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- 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.

- A numerical renormalization group approach to dissipative quantum impurity systems (2011)
- The miniaturization of electronics is reaching its limits. Structures necessary to build integrated circuits from semiconductors are shrinking and could reach the size of only a few atoms within the next few years. It will be at the latest at this point in time that the physics of nanostructures gains importance in our every day life. This thesis deals with the physics of quantum impurity models. All models of this class exhibit an identical structure: the simple and small impurity only has few degrees of freedom. It can be built out of a small number of atoms or a single molecule, for example. In the simplest case it can be described by a single spin degree of freedom, in many quantum impurity models, it can be treated exactly. The complexity of the description arises from its coupling to a large number of fermionic or bosonic degrees of freedom (large meaning that we have to deal with particle numbers of the order of 10^{23}). An exact treatment thus remains impossible. At the same time, physical effects which arise in quantum impurity systems often cannot be described within a perturbative theory, since multiple energy scales may play an important role. One example for such an effect is the Kondo effect, where the free magnetic moment of the impurity is screened by a "cloud" of fermionic particles of the quantum bath. The Kondo effect is only one example for the rich physics stemming from correlation effects in many body systems. Quantum impurity models, and the oftentimes related Kondo effect, have regained the attention of experimental and theoretical physicists since the advent of quantum dots, which are sometimes also referred to as as artificial atoms. Quantum dots offer a unprecedented control and tunability of many system parameters. Hence, they constitute a nice "playground" for fundamental research, while being promising candidates for building blocks of future technological devices as well. Recently Loss' and DiVincenzo's p roposal of a quantum computing scheme based on spins in quantum dots, increased the efforts of experimentalists to coherently manipulate and read out the spins of quantum dots one by one. In this context two topics are of paramount importance for future quantum information processing: since decoherence times have to be large enough to allow for good error correction schemes, understanding the loss of phase coherence in quantum impurity systems is a prerequisite for quantum computation in these systems. Nonequilibrium phenomena in quantum impurity systems also have to be understood, before one may gain control of manipulating quantum bits. As a first step towards more complicated nonequilibrium situations, the reaction of a system to a quantum quench, i.e. a sudden change of external fields or other parameters of the system can be investigated. We give an introduction to a powerful numerical method used in this field of research, the numerical renormalization group method, and apply this method and its recent enhancements to various quantum impurity systems. The main part of this thesis may be structured in the following way: - Ferromagnetic Kondo Model, - Spin-Dynamics in the Anisotropic Kondo and the Spin-Boson Model, - Two Ising-coupled Spins in a Bosonic Bath, - Decoherence in an Aharanov-Bohm Interferometer.

- Ab-initio simulations of pressure effects on structural and electronic properties of iron based superconductors (2014)
- The ab-initio molecular dynamics framework has been the cornerstone of computational solid state physics in the last few decades. Although it is already a mature field it is still rapidly developing to accommodate the growth in solid state research as well as to efficiently utilize the increase in computing power. Starting from the first principles, the ab-initio molecular dynamics provides essential information about structural and electronic properties of matter under various external conditions. In this thesis we use the ab-initio molecular dynamics to study the behavior of BaFe2As2 and CaFe2As2 under the application of external pressure. BaFe2As2 and CaFe2As2 belong to the family of iron based superconductors which are a novel and promising superconducting materials. The application of pressure is one of two key methods by which electronic and structural properties of iron based superconductors can be modified, the other one being doping (or chemical pressure). In particular, it has been noted that pressure conditions have an important effect, but their exact role is not fully understood. To better understand the effect of different pressure conditions we have performed a series of ab-initio simulations of pressure application. In order to apply the pressure with arbitrary stress tensor we have developed a method based on the Fast Inertial Relaxation Engine, whereby the unit cell and the atomic positions are evolved according to the metadynamical equations of motion. We have found that the application of hydrostatic and c axis uniaxial pressure induces a phase transition from the magnetically ordered orthorhombic phase to the non-magnetic collapsed tetragonal phase in both BaFe2As2 and CaFe2As2. In the case of BaFe2As2, an intermediate tetragonal non-magnetic tetragonal phase is observed in addition. Application of the uniaxial pressure parallel to the c axis reduces the critical pressure of the phase transition by an order of magnitude, in agreement with the experimental findings. The in-plane pressure application did not result in transition to the non-magnetic tetragonal phase and instead, rotation of the magnetic order direction could be observed. This is discussed in the context of Ginzburg-Landau theory. We have also found that the magnetostructural phase transition is accompanied by a change in the Fermi surface topology, whereby the hole cylinders centered around the Gamma point disappear, restricting the possible Cooper pair scattering channels in the tetragonal phase. Our calculations also permit us to estimate the bulk moduli and the orthorhombic elastic constants of BaFe2As2 and CaFe2As2. To study the electronic structure in systems with broken translational symmetry, such as doped iron based superconductors, it is necessary to develop a method to unfold the complicated bandstructures arising from the supercell calculations. In this thesis we present the unfolding method based on group theoretical techniques. We achieve the unfolding by employing induced irreducible representations of space groups. The unique feature of our method is that it treats the point group operations on an equal footing with the translations. This permits us to unfold the bandstructures beyond the limit of translation symmetry and also formulate the tight-binding models of reduced dimensionality if certain conditions are met. Inclusion of point group operations in the unfolding formalism allows us to reach important conclusions about the two versus one iron picture in iron based superconductors. And finally, we present the results of ab-initio structure prediction in the cases of giant volume collapse in MnS2 and alkaline doped picene. In the case of MnS2, a previously unobserved high pressure arsenopyrite structure of MnS2 is predicted and stability regions for the two competing metastable phases under pressure are determined. In the case of alkaline doped picene, crystal structures with different levels of doping were predicted and used to study the role of electronic correlations.

- Aspects of electron correlations in two-dimensional metals (2015)
- Landau's Fermi liquid theory has been the main tool for investigating interactions between fermions at low energies for more than 50 years. It has been successful in describing, amongst other things, the mass enhancement in ³He and the thermodynamics of a large class of metals. Whilst this in itself is remarkable given the phenomenological nature of the original theory, experiments have found several materials, such as some superconducting and heavy-fermion materials, which cannot be described within the Fermi liquid picture. Because of this, many attempts have been made to understand these ''non Fermi liquid'' phases from a theoretical perspective. This will be the broad topic of the first part of this thesis and will be investigated in Chapter 2, where we consider a two-dimensional system of electrons interacting close to a Fermi surface through a damped gapless bosonic field. Such systems are known to give rise to non Fermi liquid behaviour. In particular we will consider the Ising-nematic quantum critical point of a two-dimensional metal. At this quantum critical point the Fermi liquid theory breaks down and the fermionic self-energy acquires the non Fermi liquid like {omega}²/³ frequency dependence at lowest order and within the canonical Hertz-Millis approach to quantum criticality of interacting fermions. Previous studies have however shown that, due to the gapless nature of the electronic single-particle excitations, the exponent of 2/3 is modified by an anomalous dimension {eta_psi} which changes, not only the exponent of the frequency dependence, but also the exponent of the momentum dependence of the self-energy. These studies also show that the usual 1/N-expansion breaks down for this problem. We therefore develop an alternative approach to calculate the anomalous dimensions based on the functional renormalization group, which will be introduced in the introductory Chapter 1. Doing so we will be able to calculate both the anomalous dimension renormalizing the exponent of the frequency dependence and the exponent renormalizing the momentum dependence of the self-energy. Moreover we will see that an effective interaction between the bosonic fields, mediated by the fermions, is crucial in order to obtain these renormalizations. In the second part of this thesis, presented in Chapter 3, we return to Fermi liquid theory itself. Indeed, despite its conceptual simplicity of expressing interacting electrons through long-lived quasi-particles which behave in a similar fashion as free particles, albeit with renormalized parameters, it remains an active area of research. In particular, in order to take into account the full effects of interactions between quasi-particles, it is crucial to consider specific microscopic models. One such effect, which is not captured by the phenomenological theory itself, is the appearance of non-analytic terms in the expansions of various thermodynamic quantities such as heat-capacity and susceptibility with respect to an external magnetic field, temperature, or momentum. Such non-analyticities may have a large impact on the phase diagram of, for example, itinerant electrons near a ferromagnetic quantum phase transition. Inspired by this we consider a system of interacting electrons in a weak external magnetic field within Fermi liquid theory. For this system we calculate various quasi-particle properties such as the quasi-particle residue, momentum-renormalization factor, and a renormalization factor which relates to the self-energy on the Fermi surface. From these renormalization factors we then extract physical quantities such as the renormalized mass and renormalized electron Lande g-factor. By calculating the renormalization factors within second order perturbation theory numerically and analytically, using a phase-space decomposition, we show that all renormalization factors acquire a non-analytic term proportional to the absolute value of the magnetic field. We moreover explicitly calculate the prefactors of these terms and find that they are all universal and determined by low-energy scattering processes which we classify. We also consider the non-analytic contributions to the same renormalization factors at finite temperatures and for finite external frequencies and discuss possible experimental ways of measuring the prefactors. Specifically we find that the tunnelling density of states and the conductivity acquire a non-analytic dependence on magnetic field (and temperature) coming from the momentum-renormalization factor. For the latter we discuss how this relates to previous works which show the existence of non-analyticities in the conductivity at first order in the interaction.

- Atomistic molecular dynamics approach for channeling of charged particles in oriented crystals (2015)

- Chopping and transport of high-intensity ion beams (2014)
- In this thesis, a novel 257 kHz chopper device was numerically developed, technically designed and experimentally commissioned; a 4-solenoid, low-energy ion beam transport line was numerically investigated, installed and experimentally commissioned; and a novel massless beam-separation system was numerically developed. The chopper combines a pulsed electric field with a static magnetic field in an ExB or Wien-filter type field configuration. Chopped beam pulses with a 257 kHz repetition rate and rise times of 110 ns were experimentally achieved using a 14 keV helium beam. Due to the achieved results, the complete LEBT line for the future Frankfurt Neutron Source FRANZ is ready to deliver a dc or a pulsed beam. At the same time, the LEBT section represents an attractive test stand for the study of low-energy ion beams. It combines magnetic lenses, which allow space-charge compensated beam transport, and a chopper system capable of producing short beam pulses in the hundred nanosecond range. Since these beam pulses are transported onwards, their longitudinal and transverse properties can be analyzed. The pulse duration and time of flight are well below the rise time for the space-charge compensation through residual gas ionization. This opens the possibility for dedicated investigations of the transport of short, low-energy beam pulses including longitudinal and transverse space-charge effects and of relevant issues like the dynamics of space-charge compensation and electron effects in short pulses.

- Commissioning of the ALICE High-Level Trigger (2012)
- A new era in experimental nuclear physics has begun with the start-up of the Large Hadron Collider at CERN and its dedicated heavy-ion detector system ALICE. Measuring the highest energy density ever produced in nucleus-nucleus collisions, the detector has been designed to study the properties of the created hot and dense medium, assumed to be a Quark-Gluon Plasma. Comprised of 18 high granularity sub-detectors, ALICE delivers data from a few million electronic channels of proton-proton and heavy-ion collisions. The produced data volume can reach up to 26 GByte/s for central Pb–Pb collisions at design luminosity of L = 1027 cm−2 s−1 , challenging not only the data storage, but also the physics analysis. A High-Level Trigger (HLT) has been built and commissioned to reduce that amount of data to a storable value prior to archiving with the means of data filtering and compression without the loss of physics information. Implemented as a large high performance compute cluster, the HLT is able to perform a full reconstruction of all events at the time of data-taking, which allows to trigger, based on the information of a complete event. Rare physics probes, with high transverse momentum, can be identified and selected to enhance the overall physics reach of the experiment. The commissioning of the HLT is at the center of this thesis. Being deeply embedded in the ALICE data path and, therefore, interfacing all other ALICE subsystems, this commissioning imposed not only a major challenge, but also a massive coordination effort, which was completed with the first proton-proton collisions reconstructed by the HLT. Furthermore, this thesis is completed with the study and implementation of on-line high transverse momentum triggers.

- Coulomb dissociation of 31Cl and 32Ar - constraining the rp process (2012)
- The subject of this thesis aimed at a better understanding of the spectacular X-ray burst. The most likely astrophysical site is a very dense neutron star, which accretes H/He-rich matter from a close companion. While falling towards the neutron star, the matter is heated up and a thermonuclear runaway is ignited. The exact description of this process is dominated by the properties of a few proton-rich radioactive isotopes, which have a low interaction probability, hence a high abundance. The topic of this thesis was therefore an investigation of the short-lived, proton-rich isotopes 31Cl and 32Ar. The Coulomb dissociation method is the modern technique of choice. Excitations with energies up to 20 MeV can be induced by the Lorentz contracted Coulomb ﬁeld of a lead target. At the GSI Helmholtzzentrum für Schwerionenforschung GmbH in Darmstadt, Germany, a Ar beam was accelerated to an energy of 825 AMeV and fragmented in a beryllium target. The fragment separator was used to select the desired isotopes with a remaining energy of 650 AMeV. They were subsequently directed onto a 208 Pb target in the ALAND/LAND setup. The measurement was performed in inverse kinematics. All reaction products were detected and inclusive and exclusive measurements of the respective Coulomb dissociation cross sections were possible. During the analysis of the experiment, it was possible to extract the energy-diﬀerential excitation spectrum of 31Cl, and to constrain astrophysically important parameters for the time-reversed 30S(p,γ)31Cl reaction. A single resonance at 0.443(37) MeV dominates the stellar reaction rate, which was also deduced and compared to previous calculations. The integrated Coulomb dissociation cross section of this resonance was determined to 15(6) mb. The astrophysically important one- and two-proton emission channels were analyzed for 32Ar and energy-diﬀerential excitation spectra could be derived. The integrated Coulomb dissociation cross section for two proton emission were determined with two diﬀerent techniques. The inclusive measurement yields a cross section of 214(29stat)(20sys) mb, whereas the exclusive reconstruction results in a cross section of 226(14stat)(23sys) mb. Both results are in very good agreement. The Coulomb dissociation cross section for the one-proton emission channel is extracted solely from the exclusive measurement and is 54(8stat)(6sys) mb. Furthermore, the development of the Low Energy Neutron detector Array (LENA) for the upcoming R3B setup is described. The detector will be utilized in charge-exchange reactions to detect the low-energy recoil neutrons from (p,n)-type reactions. These reaction studies are of particular importance in the astrophysical context and can be used to constrain half lifes under stellar conditions. In the frame of this work, prototypes of the detector were built and successfully commissioned in several international laboratories. The analysis was supported by detailed simulations of the detection characteristics.

- Density functional theory and dynamical mean field theory: applications to correlated electron materials (2012)
- The study of systems whose properties are governed by electronic correlations is a corner stone of modern solid-state physics. Often, such systems feature unique and distinct properties like Mott metal-insulator transitions, rich phase diagrams, and high sensitivity to subtle changes in the applied conditions. Whereas the standard approach to electronic structure calculations, density functional theory (DFT), is able to address the complexity of real-world materials but is known to have serious limitations in the description of correlations, the dynamical mean-field theory (DMFT) has become an established method for the treatment of correlated fermions, first on the level of minimal models and later in combination with DFT, termed LDA+DMFT. This thesis presents theoretical calculations on different materials exhibiting correlated physics, where we aim at covering a range in terms of systems --from rather weakly correlated to strongy correlated-- as well as in terms of methods, from DFT calculations to combined LDA+DMFT calculations. We begin with a study on a selection of iron pnictides, a recently discovered family of high-temperature superconductors with varying degree of correlation strength, and show that their magnetic and optical properties can be assessed to some degree within DFT, despite the correlated nature of these systems. Next, extending our analysis to the inclusion of correlations in the framework of LDA+DMFT, we discuss the electronic structure of the iron pnictide LiFeAs which we find to be well described by Fermi liquid theory with regard to many of its properties, yet we see distinct changes in its Fermi surface upon inclusion of correlations. We continue the study of low-energy properties and specifically Fermi surfaces on two more iron pnictides, LaFePO and LiFeP, and predict a topology change of their Fermi surfaces due to the effect of correlations, with possible implications for their superconducting properties. In our last study, we close the circle by presenting LDA+DMFT calculations on an organic molecular crystal on the verge of a Mott metal-insulator transition; there, we find the spectral and optical properties to display signatures of strong electronic correlations beyond Fermi liquid theory.