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Great interest has emerged recently in the search for Kitaev spin liquid states in real materials. Such states rely on strongly anisotropic magnetic interactions, which have been suggested to exist in a number of candidate materials based on Ir and Ru. This thesis concentrates on two priority purposes. The first is the investigation of electronic and magnetic properties of candidate materials Na2IrO3, α-Li2IrO3, α-RuCl3, γ-Li2IrO3, and Ba3YIr2O9 for Kitaev physics where both spin-orbit coupling and correlation effects are important. The second is the method development for the microscopic description of correlated materials combining many-body methods and density functional theory (DFT). ...
In this thesis we explore the characteristics of strongly interacting matter, described by Quantum Chromodynamics (QCD). In particular, we investigate the properties of QCD at extreme densities, a region yet to be explored by first principle methods. We base the study on lattice gauge theory with Wilson fermions in the strong coupling, heavy quark regime. We expand the lattice action around this limit, and carry out analytic integrals over the gauge links to obtain an effective, dimensionally reduced, theory of Polyakov loop interactions.
The 3D effective theory suffers only from a mild sign problem, and we briefly outline how it can be simulated using either Monte Carlo techniques with reweighting, or the Complex Langevin flow. We then continue to the main topic of the thesis, namely the analytic treatment of the effective theory. We introduce the linked cluster expansion, a method ideal for studying thermodynamic expansions. The complex nature of the effective theory action requires the development of a generalisation of the linked cluster expansion. We find a mapping between generalised linked cluster expansion and our effective theory, and use this to compute the thermodynamic quantities.
Lastly, various resummation techniques are explored, and a chain resummation is implemented on the level of the effective theory itself. The resummed effective theory describes not only nearest neighbour, next to nearest neighbour, and so on, interactions, but couplings at all distances, making it well suited for describing macroscopic effects. We compute the equation of state for cold and dense heavy QCD, and find a correspondence with that of non-relativistic free fermions, indicating a shift of the dynamics in the continuum.
We conclude this thesis by presenting two possible extensions to new physics using the techniques outlined within. First is the application of the effective theory in the large-$N_c$ limit, of particular interest to the study of conformal field theory. Second is the computation of analytic Yang Lee zeros, which can be applied in the search for real phase transitions.
Using a partonic transport model we investigate the evolution of conical structures in ultrarelativistic matter. Using two different source terms and varying the transport properties of the matter we study the formation of Mach Cones. Furthermore, in an additional study we extract the two-particle correlations from the numerical calculations and compare them to an analytical approximation. The influence of the viscosity to the shape of Mach Cones and the corresponding two-particle correlations is studied by adjusting the cross section of the medium.
In the 1960s, theoretical concepts prepared the path to nuclear matter with proton and neutron numbers far beyond the nuclei known at that time. The new laboratory GSI was founded for research on reactions with heavy ions, in particular those for production of the predicted super-heavy nuclei. In this contribution it is presented how the interaction between experiment and theory resulted in a continuous improvement of the experimental set-ups on the one hand, and of the knowledge of the processes during the nuclear reaction and of the properties of the produced nuclei on the other hand. In the course of this work six new elements from 107 to 112 were produced and identified. An overview of the present status of experimental results and a comparison with theoretical interpretations is given.
In this thesis, the production of charged kaons and Φ mesons in Au+Au collisions at sqrt sAuAu = 2.4 GeV is studied. At this energy, all particles carrying open and hidden strangeness are produced below their respective free nucleon-nucleon threshold with the corresponding so-called excess energies: sqrt sK+ exc = -0.15 GeV, sqrt sK- exc = -0.46 GeV, sqrt sΦ exc = -0.49 GeVGeV. As a consequence, the production cross sections are very sensitive to medium effects like momentum distributions, two- or multistep collisions, and modification of the in-medium spectral distribution of the produced states [1]. K+ and K- mesons exhibit different properties in baryon dominated matter, since only K- can be resonantly absorbed by nucleons. Although strangeness exchange reactions have been proposed to be the dominant channel for K- production in the analyzed energy regime, the production yield and kinematic distributions could also be explained in smaller systems based on statistical hadronization model fits to the measured particle yields, including a canonical strangeness suppression radius RC, and taking the Φ feed-down to kaons into account [2, 3]. For the first time in central Au+Au collisions at such low energies, it is possible to reconstruct and do a multi differential analysis of K- and Φ mesons. In principle, this should be the ideal environment for strangeness exchange reactions to occur, as the particles are produced deeply sub-threshold in a large and long-living system. Therefore, it is the ultimate test to differentiate between the different sources for K- production in HIC.
In total 7.3x10exp9 of the 40% most central Au(1.23 GeV per nucleon)+Au collisions are analyzed. The data has been recorded with the High Acceptance DiElectron Spectrometer HADES located at Helmholtzzentrum für Schwerionenforschung GSI in April/May 2012. A substantially improved reconstruction method has been employed to reconstruct the hadrons with high purity in a wide phase space region.
The estimated particle multiplicities follow a clear hierarchy of the excess energy: 41.5 ± 2.1|sys protons at mid-rapidity per unit in rapidity, 11.1 ± 0.6|sys ± 0.4|extrapol π-, (3.01 ± 0.03|stat ± 0.15|sys ± 0.30|extrapól) x10 exp -2 K+, (1.94 ± 0.09|stat ± 0.10|sys ± 0.10|extrapol)x10 exp -4 K- and (0.99 ± 0.24|stat ± 0.10|sys ± 0.05|extrapol)x10 exp -4 Φ per event. The multiplicities of the strange hadrons increase more than linear with the mean number of participating nucleons hAparti, supporting the assumption that the necessary energy to overcome the elementary production threshold is accumulated in multi-particle interactions. Transport models predict such an increase, but are overestimating the measured particle yield and are not able to describe the kinematic distributions of K+ mesons perfectly. However, the best description is given by the IQMD model with a density dependent kaonnucleon potential of 40 MeV at nuclear ground state density.
The K-=K+ multiplicity ratio is constant as a function of centrality and follows with (6.45 ± 0.77)x10 exp -3 the trend of increasing with beam energy indicated from previous experiments [4]. The effective temperature of K- TK+eff = (84 ± 6) MeV is found to be systematically lower than the one of K+ TK+eff = (104 ± 1) MeV, which has also been observed by the other experiments.
The Φ=K- ratio is with a value of 0.52 ± 0.16 higher than the one obtained at higher center-of-mass energies and smaller systems. This behavior is predicted from a tuned version of the UrQMD transport model [5], when including higher mass baryonic resonances which can decay into Φ mesons and from statistical hadronization models when suppressing open strangeness canonically. The found ratio is constant as a function of centrality and results with a branching ratio of 48.9%, that ~ 25% of all measured K- originate from Φ feed-down decays. A two component PLUTO simulation, consisting of a pure thermal and a K- contribution originating from Φ decays, can fully explain the observed lower effective temperature in comparison to K+ and the shape of the measured rapidity distribution of K-. As a result, we find no indication for strangeness exchange reactions being the dominant mechanism for K- production in the SIS18 energy regime, if taking the contribution from Φ feed-down decays into account.
The hadron yields for the 20% most central collisions can be described by a statistical hadronization model fit with the chemical freeze-out temperature of Tchem = (68 ± 2) MeV and baryochemical potential of μB = (883 ± 25) MeV, which is higher than expected from previous parameterizations. The analysis of the transverse mass spectra of protons indicate a kinetic freeze-out temperature of Tkin = (70 ± 4) MeV and radial flow velocity of βr = 0.43 ± 0.01, which is in agreement with the parameters obtained from the linear dependence of the effective temperatures on the particle mass Tkin = (71.5 ± 4.2) MeV and βr = 0.28 ± 0.09.
The Standard Model is one of the greatest successes of modern theoretical physics. Itl describes the physics of elementary particles by means of three forces, the electro-magnetisc, the weak and the strong interactions. The electro-magnetic and the weak interaction are rather well understood in comparison to the strong interaction.
The latest is as fundamental as the others, it is responsible for the formation of all hadrons which are classified into mesons and baryons. Well-known examples of the former is the pion and of the latter is the proton and the neutron, which form the nucleus of every atom. This fundamental force is believed to be described by the Quantum Chromodynamics (QCD) theory. According to this theory, hadrons are not elementary particles but are composed of quarks and gluons. The latter are the vector particles of the force and so are bosons of spin 1 and the former constitute the matter and are fermions with spin 1/2. To describe the interaction a new quantum number had to be introduced: the color charge which exists in three different types (blue, green and red). The name has not been chosen arbitrary as elements created from three quarks of different colors are colorless in the same way that mixing the three primary colors leads to white. However, experimentally no colored structure has ever been observed. The quarks and the gluons seem to be confined in colorless hadrons. This property of QCD is called confinement and results from a large coupling constant at low energy (or large distance). For high energy (or small distance), the perturbative analysis of QCD permits to establish the coupling constant to be small and quarks and gluons are almost free. This property is called asymptotic freedom. The possibility for QCD to describe both behaviors is one of its amazing characteristics. However, both phenomena are not well understood and one needs a method to study both the pertubative and the confining regime.
The only known method which fulfills the above criteria is Lattice QCD and more generally Lattice Quantum Field Theory (LQFT). It consists of a discretization of the spacetime and a formulation of QCD on a four-dimensional Euclidean spacetime grid of spacing a. In this way, the theory is naturally regularized and mathematically well-defined. On the other hand, the path integral formalism allows the theory to be treated as a Statistical Mechanics system which can be evaluated via a Markov chain Monte-Carlo algorithm. This method was first suggested by Wilson in 1974 [1] and shortly after Creutz performed the first numerical simulations of Yang-Mills theory [2] using a heath-bath Monte-Carlo algorithm. It appears that this method is extremely demanding in computational power. In its early days the method was criticized as the only feasible simulations involved non-physical values such as extremely large quark masses, large lattice spacing a and no dynamical quarks. With the progress of the computers and the appearance of the super-computer, the studies have come close to the physical point. But one still needs to deal with discrete space time and finite volume. Several techniques have been developed to estimate the infinite volume limit and the continuum limit. The smaller the lattice spacing and the larger the volume, the better the extrapolation to continuum and infinite volume limits is. The simulations are still very expensive and for the moment a typical length of the box is L ≈ 4fm and a ≈ 0.08fm. However, it has been realized simulating pure Yang-Mills theory and other lower dimensional models that the topology is freezing at small a [3]. It was also observed recently on full QCD simulations [4,5].
The typical lattice spacing for which this problem appears in QCD is a ≈ 0.05fm but this value depends on the quark mass used and on the algorithm. The freezing of topology leads to results which differ from physical results. Solving this issue is important for the future of LQCD [6]. Recently several methods to overcome the problem have been suggested, one of the most popular is the used of open boundary conditions [7] but this promising method has still its own issues, mainly the breaking of translation invariance.
Electronic states with non-trivial topology host a number of novel phenomena with potential for revolutionizing information technology. The quantum anomalous Hall effect provides spin-polarized dissipation-free transport of electrons, while the quantum spin Hall effect in combination with superconductivity has been proposed as the basis for realizing decoherence-free quantum computing. We introduce a new strategy for realizing these effects, namely by hole and electron doping kagome lattice Mott insulators through, for instance, chemical substitution. As an example, we apply this new approach to the natural mineral herbertsmithite. We prove the feasibility of the proposed modifications by performing ab-initio density functional theory calculations and demonstrate the occurrence of the predicted effects using realistic models. Our results herald a new family of quantum anomalous Hall and quantum spin Hall insulators at affordable energy/temperature scales based on kagome lattices of transition metal ions.
For the transport of high-intensity hadron beams in low-energy beam lines of linear accelerators, the compensation of space charge forces by the accumulation of particles of opposite charge is an important effect, reducing the required focusing strength and potentially the emittance growth due to space charge forces. In this thesis, space charge compensation was studied by including the secondary particles in particle-in-cell simulations.
For this purpose, a new electrostatic particle-in-cell code named bender was developed. The software was tested using known self-consistent solutions for an electron plasma confined in an external potential as well as for a KV distributed beam in a periodic focusing lattice. For the simulation of compensation, models for residual gas ionisation by proton and electron impact were implemented.
The compensation process was studied for a 120 keV, 100 mA proton beam transported through a short drift section. Various features in the particle distributions were identified, which can not explained by a uniform reduction in the electric field of the beam. These were tied to the presence of thermal electrons confined within the beam potential. Using the Poisson-Boltzmann equation, their distribution could be reproduced and their influence on the beam for a wider range of parameters studied. However, the observed temperatures show a significant numerical influence. The hypothesis was formed, that stochastical heating present in particle-in-cell simulations is the mechanism leading to the formation of the observed (partial) thermal equilibrium.
For the low-energy beam transport line of the Frankfurt neutron source FRANZ, bender was used to predict the pulse shaping in the novel ExB chopper system. The code was also used for the design and the study of an electron lens for the Integrable Optics Test Accelerator at Fermi National Accelerator Laboratory. Aberrations due to guiding center drifts and the strong electric field of the electron beam as well as the current limits in such a system were investigated.