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

In this thesis, I study the formation of structure within the current standard cosmological model using two numerical methods: N-body simulations and semi-analytic models of galaxy formation. In Chapter 1 & 2, I will explain the motivations and objectives of the analysis presented in this thesis, and give a brief review of the relevant background. Chapter 3 is focused on the discreteness effects in $N$-body simulation: Hot/Warm Dark Matter (H/WDM) $N$-body simulations in which the initial uniform particle load is a cubic lattice, exhibit artefacts related to this lattice. In particular, the filaments which form in these simulations break up into regularly spaced clumps which reflect the initial grid pattern. Using numerical simulations, I demonstrate that a similar artefact is present even when the initial uniform particle load is not a lattice, but rather a glass with no preferred directions and no long-range coherence. My study shows that such regular fragmentation occurs also in simulations of the collapse of idealized, uniform filaments, but not in simulations of the collapse of infinite uniform sheets. In H/WDM simulations, all self-bound non-linear structures with masses much smaller than the free streaming mass appear to originate through spurious fragmentation of filaments. These artificial fragments form below a characteristic mass which scales as $M_p^{1/3}k^{-2}_{peak}$. This has the unfortunate consequence that the effective mass resolution of such simulations improves only as the cube root of the number of particles employed. In Chapter 4, I combine $N$-body simulations of structure growth with physical modelling of galaxy evolution to investigate whether the shift in cosmological parameters between the 1-year and 3-year results from the Wilkinson Microwave Anisotropy Probe (WMAP) affects predictions for the galaxy population. Structure formation is significantly delayed in the WMAP3 cosmology, because the initial matter fluctuation amplitude is lower on the relevant scales. The decrease in dark matter clustering strength is, however, almost entirely offset by an increase in halo bias, so predictions for galaxy clustering are barely altered. In both cosmologies, several combinations of physical parameters can reproduce observed, low-redshift galaxy properties; the star formation, supernova feedback, and AGN feedback efficiencies can be played off against each other to give similar results for a variety of combinations. Models which fit observed luminosity functions predict projected 2-point correlation functions which scatter by about 10-20 per cent on large scale and by larger factors on small scale, depending both on cosmology and on details of galaxy formation. Measurements of the pairwise velocity distribution prefer the WMAP1 cosmology, but careful treatment of the systematics is needed. Given current modelling uncertainties, it is not easy to distinguish the WMAP1 and WMAP3 cosmologies on the basis of low-redshift galaxy properties. Model predictions diverge more dramatically at high redshift. Better observational data at z>2 will better constrain galaxy formation and perhaps also cosmological parameters. In Chapter 5, I study whether the apparent universality of halo properties in hierarchical clustering cosmologies is a consequence of their growth through mergers. N-body simulations of Cold Dark Matter (CDM) have shown that, in this hierarchical structure formation model, dark matter halo properties, such as the density profile, the phase-space density profile, the distribution of axial ratio, the distribution of spin parameter, and the distribution of internal specific angular momentum follow `universal' laws or distributions. Here I study the properties of the first generation of haloes in a Hot Dark Matter (HDM) dominated universe, as an example of halo formation through monolithic collapse. I find all these universalities to be present in this case also. Halo density profiles are very well fit by the Navarro et al (1997) profile over two orders of magnitude in mass. The concentration parameter depends on mass as $c \propto M^{0.2}$, reversing the dependence found in a hierarchical CDM universe.However, the concentration-formation time relation is similar in the two cases: earlier forming haloes tend to be more concentrated than their later forming counterparts. Halo formation histories are also characterized by two phases in the HDM case: an early phase of rapid accretion followed by slower growth. Furthermore, there is no significant difference between the HDM and CDM cases concerning the statistics of other halo properties: the phase-space density profile; the velocity anisotropy profile; the distribution of shape parameters; the distribution of spin parameter, and the distribution of internal specific angular momentum are all similar in the two cases. Only substructure content differs dramatically. These results indicate that mergers do not play a pivotal role in establishing the universalities, thus contradicting models which explain them as consequences of mergers.

Since the awareness of entanglement was raised by Einstein, Podolski, Rosen and Schrödinger in the beginning of the last century, it took almost 55 years until entanglement entered the laboratories as a new resource. Meanwhile, entangled states of various quantum systems have been investigated. Sofar, their biggest variety was observed in photonic qubit systems. Thereby, the setups of today's experiments on multi-photon entanglement can all be structured in the following way: They consist of a photon source, a linear optics network by which the photons are processed and the conditional detection of the photons at the output of the network. In this thesis, two new linear optics networks are introduced and their application for several quantum information tasks is presented. The workhorse of multi-photon quantum information, spontaneous parametric down conversion, is used in different configurations to provide the input states for the networks. The first network is a new design of a controlled phase gate which is particularly interesting for applications in multi-photon experiments as it constitutes an improvement of former realizations with respect to stability and reliability. This is explicitly demonstrated by employing the gate in four-photon experiments. In this context, a teleportation and entanglement swapping protocol is performed in which all four Bell states are distinguished by means of the phase gate. A similar type of measurement applied to the subsystem parts of two copies of a quantum state, allows further the direct estimation of the state's entanglement in terms of its concurrence. Finally, starting from two Bell states, the controlled phase gate is applied for the observation of a four photon cluster state. The analysis of the results focuses on measurement based quantum computation, the main usage of cluster states. The second network, fed with the second order emission of non-collinear type II spontaneous parametric down conversion, constitutes a tunable source of a whole family of states. Up to now the observation of one particular state required one individually tailored setup. With the network introduced here many different states can be obtained within the same arrangement by tuning a single, easily accessible experimental parameter. These states exhibit many useful properties and play a central role in several applications of quantum information. Here, they are used for the solution of a four-player quantum Minority game. It is shown that, by employing four-qubit entanglement, the quantum version of the game clearly outperforms its classical counterpart. Experimental data obtained with both networks are utilized to demonstrate a new method for the experimental discrimination of different multi-partite entangled states. Although theoretical classifications of four-qubit entangled states exist, sofar there was no experimental tool to easily assign an observed state to the one or the other class. The new tool presented here is based on operators which are formed by the correlations between local measurement settings that are typical for the respective quantum state.

This thesis contributes to the field of transport through quantum dots. These devices allow for a controlled study of quantum transport and fundamental physical effects, like the Kondo effect. In this thesis we will focus on dots that are well described by generalized Anderson impurity models, where the discrete levels of the quantum dot are tunnel-coupled to fermionic reservoirs. The model parameters, like level energy and width, can be tuned in experiments. Therefore these systems constitute a valuable arena for testing experiment against theory and vice versa. In order to describe these strongly correlated systems, we employ the numerical renormalization group method. This allows us to address both longstanding questions concerning experimental results and new physical phenomena in these fundamental models. This thesis consists of three major projects. The first and most extensive one is concerned with the phase of the transmission amplitude through a quantum dot. Measurements of many-electron quantum dots with small level spacing reveal universal phase behaviour, a result not fully understood for almost 10 years. Recent experiments have seen that, contrarily, for dots with only a few electrons, i.e. large level spacing, the phase depends on the mesoscopic dot parameters. Analyzing a multi-level Anderson model, we show that the generic feature of the two regimes can be reproduced in the regime of overlapping levels or well separated levels, respectively. Thereby the universal character follows from Fano-type antiresonances of the renormalized single-particle levels. Moderate temperature supports the universal character. In the mesoscopic regime, we also investigate the effect of Kondo correlations on the transmission phase. In a second project we analyze a quantum dot coupled to a superconducting reservoir. In contrast to previous belief, the energy resolution of our method is not restricted by the energy scale of the superconducting gap, leading to new insights into the method. The high resolution allows us to resolve sharp peaks in the spectral function that emerge for a certain regime of parameters. A third project deals with a quantum dot coupled to two independent channels, a system known to exhibit non-Fermi liquid behaviour. We investigate the existence of the non-Fermi liquid regime when driving the system out of the Kondo regime by emptying the dot. We find that the extent of the non-Fermi liquid regime strongly depends on the mechanisms that couple impurity and reservoirs but prevent mixing of the latter.

This thesis is concerned with two aspects of intersecting D6-brane models: We treat some of the effects that are induced by E2-instantons and we consider one-loop corrections to the gauge kinetic functions in the low-energy effective field theory. We begin in chapter 1 with a general introduction covering the question why to consider string theory as a candidate theory of nature. After that, in chapter 2, we go over some topics related to field theory instantons and finally discuss the instanton generated superpotential in supersymmetric QCD (SQCD), the so-called Affleck–Dine–Seiberg (ADS) superpotential. In chapter 3 we then proceed to reproduce the ADS superpotential in an intersecting D6-brane realization of SQCD as the effect of a single E2-instanton. In order to do so, we first explicate the necessary formalism for calculating the E2-instanton contribution to the superpotential, then construct a (local) intersecting D6-brane realization of SQCD, and finally show that the formalism indeed leads to the Affleck–Dine–Seiberg superpotential. In chapter 4 we consider one-loop corrections to the gauge kinetic functions. These one-loop corrections are related quite intricately to gauge threshold corrections which we compute for intersecting D6-brane models on the Z_2xZ_2 toroidal orbifold. An analysis of the formulas for calculating the E2-instanton contribution to the superpotential raises the question whether this contribution is a holomorphic quantity. In chapter 5 we take up this question showing that indeed it is holomorphic. In addition, we discuss under which circumstances one can expect E2-instanton corrections to the gauge kinetic functions. There follow a number of appendices, some elaborating on points touched upon in the main text, some collecting necessary formulas.

The Large Hadron Collider, starting in 2008, will be a "top factory" as top-antitop pairs will be produced with a cross section of about 830 pb at an instantaneous luminosity of 10^33 cm^-2 s^-1 during the first year. With about 30% probability top pairs decay semileptonically into a final state with four jets, lepton (electron or muon) and respective neutrino. For another 5% of the top pair events a dileptonic decay is expected. Here the final state signature is composed of two jets, two leptons and two neutrinos. In this thesis the precision for a top pair cross section measurement at the ATLAS experiment in the semileptonic and dileptonic channels with cut based analyses, applicable to the first data, was estimated. The analysis of the semileptonic decay focused especially on the study of background from QCD events either with leptons from semileptonic hadron decays or from hadrons falsely identified as electrons by the calorimeter. For the first 10 fb^-1 and assuming a fake electron probability of 10^-3 a precision for the cross section times the branching ratio of +- 0.5(stat) +- 30.4(syst) +- 24.0(lumi) pb has been estimated, corresponding to a relative precision of 16% for the theoretically predicted cross section times branching ratio of about 240 pb. The analysis in the dileptonic channel achieves a precision of +- 0.2(stat) +- 2.5(syst) +- 2.6(lumi) pb which translates into a relative error of 10% for the cross section times branching ratio of around 38 pb. The errors for both the semileptonic and the dileptonic channel are expected to improve as progress is made on the luminosity determination and the knowledge of the backgrounds from comparisons with measured data. A measurement of the cross-section ratio between the dileptonic and semileptonic channel is sensitive to scenarios of new phenomena with competitive top quark decay modes such as decays involving a charged Higgs boson. It has been estimated that such a ratio should be measurable with a relative precision of +- 0.7%(stat) +- 7.7%(sys) +- 3.1%(lumi) during the first year of ATLAS data-taking. Even though the systematic errors partially cancel in such a ratio the total uncertainty is still around 8% as the background estimates rely on theoretical predictions. This should also improve as soon as the models can be tested against measured data.

Im Rahmen der vorliegenden Arbeit wurde ein spektral hochauflösendes Lidar (HSRL) aufgebaut und während des Feldexperiments SAMUM im Mai/Juni 2006 und im Januar/Februar 2008 an Bord des Forschungsflugzeugs Falcon betrieben. Die Intensität von Lidar–Signalen wird maßgeblich durch die Rückstreuung und die Extinktion der atmosphärischen Teilchen beeinflusst. Dabei stehen die Rückstreuung und die Extinktion der Aerosole in keinem konstanten Verhältnis zueinander. Die Messgröße eines normalen Rückstreu–Lidars ist insofern mit zwei unbekannten Größen behaftet, weshalb die direkte Messung der Aerosolextinktion mit einem solchen Lidar nicht möglich ist. Im Gegensatz dazu wird bei der Methode des HSRL neben der gesamten atmosphärischen Rückstreuung der Teil der molekularen Rückstreuung gesondert gemessen. Die Messung des molekularen Rückstreusignals wird durch die spektrale Filterung der atmosphärischen Rückstreuung mit einem schmalbandigen optischen Filter ermöglicht. Durch den Vergleich des gemessenen molekularen Signals mit dem zu erwartenden kann die Aerosolextinktion direkt bestimmt werden. Zum Aufbau des Instruments wurde eine Joddampfabsorptionszelle konstruiert und in das Empfangsmodul des bestehenden flugzeuggetragenen Lidars des Deutschen Zentrums für Luft– und Raumfahrt integriert. Außerdem wurde der Lasertransmitter des Lidars mit einem neuartigen Verfahren der opto–akustischen Modulation frequenzstabilisiert. Während SAMUM–1 wurden damit erstmalig die optischen Eigenschaften des reinen Saharastaubaerosols, insbesondere dessen Extinktion, das Verhältnis von Extinktion und Rückstreuung sowie die Depolarisation, in der Nähe seiner Quellgebiete untersucht. Die Messungen des neuen HSRL wurden zur Qualitätssicherung mit Hilfe unabhängiger Instrumente validiert. Die Lidar–Verhältnis–Messungen wurden durch Trajektorienanalysen auf mögliche Abhängigkeiten von unterschiedlichen Quellgebieten untersucht. Die HSRL–Messungen der Aerosol–optischen Dicke wurden mit satellitengestützten Messungen verglichen. Südlich des Hohen Atlas Gebirges wurden Aerosol–optische Dicken von 0,50 bis 0,60 gemessen. Es zeigte sich eine ausgeprägte laterale Variabilität der Aerosol–optischen Dicke, die bei homogenen Schichten allein auf deren unterschiedliche Dicke zurückgeführt werden konnte. Die vertikalen Variationen des Lidar–Verhältnisses zwischen 38 sr und 50 sr wurden durch Trajektorienanalysen auf die Anströmung aus unterschiedlichen Quellgebieten zurückgeführt. Im Depolarisationsverhältnis wurden jedoch keine vertikale Variationen beobachtet, was auf eine einheitliche Teilchenform schließen lässt. Die Aerosoldepolarisation betrug in den Staubaerosolschichten 0,30 ± 0,02. Dies bestärkt die Annahme, dass das Lidar–Verhältnis in erster Linie durch die unterschiedliche chemische Zusammensetzung des Aerosols beeinflusst wird. Aufgrund der hohen natürlichen Variabilität erscheint die Angabe eines mittleren Wertes als nicht sinnvoll. Der Vergleich mit MISR–Messungen der Aerosol–optischen Dicke zeigte größtenteils Übereinstimmung innerhalb der Fehlergrenzen. Direkt über dem Hohen Atlas traten signifikante Abweichungen auf, die durch die sich stark ändernde Topographie erklärt werden können.