a powerful tool that serves as a key resource for quantum communication and quantum computation schemes. Many of these applications rely on multiparticle entanglement, whose description, generation and manipulation became therefore a very active field in theoretical and experimental quantum information science. The goals are here to classify and understand the different types of entanglement, to find new applications and to control and analyze the quantum states experimentally.

In this thesis, the experimental observation and analysis of two different types of four-photon polarization entangled states is presented: The cluster state and the symmetric Dicke state with two excitations. For this purpose, experimental setups based on spontaneous parametric down conversion and linear optics with conditional detection were designed. They allowed to observe the cluster state with a fidelity of 74.1 % and the symmetric Dicke state with a fidelity of 84.4 %. The cluster state experiment included the development of a new instrument that is of interest for linear optics quantum logic in general: A probabilistic controlled phase gate that is, due to the simplification of a previous approach, highly stable and can actually be used in multiphoton experiments. The quality of the gate is evaluated by analyzing its entangling capability and by performing full process tomography. The achieved results demonstrate that this device is well suited for implementation in various multiphoton quantum information protocols.

In order to study the observed quantum states, efficient analysis tools are introduced. It was possible to verify that essential properties of the ideal states are indeed reproduced in the experiment, among others, the presence of genuine four-partite entanglement. A particular focus is put on the behavior of the states under projective measurements and photon loss. Several new insights in their entanglement structure are revealed and verified experimentally. We further demonstrate properties that are characteristic for the entanglement classes of the states. These can be used to infer the applicability of the observed states for certain distributed quantum communication applications.

The presented experiments are generic for the design of setups to observe cluster- and symmetric Dicke states with a higher number of photons. Furthermore, also the efficient non-tomographic methods for state analysis we employ can directly be generalized to experiments with higher qubit numbers, where the reduction of the experimental effort for state analysis is even more crucial.

The LHC is a top quark factory producing \ttbar events at a cross section of $833~\mathrm{pb}$ in NLO. This corresponds to about $8\cdot10^{6}$ \ttbar events in the first nominal year of the LHC at the initial low integrated luminosity of $10~\mathrm{fb^{-1}}$ being delivered.

Approximately $44~\%$ of the \ttbar pairs decay hadronically into six jets.

QCD multijet events with four to six final state partons are the main background to these \ttbar events with a cross section many orders of magnitude above the \ttbar multijet cross section.

This study deals with the generation of fully hadronic \ttbar events and QCD multijet events with up to six final state partons and their measurement in the ATLAS detector via fast parameterized simulation.

The characteristics of the QCD events with respect to the \ttbar signals are discussed and a cut-based selection for the separation of the \ttbar events from the QCD background is introduced. The presented analysis is designed to use the physical and technical information available in the start-up period of the LHC.

The extraction of the \ttbar events results in more than 3000 remaining fully hadronic \ttbar events which can be separated from the QCD multijet background in the first year of the LHC.

This analysis also includes the reconstruction of the top-mass peak from fully hadronic \ttbar events in the start-up period of the LHC and gives an estimate of the relative statistical uncertainty for the determination of the \ttbar production cross section of approximately $4~\%$ at an integrated luminosity of $10~\mathrm{fb^{-1}}$.

Tropische Zyklonen, die aus den Tropen in höhere Breiten kommen, wechselwirken dort oft mit einem außertropischen Tiefdruckgebiet. Das daraus entstandene System kann sich infolge der Wechselwirkung nochmals verstärken und hohe Windgeschwindigkeiten und starke Niederschläge in den mittleren Breiten hervorrufen, die normalerweise von solchen Wetterextremen nur selten bedroht sind. Gerade solche Ereignisse gehen oft mit erheblichen Vorhersagefehlern

einher und das, obwohl hier eine verlässliche Vorhersage aufgrund der heftigen Wettererscheinungen sehr wichtig wäre. Ein besseres Verständnis der zugrunde liegenden Dynamik könnte helfen diese Vorhersagen zu verbessern.

Hier wurden idealisierte, numerische Experimente durchgeführt, erstens um herauszufinden, ob ein hurrikan-ähnlicher Wirbel die barokline Entwicklung entscheidend beeinflussen oder sogar auslösen kann. Dazu wurde der Tropische Wirbelsturm zu verschiedenen Zeitpunkten eingesetzt, zum einem zu einem Zeitpunkt bei dem die barokline Welle gerade initialisiert wird, zum anderen zu einem reiferen Entwicklungsstadium der baroklinen Welle. Zweitens wurden die Anfangspositionen des Hurrikans variiert, um zu untersuchen, wie die Lage des tropischen Systems relativ zur Welle deren zukünftige Entwicklung verändert. Alle Experimente wurden mit dem zyklonalen und antizyklonalen Entwicklungsmuster einer baroklinen Welle durchgeführt.

Kommt der Tropische Wirbelsturm in eine fast ungestörte, barokline Umgebung, hatte er in diesen numerischen Experimenten einen erheblichen Anteil an der Entwicklung der Welle. Bei einem späteren Zeitpunkt war dies nicht der Fall. Außerdem stellte sich heraus, dass kleine Änderungen der Lage von Hurrikan relativ zur baroklinen Welle die Entwicklung entscheidend beeinflussen können. Eine hinreichend genaue Kenntnis der Position des Hurrikans und der baroklinen Welle ist nötig, um eine korrekte Vorhersage machen zu können. Eine wichtige Rolle, ob nach der Wechselwirkung eine Verstärkung stattfindet, scheinen die Größenverhältnisse zu spielen. Beim zyklonalen Entwicklungsmuster hat sich ein relativ großskaliger Trog entwickelt, bei dem keine Verstärkung auftrat nach der Wechselwirkung. Durch das typische Ausdünnen des Troges im antizyklonalen Fall hatte der Trog in etwa die gleiche Größenordnung wie der Hurrikan und es gab eine Verst¨arkung nach der Wechselwirkung.

The present work describes different techniques to control some ma jor parameters of colloidal nanocrystals. The individual techniques rely on the manipulation of the nucleation event. The sensitive control of the nanocrystals’ size and shape is discussed. Furthermore the formation of

hybrid nanocrystals composed of different materials is presented. The synthesis technique for the production of the different samples involves organic solvents and surfactants and reactions at elevated temperatures.

The presence of magic size clusters offers a possibility to control the size of the nanocrystals even at very small dimensions. The clusters produced comprise ca. 100 atoms. In the case of CdSe, nanocrystals of this size emit a blue fluorescence and therefore extend the routinely accessible spectrum for this material over the whole visible range. Samples fluorescing in the spectral range from green to red are produced with standard recipes. In this work a reaction scheme for magic size clusters is presented and a theoretical model to explain the particular behaviour of their growth dynamics is discussed. The samples are investigated by optical spectroscopy, transmission electron microscopy, X-ray diffraction and elemental analysis.

Shape controlled nanocrystals might be of interest for a variety of applications. The size dependent properties of nanocrystals are dominated by their smallest dimension. Therefore anisotropically shaped nanocrystals exhibit similar optical and electronic properties as spherical nanocrystals with a compatible diameter. This makes nanorods and nanowires an appealing object for electronics. Another possible application for these materials is to incorporate them into synthetic materials to influence their mechanical stability. Here, a method to form branched nanocrystals is discussed. It turned out that the presence of small impurities in the reaction vessel triggers the formation of branching points. Furthermore this synthesis technique offers some insights into the architecture of the branching point. The branching point is analysed by high resolution transmission electron microscopy and proves for the occurrence of a multiple twinned structure are strengthened by simulation of the observed patterns.

Incorporation of a second material into a nanocrystal adds different functionality to the entire ob ject. Ideally both materials contribute with their own functionality and they are not affected by the presence of the other material. Two different techniques to generate nanocrystals of this type are presented. The first relies on a seeded growth approach in which the nucleation of the second material is allowed only on defined sites of the seeds. Anisotropic nanorods show a reactivity that varies for the individual facets. Using such nanorods as seeds dumbbell structures are formed. The second technique uses the tips of pre-formed nano-dumbbells as sacrificial domains. The material on the tips is replaced by gold.

In any of the processes a different aspect of the nucleation event or the earliest stage of the growth is of relevance. In the growth of the magic size clusters the nucleation event itself is slowed down to a pace at which the experimenter can follow any step. The occurrence of branching can be traced down to the emergence of defects in the crystalline structure in the earliest stage of the growth. Hybrid materials are formed by a seeded-growth mechanism. Pre-formed nanocrystals provide the nucleation sites for the second material.

This PhD thesis presents a technique based on the grazing incidence crystal truncation rod (GI-CTR) X-ray diffraction method used to solve the crystal structure of substrate induced fiber structured organic thin films. The crystal structures of pentacene thin films grown on technologically relevant gate dielectric substrates are reported.

It is widely recognized, that the intrinsic charge transport properties in organic thin film transistors (OTFTs) depend strongly on the crystal structure of the organic semiconductor layer. Pentacene, showing one of the highest charge carrier mobilities among organic semiconductors, is known to crystallize in at least four polymorphs, which can be distinguished by their layer periodicity d(001). Only two polymorphs (14.4 Å and 14.1 Å), grow as single crystals and their detailed crystal structure has been solved with standard crystallography techniques. The substrate induced 15.4 Å polymorph, the so called pentacene thin-film phase, is the most relevant for OTFT applications, since it grows at room temperature on technologically relevant gate dielectrics. However, the crystal structure of the pentacene thin-film phase has remained incomplete as it only grows as a fiber structured thin film. In this thesis, the GI-CTR X-ray diffraction technique is extended to fiber structured thin films. The X-ray diffraction experiments were carried out at the synchrotron source beamline W1 at HASYLAB in Hamburg, in order to obtain enough diffraction data for the determination of the crystal structure as pentacene thin films only grow as ultra thin films with crystal grains as small as 0.4μm. Pentacene thin films are also known to be sensitive to environmental conditions, such as light and oxygen. For this reason, the X-ray synchrotron measurements were performed in-situ. A portable ultra high vacuum growth chamber equipped with a rotatable sample holder and a beryllium window was built in order to perform X-ray measurements of up to four samples right after the thin film growth process without breaking the vacuum. Parallel to this, a versatile software package coded with Matlab in order to simulate, analyze and fit the complex data measured at the synchrotron source was developed. The complete crystal structure of the 15.4 Å pentacene thin-film polymorph grown on four model types of gate dielectric materials, amorphous silicon dioxide (a−SiO2), octadecyltrichlorosilane-treated a−SiO2 (OTS), Topas (“thermoplastic olefin polymer of amorphous structure”) and polystyrene films, was solved. It was found, that the unit cell parameters are identical within measurement precision on all measured substrates. The crystal structure belongs to the space group P-1 and was found to be triclinic with the following lattice parameters: a = 5.958 ± 0.005 Å, b = 7.596 ± 0.008 Å, c = 15.61 ± 0.01 Å, alpha = 81.25 ± 0.04°, beta = 86.56 ± 0.04° and 2 gamma = 89.80 ± 0.10°. The unit cell volume V = 697 Å^3 is the largest of all pentacene polymorphs reported so far. However, the molecular arrangement within the unit cell was found to be substrate dependent. Here, the following parameters are reported: The herringbone angle is 54.3°, 55.8°, 59.4° and 55.1° for a−SiO2, OTS, Topas and polystyrene, respectively. The tilts of the two molecular axes (theta_A, theta_B) are (5.6°, 6.0°), (6.4°,6.8°), (5.6°, 6.3°) and (5.7°, 6.0°) for a−SiO2, OTS, Topas and polystyrene, respectively.

To conclude, it was shown that the molecular orientation in the unit cell differs among substrates while the unit cell dimensions of the 15.4 Å pentacene polymorph are identical. This indicates that substrate effects have to be included if one aims on understanding the molecular structure of the thin-film phase in detail. The crystal structures reported here provide a basis to apply techniques such as density functional methods to investigate intrinsic charge transport properties and optical properties of organic thin film devices on a molecular level. In prev

Diese Arbeit besch\"aftigt sich mit der Bestimmung elastischer Konstanten in amorphen Materialien. Im Mittelpunkt steht die Elastizit\"at heterogener Netzwerke aus steifen, stabartigen Polymeren. Diese Netzwerke spielen eine wichtige Rolle in der Zell-Biologie, z.B. in der Form des Zytoskeletts, welchem die Zelle einen Gro\ss teil ihrer mechanischen und dynamischen Eigenschaften

verdankt.

Bei der Bestimmung der elastischen Konstanten im Rahmen der

Elastizit\"atstheorie erh\"alt der Begriff der `Affinit\"at'' eine besondere Bedeutung, da er das Deformationsfeld \emph{homogener} elastischer Systeme

charakterisiert. Im Gegensatz dazu ist es in den hier interessierenden \emph{heterogenen} Materialsystemen gerade die Abwesenheit dieser affinen Deformationen, die im Mittelpunkt des Interesses steht. Im Verlauf der Arbeit

wird deutlich, wie Nichtaffinit\"at aus einem Zusammenspiel geometrischer Eigenschaften der Mikrostruktur und mechanischer Eigenschaften der Einzelpolymere entstehen kann. Durch die Kombination von Computersimulation und

analytischer Beschreibung werden wichtige Aspekte bez\"uglich der Rolle der heterogenen Mikrostruktur in der Ausbildung makroskopischer Elastizit\"at gekl\"art. Der Ber\"ucksichtigung nicht-affiner Deformationen kommt dabei

au{\ss}erordentliche Bedeutung bei der pr\"azisen Bestimmung makroskopischer elastischer Konstanten zu.

Es zeigt sich, dass die Struktur der Polymer-Netzwerke im Allgemeinen durch zwei L\"angenskalen beschrieben werden muss. Neben der mittleren Maschenweite $a$ tritt eine mesoskopische L\"angenskala $l_f\gg a$ auf, die aus der stabartigen Form der Polymere folgt. Es wird gezeigt, dass diese ``Faserl\"ange'' -- und nicht die Maschenweite -- die Rolle der Einheitszelle des Polymernetzwerkes spielt. Neben dieser geometrischen Komponente spielen die elastischen

Eigenschaften der Einzelpolymere eine wesentliche Rolle f\"ur die makroskopische Elastizit\"at. Diese orientieren sich an den bekannten Kraft-Ausdehnungs-Relationen steifer Polymere und k\"onnen mit Hilfe des ``worm-like chain'' Modells berechnet werden. Dar\"uber hinaus wird ein neues

``worm-like bundle'' Modell entwickelt, das vergleichbare Aussagen zu statistischen und mechanischen Eigenschaften von Polymer-\emph{B\"undeln} erlaubt.

Der erste Teil der Arbeit besch\"aftigt sich mit der athermischen Elastizit\"at des Netzwerkes, d.h. der entropische Anteil der Kraft-Ausdehnungs-Relation wird

vernachl\"assigt. Eine selbst-konsistente `effective-medium'' Theorie wird entwickelt, die auf der Annahme beruht, dass die Filamente sich wie \emph{inextensible}, biegesteife St\"abe verhalten. Die Annahme der Inextensibilit\"at kann mit der anisotropen Elastizit\"at steifer Polymere begr\"undet werden, deren Biegesteifigkeit, $\kperp$, im Allgemeinen sehr viel

kleiner ist, als deren Strecksteifigkeit, $\kpar \gg \kperp$. Das sich ergebende nicht-affine Deformationsfeld kann explizit konstruiert werden (``non-affine

floppy modes'') und erlaubt eine Berechnung der elastischen Konstanten der Netzwerke, welche mit den Ergebnissen fr\"uherer Simulationen \"ubereinstimmen.

Desweiteren erlaubt die Theorie, in Verbindung mit dem worm-like bundle Modell, eine Erkl\"arung der rheologischen Eigenschaften eines in-vitro Modellsystems aus

verkn\"upften Polymerb\"undeln.

Der zweite Teil der Arbeit diskutiert thermische Effekte, indem die entropische Strecksteifigkeit der Polymere in der Modellierung ber\"ucksichtigt wird. Es besteht ein charakteristischer Unterschied zwischen diesem entropischen Beitrag zur Strecksteifigkeit, $\kpar$, und einem energetischen Beitrag, $k_s$, der sich z.B. aus der Streckung des Polymer-R\"uckgrats ergibt. Dieser Unterschied

betrifft die Abh\"angigkeit von der L\"ange $l$ des betrachteten Polymersegments. Die starke Abh\"angigkeit $\kpar\sim l^{-4}$ (im Vergleich zu $k_s\sim l^{-1}$) f\"uhrt dazu, dass thermische Netzwerke steifer Polymere eine starke Sensitivit\"at f\"ur strukturelle Unordnung aufweisen, die in

Extremal black holes in theories of gravity coupled to abelian gauge fields and neutral scalars, such as those arising in the low-energy description of compactifications of string theory on Calabi-Yau manifolds, exhibit the attractor phenomenon: on the event horizon the scalars settle to values determined by the charges carried by the black hole and independent of the values at infinity. It is so, because on the horizon the energy contained in vector fields acts as an effective potential (the black hole potential), driving the scalars towards its minima.

For spherically symmetric black holes in theories where gauge potentials appear in the Lagrangian solely through field strengths, the attractor phenomenon can be alternatively described by a variational principle based on the so-called entropy function, defined as the Legendre transform with respect to electric fields of the Lagrangian density integrated over the horizon. Stationarity conditions for the entropy function then take the form of attractor equations relating the horizon values of the scalars to the black hole charges, while the stationary value itself yields the entropy of the black hole.

In this study we examine the relationship between the entropy function and the black hole potential in four-dimensional N=2 supergravity and demonstrate that in the absence of higher-order corrections to the Lagrangian these two notions are equivalent. We also exemplify their practical application by finding a supersymmetric and a non-supersymmetric solution to the attractor equations for a conifold prepotential.

Exploiting a connection between four- and five-dimensional black holes we then extend the definition of the entropy function to a class of rotating black holes in five-dimensional N=2 supergravity with cubic prepotentials, to which the original formulation did not apply because of broken spherical symmetry and explicit dependence of the Lagrangian on the gauge potentials in the Chern-Simons term. We also display two types of solutions to the respective attractor equations.

The link between four- and five-dimensional black holes allows us further to derive five-dimensional first-order differential flow equations governing the profile of the fields from infinity to the horizon and construct non-supersymmetric solutions in four dimensions by dimensional reduction.

Finally, four-dimensional extremal black holes in N=2 supergravity can be also viewed as certain two-dimensional string compactifications with fluxes. Motivated by this fact the recently proposed entropic principle postulates as a probability measure on the space of these string compactifications the exponentiated entropy of the corresponding black holes. Invoking the conifold example we find that the entropic principle would favor compactifications that result in infrared-free gauge theories.