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

This thesis is devoted to the study of optical spectra of thermonuclear supernovae, known as ``Type Ia'' supernovae (SN Ia). These violent stellar explosions, visible across a large fraction of the observable universe, are used to measure distances on cosmological scales. By directly probing the expansion dynamics of the universe, measurements of relative luminosity distances to SN Ia have shown the universal expansion to be accelerating. Such an acceleration can only be explained if the universe is pervaded by a new form of energy with negative pressure -- or ``Dark Energy'', such as Einstein's cosmological constant, Lambda.

The use of SN Ia as distance indicators requires the use of a purely empirical calibration scheme relating the shape of the SN~Ia light curve with its peak luminosity. Although this relation is well verified for SN Ia in the local universe, it lacks convincing theoretical basis. Moreover, in view of the current uncertainties in modeling the explosion mechanisms and inferring the progenitor systems of SN Ia, its extrapolation to higher redshifts could be systematically affected by evolutionary effects, thereby biasing the cosmological results.

Spectroscopy is better suited than photometry to make quantitative comparisons between SN Ia at different redshifts. Large amounts of information are conveyed by spectra on the properties of the ejecta (chemical composition, velocity/density gradients, excitation level); subtle differences, blurred together in photometric measurements, will show up in the spectra. However, comparisons of SN Ia at different redshifts have so far only been qualitative in nature. This thesis presents original results on a quantitative comparison, based on several analysis tools developed and/or tested during the course of the past three years.

The thesis is structured as follows: the first two chapters serve as an introduction to the reader on the cosmological use of SN Ia, and on their optical spectra (theory and observation). Chap. 3 (Blondin et al. 2005a) presents a two-dimensional deconvolution method to separate a supernova spectrum from the contaminating background of its host galaxy. This algorithm was used to reduce the SN~Ia spectra, taken with the ESO Very Large Telescope, presented in Matheson et al. 2005 (see Appendix A). In Chap. 4, we discuss the use of a cross-correlation tool to determine the redshift of a SN Ia based on its spectrum alone -- i.e., not relying on narrow lines in the spectrum of the host galaxy. The main focus of this thesis is Chap. 5 (Blondin et al. 2005b): using characteristics of line-profile shapes in SN Ia, we provide the first clear quantitative evidence that the high-redshift SN~Ia are indeed similar to their local counterparts, providing a confirmation of their use as reliable cosmological distance indicators. Finally, in Chap. 6 we present preliminary results on cosmological time-dilation effects in high-redshift SN Ia spectra.

In der vorliegenden Arbeit wurden die diffusiven und elektrophoretischen Eigenschaften von Desoxyribonuklein-säure (DNA) und die Selbstassemblierung von DNA-Chromophor-Hybridmolekülen untersucht. Hierzu wurden, neben Gelelektrophorese und temperaturabhängigen Absorptionsmessungen, vor allem Fluoreszenz-Korre-lationsmethoden angewandt.

Um quantitative Aussagen mittels Fluoreszenz-Korrelations-Spektroskopie (FCS) über die freie Diffusion von doppelsträngigen (ds) DNA-Fragmenten (75 bp - 1019 bp) in wässrigen Lösungen zu treffen, wurden laserleis-tungsabhängige Messungen durchgeführt. Diese Experimente ergaben, dass photophysikalische Effekte wie Triplettrelaxation, Isomerisations- oder Bleichprozesse die Autokorrelation entscheidend beeinflussen. Die Län-genabhängigkeit der gemessenen Diffusionskonstanten kann mit einem Stabmodell beschrieben werden, das für alle verwendeten dsDNA-Fragmente, die Konturlängen von bis zu 7 Persistenzlängen aufweisen, Gültigkeit besitzt. In diesem Zusammenhang konnte auch gezeigt werden, dass kleinere Diffusionskonstanten lediglich bei der Zuga-be von zweiwertigen Salzen und bei hohen Salzstärken (> 0,1 M) beobachtet werden. Durch eine Komplexierung der dsDNA-Fragmente mit kationischen und neutralen Lipiden war es möglich, dsDNA in ein unpolares Lösungs-mittel (n-Alkan) zu überführen. Durch Messung der freien Diffusion konnte die Monodispersität von Lipid-dekorierten dsDNA-Fragmenten festgestellt werden. In der unpolaren Phase wurde eine kritische DNA-Konzentration (≈ 10 nM) festgestellt, die für die Stabilität der DNA-Lipid-Komplexe notwendig ist.

In der Arbeitsgruppe von Prof. Dr. Müllen am Max-Planck-Institut für Polymerforschung in Mainz wurde ein DNA-Chromophor-Hybrid synthetisiert, bei dem an ein zentrales Farbstoffmolekül (Perylen) beidseitig jeweils ein kurzes ca. 20 Basen langes Oligonukleotid (ODN) kovalent angebunden wurde. FCS-Messungen, die die intrinsi-schen Fluoreszenzeigenschaften des Hybrids ausnutzten, konnten die Löslichkeit und Monodispersität der Hybride bzw. der Lipid-Hybrid-Komplexe sowohl in wässriger Phase als auch in Alkanen nachweisen. Durch eine geeigne-te Wahl der ODN-Sequenzen und der Anknüpfungsstelle der ODN an den Farbstoffkern entstanden durch Basen-paarung unterschiedliche, supramolekulare Strukturen, die in Gelelektrophorese-Experimenten nachgewiesen wur-den. Symmetrische DNA-Chromophor-Hybride können neben beliebig langen, linearen Ketten bei entsprechender Modifikation der Bausteine sandwichartige Dimere ausbilden. Asymmetrische Hybride ermöglichen den Aufbau linearer Strukturen definierter Länge (z. B. Dimere).

Die thermodynamischen Eigenschaften der unterschiedlichen, supramolekularen Konstrukte wurden durch tempe-raturabhängige Absorptionsexperimente untersucht. Die Denaturierung der linearen kettenartigen Strukturen kann durch ein Zwei-Zustands-Modell beschrieben werden, dessen energetische Eigenschaften sehr gut mit denen der verwendeten ODN übereinstimmen. Im Fall der sandwichartigen Strukturen musste für den Schmelzübergang ein Drei-Zustands-Modell angenommen werden, wobei die eingebauten Farbstoffkerne eine energetische Wechselwir-kung vermittelten.

Neben der freien Diffusion von dsDNA wurde deren elektrophoretische Drift untersucht. Dazu wurde ein Mikroe-lektrophorese-System entwickelt, bei dem die Drift im elektrischen Feld mittels zweier Laserfoki detektiert wird, die einen Abstand von ca. 5 µm aufweisen. Hierbei wirken die beiden Foki wie eine mikroskopische „Lichtschran-ke“; die Driftzeit wird dabei durch eine Orts-Orts-Kreuzkorrelation der beiden Fluoreszenzsignale zugänglich ge-macht. Auf Grund der methodisch bedingten sehr hohen Ortsauflösung ist es möglich, detaillierte Aussagen über die elektrophoretischen und elektroosmotischen Anteile an der Drift zu treffen. Experimente mit unterschiedlichen Feldstärken zeigen, dass eine Temperaturänderung durch den Eintrag von Joulscher Wärme nicht vernachlässigbar ist. Die elektrophoretische Mobilität ist

We take a multi-faceted approach to study galaxy populations in the local universe, using the completed Two Degree Field Galaxy Redshift Survey (2dFGRS), the ``Millennium Run'' LCDM N-body simulation, and a semi-analytic model of galaxy formation. Our investigation covers both small and large scale aspects of the galaxy distribution. This work can be broken into three sections, outlined below.

Using the 2dFGRS we explore the higher-order clustering properties of local galaxies to quantify both (i) the linear and non-linear bias of the distribution relative to the underlying matter field, and (ii) the nature of hierarchical scaling in the clustering moments of the galaxy distribution. This last point is the expected signature of an initially Gaussian distribution of matter density fluctuations that evolved under the action of gravitational instability. We show in Chapters 2, 3, and 4 that the 2dFGRS higher-order clustering moments are indeed hierarchical, which we measure up to sixth order for galaxies brighter than M_bJ-5log10 h=-17 and which sample the survey volume out to z~0.3. The moments are found to be well described by the negative binomial probability distribution function, and we rule out, at high significance, other models of galaxy clustering, such as the lognormal distribution. This result holds in redshift space on all scales where we obtain a good statistical signal, typically 0.5< R (h^-1 Mpc) < 30 (i.e. from strongly non-linear to quasi-linear regimes). Interestingly, we find that the moments on larger scales can be significantly altered by two massive superclusters present in the 2dFGRS. The skewness of the galaxy distribution is found to have a weak dependence on galaxy luminosity. We show that a simple linear biasing model provides an inadequate description of the higher order results, suggesting that non-linear biasing is present in the clustering moments of the 2dFGRS.

The large-scale distribution of structure within the 2dFGRS allows us to study the properties of the galaxy population as a function of local environment. In Chapter 5 we measure the luminosity function of early and late-types galaxies in survey regions ranging from sparse voids to dense clusters to reveal the dominant population in each. Fitting each luminosity function with a Schechter function allows us to quantify how the bright and faint populations transform with changing density contrast. We find that (i) the population in voids is dominated by late types, with a noticeable deficit of

intermediate and bright galaxies relative to the mean, and (ii) cluster regions have an excess of very bright early-type galaxies relative to the mean. When directly comparing faint early and late type galaxies in void and cluster regions, the cluster population shows comparable abundances of both types, whereas in voids the late types dominate by almost an order of magnitude. Of interest to many galaxy formation models is our measurement that reveals that the faint-end slope of the overall luminosity function depends at most weakly on density environment.

Finally, in Chapter 6, we develop a self-consistent model of galaxy formation and couple this to the Millennium Run LCDM N-body simulation. This simulation represents a significant step forward in both size and resolution, allowing us to follow the the complete evolutionary histories of approximately 20 million galaxies down to luminosities as faint as the Small Magellanic Cloud in a volume comparable to that sampled by the 2dFGRS. In our galaxy formation model we supplement previous treatments of the growth and activity of central black holes with a new model for `radio' feedback from those active galactic nuclei that lie at the centre of a quasistatic X-ray emitting atmosphere in a galaxy group or cluster. With this we can simultaneously explain (i) the low observed mass drop-out rate in cooling flows, (ii) the exponential cut-off at the bright end of the galaxy luminosity function

Canonically deformed spacetime, where the commutator of two coordinates is a constant, is the most commonly studied noncommutative space. Noncommutative gauge theories that have ordinary gauge theory as their commutative limit have been constructed there. But these theories have their drawbacks: First of all, constant noncommutativity can only be an approximation of a realistic theory, and therefore it is necessary to study more complicated space-dependent structures as well. Secondly, in the canonical case, the noncommutativity didn't fulfill the initial hope of curing the divergencies of quantum field theory. Therefore it is very desirable to understand noncommutative spaces that really admit finite QFTs.

These two aspects of going beyond the canonical case will be the main focus of this thesis. They will be addressed within two different formalisms, each of which is especially suited for the purpose.

In the first part noncommutative spaces created by star-products are studied. In the case of nonconstant noncommutativity, the ordinary derivatives possess a deformed Leibniz rule, i.e. d_i (f star g) \neq d_i f star g + f star d_i g. Therefore we construct new objects that still have an undeformed Leibniz rule. These derivations of the star-product algebra can be gauged much in the same way as in the canonical case and lead to function-valued gauge fields. By linking the derivations to frames (vielbeins) of a curved manifold, it is possible to formulate noncommutative gauge theories that admit nonconstant noncommutativity and go to gauge theory on curved spacetime in the commutative limit. We are also able to express the dependence of the noncommutative quantities on their corresponding commutative counterparts by using Seiberg-Witten maps.

In the second part we will study noncommutative gauge theory in the matrix theory approach. There, the noncommutative space is the ground state of a matrix action, the fluctuations around this ground state creating the gauge theory. In the canonical case the matrices used are infinite-dimensional (they are the Fock-space representation of the Heisenberg algebra), leading to a number of problems, especially with divergencies. Therefore we construct gauge theory using finite dimensional matrices (fuzzy spaces). This gauge theory is finite, goes to gauge theory on a 4-dimensional manifold in the commutative limit and can also be used to regularize the noncommutative gauge theory of the canonical case. In particular, we are able to match parts of the known instanton sector of the canonical case with the instantons of the finite theory.

This thesis studies the performance of statistical learning methods

in high energy and astrophysics where they have become a standard tool in physics analysis.

They are used to perform complex classification or regression by intelligent pattern recognition.

This kind of artificial intelligence is achieved by the principle ``learning from examples'':

The examples describe the relationship between detector events and their classification.

The application of statistical learning methods is either motivated by the lack of

knowledge about this relationship or by tight time restrictions. In the

first case learning from examples is the only possibility since no theory is available

which would allow to build an algorithm in the classical way. In the second case

a classical algorithm exists but is too slow to cope with the time restrictions.

It is therefore replaced by a pattern recognition machine which implements a

fast statistical learning method.

But even in applications where some kind of classical algorithm had done a good job,

statistical learning methods convinced by their remarkable performance.

This thesis gives an introduction to statistical learning methods and how they

are applied correctly in physics analysis. Their flexibility and high performance will

be discussed by showing intriguing results from high energy and astrophysics.

These include the development of highly efficient triggers, powerful purification of

event samples and exact reconstruction of hidden event parameters.

The presented studies also show typical problems in the application of

statistical learning methods. They should be only second choice in all cases

where an algorithm based on prior knowledge exists.

Some examples in physics analyses are found where these methods are not used

in the right way leading either to wrong predictions or bad performance. Physicists also

often hesitate to profit from these methods because they fear that

statistical learning methods cannot be controlled in a physically correct way.

Besides there are many different statistical learning methods to choose from

and all the different methods have

their advantages and disadvantages -- compared to each other and to classical

algorithms.

By discussing several examples from high energy and astrophysics experiments

the principles, advantages and weaknesses of all popular statistical learning methods

will be analysed. A focus will be put on neural networks as they form some kind of standard

among different learning methods in physics analysis.

The mass of the top quark is a fundamental parameter of the Standard Model. Its precise knowledge yields valuable insights into unresolved phenomena in and beyond the Standard Model. A measurement of the top quark mass with the matrix element method in the lepton+jets final state in D0 Run II is presented. Events are selected requiring an isolated energetic charged lepton (electron or muon), significant missing transverse energy, and exactly four calorimeter jets. For each event, the probabilities to originate from the signal and background processes are calculated based on the measured kinematics, the object resolutions and the respective matrix elements. The jet energy scale is known to be the dominant source of systematic uncertainty. The reference scale for the mass measurement is derived from Monte Carlo events. The matrix element likelihood is defined as a function of both, mtop

and jet energy scale JES, where the latter represents a scale factor with respect to the reference scale. The top mass is obtained from a two-dimensional correlated fit, and the likelihood yields both the statistical and jet energy scale uncertainty. Using a dataset of 320 pb-1 of D0 Run II data, the mass of the top quark is measured to be

mtop (ljets) = 169.5 +/- 4.4(stat.+JES) +1.7-1.6(syst.) GeV

mtop (ejets) = 168.8 +/- 6.0(stat.+JES) +1.9-1.9(syst.) GeV

mtop (mujets)= 172.3 +/- 9.6(stat.+JES) +3.4-3.3(syst.) GeV

The jet energy scale measurement in the lepton+jets sample yields JES=1.034 +/- 0.034, suggesting good consistency of the data with the simulation. The measurement forecasts significant improvements to the total top mass uncertainty during Run II before the startup of the LHC, as the data sample will grow by a factor of ten and D0's tracking capabilities will be employed in jet energy reconstruction and flavor identification.

In this thesis, theoretical studies of decoherence properties and the measurement process of a charge qubit defined in a double quantum dot structure are summarized. There have been three experimental realizations of charge qubits in double quantum dots already, where the quality factors have been quite small. Therefore, the theoretical analysis of possible decoherence mechanisms and how measurements can ideally be performed could be beneficial for the further development in new experiments.

A search for associated chargino neutralino pair production is performed in the trilepton decay channel qq -> chi^+-_1 + chi^0_2 -> l+- + nu + chi^0_1 + mu^+- + mu^+- chi^0_1, using data collected with the D0 detector at a center-of-mass energy of 1.96 TeV at the Fermilab Tevatron Collider. The data sample corresponds to an integrated luminosity of ~300 pb^-1.

A dedicated event selection is applied to all samples including the data sample and the Monte Carlo simulated samples for the Standard Model background and the Supersymmetry signal. Events with two muons plus an additional isolated track, replacing the requirement of a third charged lepton in the event, are analyzed. Additionally, selected events must have a large amount of missing transverse energy due to the neutrino and the two LSP.

After all selection cuts are applied, 2 data events are found, with an expected number of background events of 1.75 +- 0.34(stat.) +- 0.46 (syst.). No evidence for Supersymmetry is found and limits on the production cross-section times leptonic branching fraction are set.

When the presented analysis is considered in combination with three other decay channels, no evidence for Supersymmetry is found. Limits on the production cross-section times leptonic branching fraction are set. A lower chargino mass limit of 117 GeV at 95% CL is then derived for the mSUGRA model in a region of parameter space with enhanced leptonic branching fractions.

The description and control of decoherence of quantum bit systems have become a field of increasing interest during the last decade. We discuss different techniques to estimate and model decoherence sources of solid state quantum bit realizations.

At first, we derive a microscopic, perturbation theoretical approach for Lindblad master equations of a spin-Boson model at low temperatures.

A different sort of decoherence is investigate by means of the bistable fluctuator model.

For this particular but nevertheless for solid state qubits relevant noise source, we present a suitably designed dynamical decoupling method (so-called quantum bang-bang).

This works as a high-pass filter, suppressing low frequency parts of the noise most effectively and thus being a promising method to compensate the ubiquituous 1/f noise.

Furthermore, we investigate the behaviour of a two coupled spin system exposed to collective and localized bath.

For this dressed-spin system we receive by means of scaling-analysis in first order a quantum phase diagram.

On that we can identify the various quantum dynamical and entanglement phases.