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

Im Rahmen der Arbeit wird eine neue, von Beobachtungen der Dynamik angetriebene Version des gekoppelten Klima-Chemiemodellsystems ECHAM5/MESSy vorgestellt. Ein wesentlicher Vorteil dieser Modellversion ist die Möglichkeit, die modellierten chemischen Spurengase erstmals direkt mit Einzelmessungen zu vergleichen.

Es werden verschiedene Parametrisierungen für Stickoxidemissionen aus Blitzen getestet. Die modellierten Stickoxid- und Ozonmischungsverhältnisse werden anhand von Flugzeugmessungen aus der oberen tropischen Troposphäre validiert.

Ein Vergleich der simulierten Spurengasverteilung in der unteren Stratosphäre mit MIPAS/ENVISAT Beobachtungen belegt, dass ein realistisches Transportverhalten, speziell in der polaren Stratosphäre, erst mit der im Rahmen dieser Arbeit entwickelten vertikal höher aufgelösten Modellversion garantiert werden kann.

Gegenstand der vorliegenden Arbeit war die Entwicklung und Analyse einer neuartigen abbildenden Optik mit dem Ziel, das räumliche Auflösungsvermögen im Röntgenband zwischen 1 keV und 20 keV auf wenigstens 1 mas zu verbessern. Aufgrund ihrer hohen Toleranz gegenüber Fertigungsfehlern besitzen transmissive Linsen das prinzipielle Potential zur beugungsbegrenzten Abbildung. Je nach Ausführung dürfen Abweichungen von mehreren 100 – 1000 nm gegenüber der idealen Formgebung auftreten. Im Gegensatz zur absorptionsbehafteten, massiven Version weist die diffraktive, profiloptimierte Fresnel-Linse auch in höheren Ordnungen eine Beugungseffizienz zwischen 40% und 100% auf. Der Kontamination der Bildebene durch Streustrahlung benachbarter Ordnungen ist ggf. durch eine ausreichende Zentralobstruktion zu begegnen, deren Radius dem doppelten Detektor-Halbmesser entspricht. Strahlenoptische Berechnungen weisen diffraktive Linsen als vergleichsweise tolerant gegenüber Aberrationen sphärischen wie winkelabhängigen Ursprungs aus. Typische Öffnungsverhältnisse f von (10^4 – 10^5) erlauben Verkippungen von bis zu 1°. Die Lichtstärke, definiert als Produkt von effektiver Sammelfläche und Bandpass, skaliert für Fresnel-Linsen ausschließlich linear mit der Brennweite, bleibt allerdings selbst für Fokaldistanzen von wenigen 100 km auf wenige cm^2 keV beschränkt.

Mit der segmentierten Apertur lässt sich jedoch die Lichtstärke erhöhen, ohne das Prinzip der beugungsbegrenzten Abbildung und den klassischen Einzelfokus aufzugeben. Bei einer Ortsauflösung von 1 mm erreichen derlei inkohärent operierende Objektive eine Lichtstärke von über 1000 cm^2 keV. Unter Einsatz eines dem diffraktiven Bandpass adäquaten Kristallspektrographen bedarf es dazu tendenziell großer Radien von rund 10 m und typischer Brennweiten im Bereich einiger 100 km.

Ferner wurden im Rahmen dieser Arbeit mutmaßlich erstmals Multiband-Objektive zur wissenschaftlich vorteilhaften Simultanfokussierung von bis zu drei Energiebändern implementiert. Bestehend aus Partial-Linsen unterschiedlicher Gitterfrequenz, erweisen sie sich der Monoband-Ausführung als bzgl. Auflösung, Brennweite und Lichtstärke prinzipiell ebenbürtig.

Die Dispersionskorrektur mittels eines additiven refraktiven Linsenprofils erweitert den spektralen Bandpass auf dem Detektor direkt zugängliche 100 eV oder mehr. Mit der Absorption geht eine reduzierte Sammelfläche für kompakte Hybridlinsen einher. Trotzdem resultiert unter Beibehalt der Winkelauflösung für Materialien wie Li oder Be jenseits weniger keV eine gegenüber dem diffraktiven Analogon verbesserte Lichtstärke. Optimiert bzgl. Material und Energie, steigern derartige Achromaten die Nachweisempfindlichkeit um das bis zu 40-fache – entsprechend einer Lichtstärke von rund 100 cm^2 keV bei Brennweiten von 100 km oder mehr.

Wiederum segmentiert, wirkt sich die Absorption vergleichsweise geringfügig auf die Winkelauflösung aus, die Sensitivität des dispersionskorrigierten Objektivs steigt gegenüber der diffraktiven Version unter sonst gleichen Bedingungen jetzt um bis zu zwei Größenordnungen. Bei gegebener Ortsauflösung von 0.75 mm ergeben sich für Li oberhalb von 6 keV und Be jenseits von 8 keV optimierte Lichtstärken zwischen 10^3 und 10^4 cm^2 keV, vergleichbar jenen der gegenwärtig aktiven Observatorien Chandra und XMM-Newton. Die Winkelschärfe skaliert invers mit der Fokaldistanz, für höchstens 1 mas ergeben sich Brennweiten von rund 100 – 1000 km.

Plankonvexe Profile werden den zumeist kleinen Krümmungsradien der refraktiven Komponente hinsichtlich ihrer Aberrationen dritten Grades im allgemeinen nicht gerecht. Hingegen reduziert das aplanatische, nahezu bikonvexe Profil sowohl sphärische als auch winkelabhängige Bildfehler auf ihre diffraktiven Beiträge und legt daher im segmentierten Hybrid-Achromaten die Konstruktion symmetrischer, prismen-ähnlicher Bausteine nahe.

Die mit der kohärenten Profilreduktion einhergehende Interferenz erfordert den Einsatz abbildender

In this thesis we analysed the deepest XMM-Newton observations of the Chandra Deep Field South and the Lockman Hole. These two reference fields for studies of different X-ray background source classes, provide a unique opportunity to study physical and evolutionary properties of distant normal and active galaxies, clusters of galaxies and even faint Galactic stars using statistically significant

samples. The main goal of the work was a further improvement of the knowledge about X-ray properties of AGN and galaxies in the distant Universe using the statistical treatment of these large samples of detected sources.

In the state of the art the Standard Model is the best gauge

theory describing interactions among elementary particles. It

comprises all of the fundamental interactions in nature except

gravitation. Its predictions have been experimentally tested to a

high level of accuracy. However, it is not considered to be the

fundamental theory of gauge interactions. It contains a lot of

arbitrary parameters. It can not predict the fermion masses and

fails to explain the smallness of neutrino masses which have been

observed by recent experiments. It contains no gauge bosons that

can mediate nucleon decays via baryon and lepton number violating

process, which are needed to explain the baryon asymmetry in our

universe. Furthermore, CP violation has to be introduced into

the CKM and MNS matrices by hand.

The shortcomings of the Standard Model can be solved in the

framework of grand unified gauge theories (GUTs) which have

greater degrees of freedom. GUT's which have truly one coupling

constant are based on gauge groups that contain the Standard Model

as a subgroup. There are a limited number of such gauge groups.

SO(10) is a fully symmetric gauge group that has two outstanding

features: It unifies all the known gauge interactions under a

single coupling strength and classifies all the known fermions of

a family under a single spinor.

In this work, we will study SO(10) grand unification in its full

extent by using different explicit matrix representations which

exhibit the structure of SO(10) in a very transparent way. Our

approach consists mainly of two stages: We will derive the

explicit expressions of the mass-eigenvalues and mass-eigenstates

of the physical gauge bosons from a mass squared-matrix that

contains all the information about the mixing parameters among the

gauge fields and the phases which are sources for CP violation.

In the light of this analysis, we will derive the explicit

expressions for the interaction Lagrangians of the charged

currents, the neutral currents and the charged and colored

currents in SO(10). We will present explicit expressions of the

vector and axial-vector couplings of the two neutral currents in

SO(10). We will show how the baryon, lepton and baryon minus

lepton number violating processes and their explicit CP

violating phases are accommodated in the SO(10) theory.

The Higgs potential that we use to implement in the Higgs

mechanism will be constructed in a most general fashion through a

careful study of the Higgs fields of SO(10), where we give

special emphasis on illustrating the explicit matrix

representation of these Higgs fields. The potential part of the

Higgs Lagrangian will give us the properties of the minimum of the

vacuum, and the kinetic part will give us the mass-squared matrix

of the gauge bosons via spontaneous symmetry breakdown. The same

Higgs multiplets will be coupled to fermions through a democratic

Yukawa matrix. Thereby, we will derive explicit expressions for

the fermion masses of the third family including Majorana and

Dirac masses for neutrinos. We will introduce a flavor-eigenbasis

for neutrinos and find the mass-eigenstates and mass-eigenvalues

of the neutrinos. Explicit expressions for CP violation in the

neutrino sector will be obtained.

In the second stage of our work, we will evaluate all the above

mentioned quantities. We will compare our results with those of

the Standard Model like the W and Z masses and the vector and

axial-vector coupling of the NC current and the fermion masses

of the third family. In addition, we will present the values of

the physical quantities that are not present in the Standard Model

like the masses of new gauge bosons, the vector and axial-vector

couplings of a new NC current, the masses of a light left-handed

and a heavier right-neutrino, the values of various mixing

parameters and CP phases etc.

The input values required for these evaluations will be acquired

mainly from two sources: First, we will determine the vacuum

expectation

The subject of this thesis is the muonic hydrogen (µp) Lamb shift experiment being performed at the Paul Scherrer Institute, Switzerland. Its goal is to measure the 2S-2P energy difference in µp atoms by laser spectroscopy and to deduce the proton root ­mean­ square (rms) charge radius with 10-3 precision, an order of magnitude better than

presently known. This would make it possible to test bound-state quantum electrodynamics (QED) in hydrogen at the relative accuracy level of 10-7, and will lead to an improvement in the determination of the Rydberg constant by more than a factor of seven. Moreover it will represent a benchmark for QCD theories.

The experiment is based on the measurement of the energy difference between the 2S(F=1) and 2P(F=2) levels in µp atoms to a precision of 30 ppm, using a pulsed laser tunable

at wavelengths around 6 µm. Negative muons from a unique low energy muon beam are stopped at a rate of 70 s-1 in 0.6 hPa of hydrogen gas. Highly excited µp atoms are formed, and most of them promptly deexcite to the ground state within 100 ns. However, there is a roughly 1% probability that long­live µp(2S) atoms with a lifetime of 1.3 µs are formed.

An incoming muon triggers a pulsed, multi­stage laser system which delivers 0.2 mJ per pulse at 6 µm with 55 s-1 repetition rate. It consists of two XeCl excimer lasers followed by dye lasers which pump an oscillator ­amplifier frequency ­controlled Ti:Sa laser. Its 6 ns long pulse at 708 nm is then frequency shifted to 6 µm via third Stokes production in a Raman cell filled with hydrogen. The laser pulse has a delay of about 1.5 µs with respect to the prompt muon cascade.

If the laser is on resonance, it induces 2S-2P transitions. The subsequent deexcitation to the 1S state emits a 1.9 keV Lyman-alpha x ray which is detected by large area avalanche photo diodes. The resonance frequency, and hence the Lamb shift and the proton radius, are determined by measuring the intensity of these x rays as a function of the laser wavelength.

A search for the 2S-2P resonance line was performed in November 2003 when a broad range of laser frequencies was scanned (49.7409 - 49.8757 THz), corresponding to proton radii between 0.844 and 0.905 fm. The result of the data analysis is that no significant 2S-2P resonance was observed. The negative result is with high probability due to the low statistics and not to an incorrect search region.

The first part of this thesis reports on the present status of the Lamb shift theory in µp. Following, there is a detailed description of the apparatus and analysis of the data. An estimate of the present and future laser-­induced event rates are given, together with a study of the present and future background. In the Appendices are discussed: the energy levels in hydrogen, the proton radius definition, the relevance of this experiment, the 2S state population and lifetime, and the spectroscopic properties of the 2S-2P transition.

Time-resolved vibrational spectroscopy (Raman and IR) provides insight into energy relaxation processes and information about structural dynamics of molecules in solution. An extremely sensitive pump-probe laser-spectrometer has been built for time-resolved IR-spectroscopy in the coursework of this thesis. It allows one to initiate photochemical processes in the visible spectral region and to observe the changes in the mid-infrared. The achieved time resolution (delta tau_(FWHM) < 100 fs) makes it possible to follow extremely fast structural changes. With this setup dynamical processes can be resolved covering 4 orders of magnitude (from 100 fs to 4 ns). The setup is tunable in the range of 3-10 micrometer (1000-3300 cm^-1) and covers the whole relevant spectral range of vibrational structure analysis.

It is known from chemical synthesis, that reaction rates can depend on the chosen solvent. This might be due to partially solvent dependent energy redistribution processes. Such processes are important for chemical reactions, e.g. in stabilizing product states. The molecule para-Nitroaniline (pNA) is especially suitable to investigate such processes. pNA returns via fast (< 400 fs) internal conversion to a hot electronic ground state after excitation by a laser pulse (lambda = 400 nm). The vibrational energy relaxation can be followed subsequently. This relaxation has been observed by the symmetrical NO_2 stretch mode. Due to anharmonic coupling this low frequency mode has been an exceptionally sensitive sensor for the energy relaxation to a solvent. The observed relaxation time constants for pNA are 3,4 ps in deuterated dimethylsulfoxide, 1,9 ps in methanol and 1,5 ps in water. Cooling behavior correlates well with macroscopic thermal conduction and heat capacity of the used solvent. In the microscopic picture we assume a connection to the forming of hydrogen bonds. As chemical reaction rates depend strongly on the internal temperature of a molecule, these results improve the understanding of solvent effects.

With the same method the question of how fast structural changes can occur in a peptide of 8 amino acids has been explored by a collaboration with the group of prof. Hamm in Zurich. Due to the addition of an azobenzene switch in this peptide, which subsequently closes the cycle of the peptide chain, an ultrafast conformational change has been triggered by a light pulse. In a driven phase the peptide backbone reacts within the first 20 ps to the fast (< 2 ps) change in length of the switch. Weakly directed diffuse processes occur on a wide range of time scales, which lead to the final structure change. The results of the measurements gave new insights into the complexity of fast protein folding. A hierarchy of time scales is a typical signature, which can be observed when moving on a rough energy landscape.

Noncommutative (deformed, quantum) spaces are deformations of the usual commutative space-time. They depend on parameters, such that for certain values of parameters they become the usual space-time. The symmetry acting on them is given in terms of a deformed quantum group symmetry. In this work we discuss two special examples, the $\theta$-deformed space and the $\kappa$-deformed space.

In the case of the $\theta$-deformed space we construct a deformed theory of gravity. In the first step the deformed diffeomorphism symmetry is introduced. It is given in terms of the Hopf algebra of deformed diffeomorphisms. The algebra structure is unchanged (as compared to the commutative diffeomorphism symmetry), but the comultiplication changes. In the commutative limit we obtain the Hopf algebra of undeformed diffeomorphisms. Based on this deformed symmetry a covariant tensor calculus is constructed and concepts such as metric, covariant derivative, curvature and torsion are defined. An action that is invariant under the deformed diffeomorphisms is constructed. In the zeroth order in the deformation parameter it reduces to the commutative Einstein-Hilbert action while in higher orders correction terms appear. They are given in terms of the commutative fields (metric, vierbein) and the deformation parameter enters as the coupling constant. One special example of this deformed symmetry, the $\theta$-deformed global Poincar\' e symmetry, is also discussed.

In the case of the $\kappa$-deformed space our aim is the construction of noncommutative gauge theories. Starting from the algebraic definition of the $\kappa$-deformed space, derivatives and the deformed Lorentz generators are introduced. Choosing one particular set of derivatives,

the $\kappa$-Poincar\' e Hopf algebra is defined. The algebraic setting is then mapped to the space of commuting coordinates. In the next step, using the enveloping algebra approach and the Seiberg-Witten map, a general nonabelian gauge theory on this deformed space is constructed. As a consequence of the deformed Leibniz rules for the derivatives used in the construction, the gauge field is derivative-valued. As in the $\theta$-deformed case, in the zeroth order of the deformation parameter the theory reduces to its commutative analog and the higher order corrections are given in terms of the usual (commutative) fields. In this way the field content of the theory is unchanged, but new interactions appear. The deformation parameter takes the role of the coupling constant. For the special case of $U(1)$ gauge theory the action for the gauge field coupled to fermionic matter is formulated and the equations of motion and the conserved current(s) are calculated. The ambiguities in the Seiberg-Witten map are discussed and partially fixed, and an effective action (up to first order in the deformation parameter) which is invariant under the usual Poincar\' e symmetry is obtained.

In this thesis we consider background geometries

resulting from string theory compactifications. In particular,

we investigate supersymmetric vacuum spaces of supergravity

theories and topological twisted sigma models

by means of classical and generalised G-structures.

In the first part we compactify 11d supergravity

on seven-dimensional manifolds due to phenomenological reasons.

A certain amount of supersymmetry forces the internal background

to admit a classical SU(3)- or G2-structure. Especially, in the case

that the four-dimensional space is maximally symmetric and four form fluxes

are present we calculate the relation to the intrinsic torsion.

The second and main part is two-fold. Firstly, we realise

that generalised geometries on six-dimensional manifolds are a natural

framework to study T-duality and mirror symmetry, in particular if the

B-field is non-vanishing. An explicit mirror map is given and we apply this

idea to the generalised formulation of a topological twisted sigma model.

Implications of mirror symmetry are studied,

e.g. observables and topological A- and B-branes.

Secondly, we show that seven-dimensional NS-NS backgrounds in

type II supergravity theories can be described by generalised

G2-geometries. A compactification on six manifolds leads to a new structure.

We call this geometry a generalised SU(3)-structure. We study the

relation between generalised SU(3)- and G2-structures on six- and

seven-manifolds and generalise the Hitchin-flow equations. Finally, we

further develop the generalised SU(3)- and

G2-structures via a constrained variational principle to incorporate

also the remaining physical R-R fields.