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- Studies on the focusing performance of a Gabor lens depending on nonneutral plasma properties (2013)
- The concept of the Gabor lens goes back to an idea by Dennis Gabor, who proposed a magnetron-type trap as an effective diverging lens for electron beams (collecting lens for positive ion beams). Electrons confined inside the lens volume by orthogonal magnetic and electric fields, create an electric space charge field that causes a radial symmetric focusing force on an ion beam passing through the lens volume. Since the beginning of the 1990s, a new design of this lens type as well as numerical models to describe the confined plasma cloud have been developed at the Institute for Applied Physics (IAP, Johann Wolfgang Goethe-University Frankfurt). Thanks to an improved understanding of the plasma confinement as a function of the external fields, two lenses have successfully been tested for low beam currents and remain in operation. In the scope of this work, the performance of a prototype Gabor lens for the transport of intense, i.e. space charge dominated ion beams, was investigated at the High Current Test Injector (HOSTI) of GSI Helmholtzzentrum für Schwerionenforschung GmbH for the first time. To ensure an optimal focusing performance of the Gabor lens a homogeneous and stable electron confinement is required. Therefore, new non-interceptive diagnostic methods were developed to investigate the parameters and state of the confined nonneutral plasma column as a function of the external fields. An essential part of the studies was the time-resolved diagnostic of an occurring plasma instability and the determination of the electron temperature via optical spectroscopy. The latter necessitated the detailed investigation of atomic excitation as well as the measurement of optical-emission cross sections. A comparison of the results from both experiments i.e. the beam transport measurements at GSI and the diagnostic experiments performed at IAP concerning the plasma state, gave first indications of possible interaction processes between the nonneutral plasma and the ion beam.

- Open heavy flavor and other hard probes in ultra-relativistic heavy-ion collisions (2014)
- In this thesis hard probes are studied in the partonic transport model BAMPS (Boltzmann Approach to MultiParton Scatterings). Employing Monte Carlo techniques, this model describes the 3+1 dimensional evolution of the quark gluon plasma phase in ultra-relativistic heavy-ion collisions by propagating all particles in space and time and carrying out their collisions according to the Boltzmann equation. Since hard probes are produced in hard processes with a large momentum transfer, the value of the running coupling is small and their interactions should be describable within perturbative QCD (pQCD). This work focuses on open heavy flavor, but also addresses the suppression of light parton jets, in particular to highlight differences due to the mass. For light partons, radiative processes are the dominant contribution to their energy loss. For heavy quarks, we show that also binary interactions with a running coupling and an improved Debye screening matched to hard-thermal-loop calculations play an important role. Furthermore, the impact of the mass in radiative interactions, prominently named the dead cone effect, and the interplay with the Landau-Pomeranchuk-Migdal (LPM) effect are studied in great detail. Since the transport model BAMPS has access to all medium properties and the space time information of heavy quarks, it is the ideal tool to study the dissociation and regeneration of J/psi mesons, which is also investigated in this thesis.

- A kinetic theory for spin waves in yttrium-iron garnet (2013)
- Spin waves in yttrium-iron garnet has been the subject of research for decades. Recently the report of Bose-Einstein condensation at room temperature has brought these experiments back into focus. Due to the small mass of quasiparticles compared to atoms for example, the condensation temperature can be much higher. With spin-wave quasiparticles, so-called magnons, even room temperature can be reached by externally injecting magnons. But also possible applications in information technologies are of interest. Using excitations as carriers for information instead of charges delivers a much more efficient way of processing data. Basic logical operations have already been realized. Finally the wavelength of spin waves which can be decreased to nanoscale, gives the opportunity to further miniaturize devices for receiving signals for example in smartphones. For all of these purposes the magnon system is driven far out of equilibrium. In order to get a better fundamental understanding, we concentrate in the main part of this thesis on the nonequilibrium aspect of magnon experiments and investigate their thermalization process. In this context we develop formalisms which are of general interest and which can be adopted to many different kinds of systems. A milestone in describing gases out of equilibrium was the Boltzmann equation discovered by Ludwig Boltzmann in 1872. In this thesis extensions to the Boltzmann equation with improved approximations are derived. For the application to yttrium-iron garnet we describe the thermalization process after magnons were excited by an external microwave field. First we consider the Bose-Einstein condensation phenomena. A special property of thin films of yttrium-iron garnet is that the dispersion of magnons has its minimum at finite wave vectors which leads to an interesting behavior of the condensate. We investigate the spatial structure of the condensate using the Gross-Pitaevskii equation and find that the magnons can not condensate only at the energy minimum but that also higher Fourier modes have to be occupied macroscopically. In principle this can lead to a localization on a lattice in real space. Next we use functional renormalization group methods to go beyond the perturbation theory expressions in the Boltzmann equation. It is a difficult task to find a suitable cutoff scheme which fits to the constraints of nonequilibrium, namely causality and the fluctuation-dissipation theorem when approaching equilibrium. Therefore the cutoff scheme we developed for bosons in the context of our considerations is of general interest for the functional renormalization group. In certain approximations we obtain a system of differential equations which have a similar transition rate structure to the Boltzmann equation. We consider a model of two kinds of free bosons of which one type of boson acts as a thermal bath to the other one. Taking a suitable initial state we can use our formalism to describe the dynamics of magnons such that an enhanced occupation of the ground state is achieved. Numerical results are in good agreement with experimental data. Finally we extend our model to consider also the pumping process and the decrease of the magnon particle number till thermal equilibrium is reached again. Additional terms which explicitly break the U(1)-symmetry make it necessary to also extend the theory from which a kinetic equation can be deduced. These extensions are complicated and we therefore restrict ourselves to perturbation theory only. Because of the weak interactions in yttrium-iron garnet this provides already good results.

- Shedding light on reaction mechanisms : structure determination of reactive intermediates and investigation of protein structural dynamics using 2D-IR spectroscopy (2012)
- Detailed knowledge of reaction mechanisms is key to understanding chemical, biological, and biophysical processes. For many reasons, it is desirable to comprehend how a reaction proceeds and what influences the reaction rate and its products. In biophysics, reaction mechanisms provide insight into enzyme and protein function, the reason why they are so efficient, and what determines their reaction rates. They also reveal the relationship between the function of a protein and its structure and dynamics. In chemistry, reaction mechanisms are able to explain side products, solvent effects, and the stereochemistry of a product. They are also the basis for potentially optimizing reactions with respect to yield, enhancing the stereoselectivity, or for modifying reactions in order to obtain other related products. A key step to investigate reaction mechanisms is the identification and characterization of intermediates, which may be reactive, short-lived, and therefore only weakly populated. Nowadays, the structures of those can in most cases only be hypothesized based on products, side products, and isolable intermediates, because intermediates with a life time of less than a few microseconds are not accessible with the commonly used techniques for structure determination such as X-ray crystallography and nuclear magnetic resonance (NMR) spectroscopy. In this thesis, two-dimensional infrared (2D-IR) spectroscopy is shown to be a powerful complement to the existing techniques for structure determination in solution. 2D-IR spectroscopy uses a femtosecond laser setup to investigate interactions between vibrations - analogous to 2D-NMR, which investigates the interactions between spins. Its ultrafast time resolution makes 2D-IR spectroscopy particularly well suited for the two topics investigated in this thesis: Structure Determination of Reactive Intermediates and Conformational Dynamics of Proteins. Structure Determination of Reactive Intermediates: The focus of this thesis is using polarization-dependent 2D-IR (P2D-IR) spectroscopy for structure determination of N-crotonyloxazolidinone (referred to as 1), a small organic compound with a chiral oxazolidinone, known as Evans auxiliary, and its reactive complexes with the Lewis acids SnCl4 and Mg(ClO4)2. Chiral oxazolidinones in combination with Lewis acids have frequently been used in stereoselective synthesis for over 30 years. Nevertheless, the detailed mechanisms are in many cases xvi ABSTRACT still mere hypotheses and have not yet been experimentally proven. By accurately measuring the angles between the transition dipole moments in the molecules using an optimized P2D-IR setup and comparing the results to DFT calculations, the conformation of 1 and the conformation and coordination of the main complexes with SnCl4 and Mg(ClO4)2 are unequivocally identified and analyzed in depth. Structural details, such as a slight twist in the solution structure of 1, are detected using P2D-IR spectroscopy; these cannot be inferred from NMR spectroscopy or DFT calculations. In addition to the main Lewis acid complexes, complexes in low concentration are detected and tentatively assigned to different conformations and complexation geometries. The knowledge of those structures is essential for rationalizing the observed stereoselectivities. Additionally, a method is introduced that enables structure determination of molecules in complex mixtures and even in the presence of molecules with similar spectral properties and in high concentration. This work sets the stage for future studies of other substrate-catalyst complexes and reaction intermediates for which the structure determination has not been possible to date. Conformational Dynamics of Proteins: Exchange 2D-IR spectroscopy allows the investigation of fast dynamics without disturbing the equilibrium of the exchanging species. It is therefore well suited to investigate fast dynamics of proteins and to reveal the speed limit of those. The temperature dependence of the conformational dynamics between the myoglobin substates A1 and A3 in equilibrium is analyzed. The various substates of myoglobin can be detected with FTIR spectroscopy, if carbon monoxide is bound to the heme. From previous studies it is known that the exchange rates at room temperature are in the picosecond time range, well suited to be investigated by 2D-IR spectroscopy. In the temperature range between 0 °C and 40 °C only a weak temperature dependence of the exchange rate in the myoglobin mutant L29I is observed in the present study. The exchange rate approximately doubles from 15 ns-1 at 0 °C to 31 ns-1 at 40 °C. It turned out that the conformational dynamics correlates linearly with the solvent viscosity, which itself is temperature dependent. Comparing our results to measurements at cryogenic temperatures, the linear relation between exchange time constant for this process and the viscosity is shown for the temperature range between -100 °C and 40 °C (corresponding to a viscosity change of 14 orders of magnitude). Thus, it is proven that the dynamics of the conformational switching are mainly determined by solvent dynamics, i.e., the protein dynamics are slaved to the solvent dynamics. This is the first time slaving is observed for such fast processes (in the picosecond time range). The observation implies a long-range structural rearrangement between the myoglobin substates A1 and A3. In addition, the exchange for other mutants and wild type myoglobin is analyzed qualitatively and found to agree with the conclusions drawn from L29I myoglobin.

- Dynamical effects and disorder in ultracold bosonic matter (2012)
- In this thesis, various aspects on the theoretical description of ultracold bosonic atoms in optical lattices are investigated. After giving a brief introduction to the fundamental concepts of BECs, atomic physics, interatomic interactions and experimental procedures in chapter (1), we derive the Bose-Hubbard model from first principles in chapter (2). In this chapter, we also introduce and discuss a technique to efficiently determine Wannier states, which, in contrast to current techniques, can also be extended to inhomogeneous systems. This technique is later extended to higher dimensional, non-separable lattices in chapter (5). The many-body physics and phases of the Bose-Hubbard is shortly presented in chapter (3) in conjunction with Gutzwiller mean-field theory, and the recently devised projection operator approach. We then return to the derivation of an improved microscopic many-body Hamiltonian, which contains higher band contributions in the presence of interactions in chapter (4). We then move on to many-particle theory. To demonstrate the conceptual relations required in the following chapter, we derive Bogoliubov theory in chapter (5.3.4) in three different ways and discuss the connections. Furthermore, this derivation goes beyond the usual version discussed in most textbooks and papers, as it accounts for the fact, that the quasi-particle Hamiltonian is not diagonalizable in the condensate and the eigenvectors have to be completed by additional vectors to form a basis. This leads to a qualitatively different quasi-particle Hamiltonian and more intricate transformation relations as a result. In the following two chapters (7, 8), we derive an extended quasi-particle theory, which goes beyond Bogoliubov theory and is not restricted to weak interactions or a large condensate fraction. This quasi-particle theory naturally contains additional modes, such as the amplitude mode in the strongly interacting condensate. Bragg spectroscopy, a momentum-resolved spectroscopic technique, is introduced and used for the first experimental detection of the amplitude mode at finite quasi-momentum in chapter (9). The closely related lattice modulation spectroscopy is discussed in chapter (10). The results of a time-dependent simulation agree with experimental data, suggesting that also the amplitude mode, and not the sound mode, was probed in these experiments. In chapter (11) the dynamics of strongly interacting bosons far from equilibrium in inhomogeneous potentials is explored. We introduce a procedure that, in conjunction with the collapse and revival of the condensate, can be used to create exotic condensates, while particularly focusing on the case of a quadratic trapping potential. Finally, in chapter (12), we turn towards the physics of disordered systems derive and discuss in detail the stochastic mean-field theory for the disordered Bose-Hubbard model.