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

We explore the phenomenon of spontaneous symmetry breaking in the context of collective neutrino flavor oscillations. Namely, we investigate the spontaneous breaking of isotropy in a homogeneous gas of neutrinos and of azimuthal isotropy in the context of core-collapse supernovae. For the homo- geneous gas, a simple one-dimensional model is analysed in order to demonstrate the phenomenon and understand the connection to the linearized stability analysis. The effect is then investigated in the context of isotropic emission from a supernova core. We show that an azimuthally isotropic flavor configuration is unstable under the differential equations of motion. We analyse the linear stability of propagation in the flavor state and the important consequences to the general prediction of collective flavor conversion. This symmetry-breaking instability is sensitive to the ordering of the neutrino masses.

In this thesis various aspects of target-space duality in closed bosonic string theory are studied. It begins by introducing generalized geometry as the main mathematical framework. In analogy to general relativity with the Riemannian metric as dynamical quantity, a unified description for string backgrounds – Riemannian metrics together with Kalb-Ramond two-form fields – is approached via Courant algebroids on the generalized tangent bundle equipped with a generalized metric. The dual background configuration, i.e. a metric and a bivector field, is described by the generalized cotangent bundle. The absence of a conventional curvature tensor and consequently the problem of defining generalized gravity theories on Courant algebroids is investigated in detail. This leads to the introduction of Lie algebroids whose differential geometry is suitable for the formulation of gravity theories. Different such theories are shown to be interrelated by appropriate homomorphisms. This proves to be useful for describing non-geometric backgrounds.

Target-space duality is introduced in terms of O(d,d)-duality which identifies two-dimensional non-linear sigma models for different string backgrounds as physically equivalent under certain conditions: The backgrounds and coordinates of the dual theories have to be related by certain O(d, d) transformations. In particular, integrability conditions of the dual coordinates are formulated in terms of Courant algebroids. Apart from (non-abelian) T-duality, O(d,d)-duality contains the novel Poisson-duality induced by Poisson structures. T- and Poisson-duality are applied to the three-torus with constant H-flux which shows the existence of non-geometric backgrounds. The latter exceed conventional conceptions of geometry as they cannot be described globally.

The problem of describing non-geometric backgrounds is approached with generalizes geometry. A unified description of T-dual backgrounds is given in terms of proto-Lie bialgebroids – one for the geometric sector and another for the non-geometric one. They combine into a Courant algebroid whose anomalous Jacobi identity provides conditions for the concurrent appearance of dual fluxes. The absence of a gravity theory leads to the restriction to Lie algebroids. Their gravity theories allow for a global description of non-geometric backgrounds by an exact prescription for the patching of these backgrounds. The description extends to all possible supergravity theories.

The question whether a unified description of dual backgrounds is possible is reconsidered in a manifestly T-duality invariant conformal field theory approach. Dual coordinates are treated on equal footing. Modular invariance of the one-loop partition function together with the premise of physical intermediate states in four-tachyon scattering inevitably leads to the appearance of the strong constraint of double field theory on non-compact spaces. Toroidally compactified directions do not require a constraint. This explains the appearance of the strong constraint and justifies possible attenuations.

Markarian 421 (Mrk~421) is one of the classical blazars at X-ray and very high energies (VHE; $>$100 GeV). Its spectral energy distribution (SED) can be accurately characterized by current instruments because of its close proximity, which makes Mrk~421 one of the best sources to study the nature of blazars. The goal of this PhD thesis is to better understand the mechanisms responsible for the broadband emission and the temporal evolution of Mrk~421. The results might be applied to other blazars which cannot be studied with this level of detail because their emissions are weaker, or they are located further away. This thesis reports results from $\sim$70 hours of observations with MAGIC in 2010 and 2011 (the first two years of the operation of the MAGIC stereo telescopes), as well as the results from the multi-wavelength (MW) observation campaigns in 2010 and 2011, where more than 20 instruments participated, covering energies from radio to VHE.

The MW data from the 2010 and 2011 campaigns show that, for both years, the fractional variability $F_{\rm var}$ increases with the energy for both the low-energy and the high-energy bumps in the SED of Mrk~421. Furthermore, $F_{\rm var}(\text{optical})$ was similar to $F_{\rm var}(\text{HE-$\gamma$-ray;$>$100 MeV})$, and $F_{\rm var}(\text{X-ray})$ was similar to $F_{\rm var}(\text{VHE-$\gamma$-ray})$. This observed characteristic is expected from the strong correlation between the synchrotron photons and the up-scattered photons by inverse-Compton effect within the synchrotron self-Compton (SSC) emission model, thus allowing for the first time of the consistency test on this widely used theoretical model.

During the MW campaign in 2010, we measured the decay of a flaring activity during 13 days in March. We could perform MW observations every day, which enables an unprecedented characterization of the time-evolution of the radio to $\gamma$-ray emission of Mrk~421. The broadband SEDs during this flaring episode, resolved on timescales of one day, were characterized with two leptonic scenarios: a one-zone SSC model, and a two-zone SSC model where one zone is responsible for the quiescent emission while the other (smaller) zone, which is spatially separated from the former one, contributes to the daily-variable emission occurring mostly at X-rays and VHE $\gamma$ rays. Both the one-zone SSC and the two-zone SSC models can describe the daily SEDs. However, the two-zone SSC model provides a better agreement to the observed SED at the narrow peaks of the low- and high-energy bumps during the highest activity. The proposed two-zone scenario would naturally lead to the correlated variability in the X-ray and VHE bands without variability in the optical/UV band, as well as to shorter timescales for the variability in the X-ray and VHE bands with respect to the variability in the other bands. This concept of a second small emission region containing a narrow electron spectrum in order to explain the short timescale flaring activity in the X-ray and VHE bands could be generalized to other blazars.

The results from the 2010 March flaring activity of Mrk~421 are reported in Sections~\ref{LightCurves} -- \ref{Discussion}, and they are the main scientific achievement of this PhD thesis. Preliminary results were reported (as an oral contribution) in the 33rd International Cosmic Ray Conference (Rio de Janeiro, July 2013), one of the most prestigious conferences in the field of the VHE astronomy and astro-particle physics in general. The final results (reviewed and approved within the \Fermic, MAGIC, and VERITAS Collaborations) have been submitted for publication in the Astronomy and Astrophysics journal in 2014 June.

During the MW campaign in 2011, Mrk~421 had an atypically high activity in the optical band, together with a very low state in the X-ray/VHE band. Typically, blazar emission models for Mrk~421 focus on the explanation of the variability in the X-ray and $\gamma$-ray bands. This

This thesis investigates bulk continuum generation. A full study of all relevant parameter is given. In addition, its application in ultrafast and widly tunable amplifiers and spectrometers is shown.

In dieser Dissertation untersuchen wir eine Vielzahl von Themen aus dem Bereich der Kosmologie und der Gravitation. Insbesondere behandeln wir Fragestellungen aus der Inflationstheorie, der Strukturbildung im neuzeitlichen Universum und massiver Gravitation, sowie Quantenaspekte schwarzer Löcher und Eigenschaften bestimmter skalare Theorien bei sehr hohen Energien.

Im sogenannten "New Higgs Inflation"-Modell spielt das Higgs-Boson die Rolle des Inflaton-Felds. Das Modell ist kompatibel mit Messungen der Higgs-Masse, weil das Higgs-Boson nichtminimal an den Einstein-Tensor gekoppelt wird. Wir untersuchen das Modell in Hinblick auf die kürzlich veröffentlichten Resultate der BICEP2- und Planck-Experimente und finden eine hervorragende Übereinstimmung mit den gemessenen Daten. Desweiteren zeigen wir auf, dass die scheinbaren Widersprüche zwischen Planck- und BICEP2-Daten dank eines negativ laufenden Spektralindex verschwinden. Wir untersuchen außerdem die Unitaritätseigenschaften der Theorie und räsonieren, dass es während der gesamten Entwicklung des Universums nicht zu Unitaritätsverletzung kommt. Während der Dauer der inflationären Phase sind Kopplungen in den Higgs-Higgs und Higgs-Graviton-Sektoren durch eine großen feldabhängige Skala unterdrückt. Die W- und Z-Bosonen hingegen entkoppeln aufgrund ihrer sehr großen Masse. Wir zeigen eine Möglichkeit auf, die es erlaubt die Eichbosonen als Teil der Niederenergietheorie zu behalten. Dies wird erreicht durch eine gravitationsabhängige nichtminimale Kopplung des Higgs-Felds an die Eichbosonen.

Im nächsten Abschnitt konzentrieren wir uns auf das neuzeitliche Universum. Wir untersuchen den sogenannten sphärischen Kollaps in Modellen gekoppelter dunkler Energie. Insbesondere leiten wir eine Formulierung des sphärischen Kollaps her, die auf den nichtlinearen Navier-Stokes-Gleichungen basiert. Im Gegensatz zu bekannten Beispielen aus der Literatur fließen alle wichtigen Fifth-Force Effekte in die Entwicklung ein. Wir zeigen, dass unsere Methode einfachen Einblick in viele Subtilitäten erlaubt, die auftreten wenn die dunkle Energie als inhomogen angenommen wird.

Es folgt eine Einleitung in die Theorien von massiven Spin-2 Teilchen. Hier erklären wir die Schwierigkeiten der Formulierung einer nichtlinearen, wechselwirkenden Theorie. Wir betrachten das bekannte Problem des Boulware-Deser-Geists und zeigen zwei Wege auf, dieses No-Go-Theorem zu vermeiden. Insbesondere konstruieren wir die eindeutige Theorie eines wechselwirkenden massiven Spin-2 Teilchens, die auf kubischer Ordnung trunkiert werden kann, ohne dass sie zu Geist-Instabilitäten führt.

Der zweite Teil dieser Arbeit widmet sich bekannten Problemen der Physik schwarzer Löcher. Hier liegt unser Fokus auf der Idee, das schwarze Löcher als Bose-Kondensate von Gravitonen aufgefasst werden können. Abweichungen von semiklassischem Verhalten sind Resultat von starken Quanteneffekten die aufgrund einer kollektiven starken Kopplung auftreten. Diese starke Kopplung führt in bekannten Systemen zu einem Quantenphasenübergang oder einer Bifurkation. Die quantenmechanischen Effekte könnten der Schlüssel zur Auflösung lang existierender Probleme in der Physik schwarzer Löcher sein. Dies umschließt zum Beispiel das Informationsparadox und das ``No-Hair''-Theorem. Außerdem könnten sie wertvolle Einblicke in die Vermutung liefern, dass schwarze Löcher die Systeme sind, die Informationen am schnellsten verschlüsseln.

Als Modell für ein schwarzes Loch studieren wir ein System von ultrakalten Bosonen auf einem Ring. Dieses System ist bekannt als eines, dass einen Quantenkritischen Punkt besitzt. Wir demonstrieren, dass am kritischen Punkt Quanteneffekte sogar für sehr große Besetzungszahlen wichtig sein können. Hierzu definieren wir die Fluktuationsverschränkung, die angibt, wie sehr verschiedene Impulsmoden miteinander verschränkt sind. Die Fluktuationsverschränkung ist maximal am kritischen Punkt und ist dominiert von sehr langwell

Due to the accessible sharp dose gradients, external beam radiotherapy with protons and heavier ions enables a highly conformal adaptation of the delivered dose to arbitrarily shaped tumour volumes. However, this high conformity is accompanied by an increased sensitivity to potential uncertainties, e.g., due to changes in the patient anatomy. Additional challenges are imposed by respiratory motion which does not only lead to rapid changes of the patient anatomy, but, in the cased of actively scanned ions beams, also to the formation of dose inhomogeneities. Therefore, it is highly desirable to verify the actual application of the treatment and to detect possible deviations with respect to the planned irradiation. At present, the only clinically implemented approach for a close-in-time verification of single treatment fractions is based on detecting the distribution of β+-emitter formed in nuclear fragmentation reactions during the irradiation by means of positron emission tomography (PET). For this purpose, a commercial PET/CT (computed tomography) scanner has been installed directly next to the treatment rooms at the Heidelberg Ion-Beam Therapy Center (HIT). Up to present, the application of this treatment verification technique is, however, still limited to static target volumes.

This thesis aimed at investigating the feasibility and performance of PET-based treatment verification under consideration of organ motion. In experimental irradiation studies with moving phantoms, not only the practicability of PET-based treatment monitoring for moving targets, using a commercial PET/CT device, could be shown for the first time, but also the potential of this technique to detect motion-related deviations from the planned treatment with sub-millimetre accuracy. The first application to four exemplary hepato-cellular carcinoma patient cases under substantially more challenging clinical conditions indicated potential for improvement by taking organ motion into consideration, particularly for patients exhibiting motion amplitudes of above 1cm and a sufficiently large number of detected true coincidences during their post-irradiation PET scan. Despite the application of an optimised PET image reconstruction scheme, as retrieved from a dedicated phantom imaging study in the scope of this work, the small number of counts and the resulting high level of image noise were identified as a major limiting factor for the detection of motion-induced dose inhomogeneities within the patient. Moreover, the biological washout modelling of the irradiation-induced isotopes proved to be not sufficiently accurate and thereby impede a quantitative analysis of measured and simulated data under consideration of target motion. In future, improvements are particularly foreseen through dedicated noise-robust time-resolved (4D) image reconstruction algorithms, an improved tracking of the organ motion, e.g., by ultrasound (US) imaging, as implemented for the first time in 4D PET imaging in the scope of this work, as well as by patient-specific washout models.

A Quantum point contact (QPC) is a one dimensional constriction, separating two extended electron

systems allowing transport between them only though a short and narrow channel.

The linear conductance of QPCs is quantized in units of the conductance quantum

G_Q=2e^2/h, where e is the electron charge and h is Planck's constant. Thus the

conductance shows a staircase when plotted as a function of gate-voltage which

defines the width of the channel. In addition measured curves show a shoulder-like

step around 0.7G_Q. In this regime QPCs show anomalous behaviour in quantities

like electrical or thermal conductance, noise, and thermopower, as a function of

external parameters such as temperature, magnetic field, or applied voltage. These

phenomena, collectively known as the 0.7-anomaly in QPCs are subject of controversial

discussion.

This thesis offers a detailed description of QPCs in the parameter regime of the

0.7-anomaly. A model is presented which reproduces the phenomenology of the

0.7-anomaly. We give an intuitive picture and a detailed description of the

microscopic mechanism leading to the anomalous behavior. Further, we offer detailed

predictions for the behavior of the 0.7-anomaly in the presence of spin-orbit

interactions.

Our best theoretical results were achieved using an approximation scheme within the

functional renormalization group (fRG) which we developed to treat inhomogeneous

interacting fermi systems. This scheme, called the coupled ladder approximation

(CLA), allows the flow of the two-particle vertex to be incorporated even if the

number of interacting sites N, is large, by reducing the number of independent

variables which represent the two-particle vertex from O(N^4) to

O (N^2).