Fakultät für Physik - Digitale Hochschulschriften der LMU - Teil 02/05 Ludwig-Maximilians-Universität München

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 wel

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.