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- 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.

- 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.

- Measurement and interpretation of laser accelerated protons at GSI (2014)
- This thesis is structured into 7 chapters: • Chapter 2 gives an overview of the ultrashort high intensity laser interaction with matter. The laser interaction with an induced plasma is described, starting from the kinematics of single electron motion, followed by collective electron effects and the ponderamotive motion in the laser focus and the plasma transparency for the laser beam. The three different mechanisms prepared to accelerate and propagate electrons through matter are discussed. The following indirect acceleration of protons is explained by the Target Normal Sheath Acceleration (TNSA) mechanism. Finally some possible applications of laser accelerated protons are explained briefly. • Chapter 3 deals with the modeling of geometry and field mapping of magnetic lens. Initial proton and electron distributions, fitted to PHELIX measured data are generated, a brief description of employed codes and used techniques in simulation is given, and the aberrations at the solenoid focal spot is studied. • Chapter 4 presents a simulation study for suggested corrections to optimize the proton beam as a later beam source. Two tools have been employed in these suggested corrections, an aperture placed at the solenoid focal spot as energy selection tool, and a scattering foil placed in the proton beam to smooth the radial energy beam profile correlation at the focal spot due to chromatic aberrations. Another suggested correction has been investigated, to optimize the beam radius at the focal spot by lens geometry controlling. • Chapter 5 presents a simulation study for the de-neutralization problem in TNSA caused by the fringing fields of pulsed magnetic solenoid and quadrupole. In this simulation, we followed an electrostatic model, wherethe evolution of both, self and mutual fields through the pulsed magnetic solenoid could be found, which is not the case in the quadrupole and only the growth of self fields could be found. The field mapping of magnetic elements is generated by the Matlab program, while the TraceWin code is employed to study the tracking through magnetic elements. • Chapter 6 describes the PHELIX laser parameters at GSI with chirp pulse amplification technique (CPA), and Gafchromic Radiochromic film RCF) as a spatial energy resolver film detector. The results of experiments with laser proton acceleration, which were performed in two experimental areas at GSI (Z6 area and PHELIX Laser Hall (PLH)), are presented in section 6.3. • Chapter 7 includes the main results of this work, conclusions and gives a perspective for future experimental activities.

- Low-energy effective models for two-flavor quantum chromodynamics and the universality hypothesis (2014)

- Modelling radiation fields of ion beams in tissue-like materials (2014)
- Fast nuclei are ionizing radiation which can cause deleterious effects to irradiated cells. The modelling of the interactions of such ions with matter and the related effects are very important to physics, radiobiology, medicine and space science and technology. A powerful method to study the interactions of ionizing radiation with biological systems was developed in the field of microdosimetry. Microdosimetry spectra characterize the energy deposition to objects of cellular size, i.e., a few micrometers. In the present thesis the interaction of ions with tissue-like media was investigated using the Monte Carlo model for Heavy-Ion Therapy (MCHIT) developed at the Frankfurt Institute for Advanced Studies. MCHIT is a Geant4-based application intended to benchmark the physical models of Geant4 and investigate the physical properties of therapeutic ion beams. We have implemented new features in MCHIT in order to calculate microdosimetric quantities characterizing the radiation fields of accelerated nucleons and nuclei. The results of our Monte Carlo simulations were compared with recent experimental microdosimetry data. In addition to microdosimetry calculations with MCHIT, we also investigated the biological properties of ion beams, e.g. their relative biological effectiveness (RBE), by means of the modified Microdosimetric-Kinetic model (MKM). The MKM uses microdosimetry spectra in describing cell response to radiation. MCHIT+MKM allowed us to study the physical and biological properties of ion beams. The main results of the thesis are as follows: MCHIT is able to describe the spatial distribution of the physical dose in tissue-like media and microdosimetry spectra for ions with energies relevant to space research and ion-beam cancer therapy; MCHIT+MKM predicts a reduction of the biological effectiveness of ions propagating in extended medium due to nuclear fragmentation reactions; We predicted favourable biological dose-depth profiles for monoenergetic helium and lithium beams similar to the one for carbon beam. Well-adjusted biological dose distributions for H-1, He-4, C-12 and O-16 with a very flat spread-out Bragg peak (SOBP) plateau were calculated with MCHIT+MKM; MCHIT+MKM predicts less damage to healthy tissues in the entrance channel for SOBP He-4 and C-12 beams compared to H-1 and O-16 ones. No definitive advantages for oxygen ions with respect to carbon were found.

- Tuning and optimization of the field distribution for 4-rod radio frequency quadrupole linacs (2014)
- In this thesis, the tuning process of the 4-rod Radio Frequency Quadrupole has been analyzed and a theory for the prediction of the tuning plate's influence on the longitudinal voltage distribution was developed together with RF design options for the optimization of the fringe fields. The basic principles of the RFQ's particle dynamics and resonant behavior are introduced in the theory part of this thesis. All studies that are presented are based on the work on four RFQs of recent linac projects. These RFQs are described in one chapter. Here, the projects are introduced together with details about the RFQ parameters and performance. In the meantime two of these RFQs are in full operation at NSCL at MSU and FNAL. One is operating in the test phase of the MedAustron Cancer Therapy Center and the fourth one for LANL is about to be built. The longitudinal voltage distribution has been studied in detail with a focus on the influence of the RF design with tuning elements and parameters like the electrodes overlap or the distance between stems. The theory for simulation methods for the field flatness that were developed as part of this thesis, as well as its simulation with CST MWS have been analyzed and compared to measurements. The lumped circuit model has proven to predict results with an accuracy that can be used in the tuning process of 4-rod RFQs. Together with results from the tuning studies, the studies on the fringe fields of the 4-rod structure lead to a proposal for a 4-rod RFQ model with an improved field distribution in the transverse and longitudinal electric field.

- Lattice QCD at finite temperature with Wilson fermions (2014)
- The subatomic world is governed by the strong interactions of quarks and gluons, described by Quantum Chromodynamics (QCD). Quarks experience confinement into colour-less objects, i.e. they can not be observed as free particles. Under extreme conditions such as high temperature or high density, this constraint softens and a transition to a phase where quarks and gluons are quasi-free particles (Quark-Gluon-Plasma) can occur. This environment resembles the conditions prevailing during the early stages of the universe shortly after the Big Bang. The phase diagram of QCD is under investigation in current and future collider experiments, for example at the Large Hadron Collider (LHC) or at the Facility for Antiproton and Ion Research (FAIR). Due to the strength of the strong interactions in the energy regime of interest, analytic methods can not be applied rigorously. The only tool to study QCD from first principles is given by simulations of its discretised version, Lattice QCD (LQCD). These simulations are in the high-performance computing area, hence, the numerical aspects of LQCD are a vital part in this field of research. In recent years, Graphic Processing Units (GPUs) have been incorporated in these simulations as they are a standard tool for general purpose calculations today. In the course of this thesis, the LQCD application cl2qcd has been developed, which allows for simulations on GPUs as well as on traditional CPUs, as it is based on OpenCL. cl2qcd constitutes the first application for Wilson type fermions in OpenCL. It provides excellent performance and has been applied in physics studies presented in this thesis. The investigation of the QCD phase diagram is hampered by the notorious sign-problem, which restricts current simulation algorithms to small values of the chemical potential. Theoretically, studying unphysical parameter ranges allows for constraints on the phase diagram. Of utmost importance is the clarification of the order of the finite temperature transition in the Nf=2 chiral limit at zero chemical potential. It is not known if it is of first or second order. To this end, simulations utilising Twisted Mass Wilson fermions aiming at the chiral limit are presented in this thesis. Another possibility is the investigation of QCD at purely imaginary chemical potential. In this region, QCD is known to posses a rich phase structure, which can be used to constrain the phase diagram of QCD at real chemical potential and to clarify the nature of the Nf=2 chiral limit. This phase structure is studied within this thesis, in particular the nature of the Roberge-Weiss endpoint is mapped out using Wilson fermions.

- Development of specially shaped laser beams for the optimized acceleration of particles (2014)
- The laser-driven acceleration of protons from thin foils irradiated by hollow high-intensity laser beams in the regime of target normal sheath acceleration is reported for the first time. The use of hollow beams aims at reducing the initial emission solid angle of the TNSA source, due to a flattening of the electron sheath at the target rear side. The experiments were conducted at the PHELIX laser facility at the GSI Helmholtzzentrum für Schwerionenforschung GmbH with laser intensities in the range from 10^18 to 10^20 W/cm^2. We observed an average reduction of the half opening angle by (3.07±0.42)° or (13.2±2)% when the targets have a thickness between 12 to 14 μm. In addition, the highest proton energies were achieved with the hollow laser beam in comparison to the typical Gaussian focal spot.