- Einfluss schwerer hadronischer Zustände auf das QCD-Phasendiagramm und die Ausfrierbedingungen in einem hadronischen chiralen Modell (2006)
- In der vorliegenden Dissertation werden mit einem chiralen SU(3)-Modell die thermodynamischen Eigenschaften von stark wechselwirkender hadronischer Materie und die mikroskopischen Medium-Eigenschaften von Hadronen bei hohen Temperaturen und hohen Baryonen-Dichten untersucht. Das verwendete chirale Modell ist ein erweitertes sigma-omega-Modell in Mittlerer-Feld-Näherung (Mean-Field) mit baryonischen und mesonischen effektiven Freiheitsgraden; es basiert auf spontan gebrochener chiraler Symmetrie und Skaleninvarianz. Das Phasenübergangsverhalten des chiralen Modells wird systematisch untersucht und dabei gezeigt, dass es signifikant von den Kopplungen zusätzlicher schwererer hadronischer Freiheitsgrade ('Resonanzen') abhängt. Durch entsprechende Ankopplung des niedrigsten baryonischen Dekupletts kann ein Phasendiagramm in qualitativer Übereinstimmung mit aktuellen Vorhersagen der Gitter-QCD erreicht werden. Alternativ wird die Ankopplung einer schweren baryonischen Test-Resonanz untersucht, welche effektiv für das Spektrum der schweren hadronischen Zustände steht. Hier ergibt sich für einen bestimmten Bereich der Kopplungen sogar eine quantitative Übereinstimmung zu den Gitter-QCD-Vorhersagen bei gleichzeitig guter Beschreibung der Grundzustandseigenschaften von Kernmaterie. Für diese Zustandsgleichung werden Vorhersagen (innerhalb der Modellannahmen) zu geplanten Experimenten gemacht -- konkret wird gezeigt, dass der Phasenübergangsbereich für das CBM Experiment des geplanten Beschleunigerzentrums FAIR an der GSI Darmstadt experimentell zugänglich ist. Weiter wird das chirale Modell auf die Beschreibung von experimentellen Teilchenzahlverhältnissen (Yield-Ratios) aus Schwerionen-Kollisionen von AGS, SPS und RHIC angewendet. Studiert werden Parametersätze mit stark unterschiedlichen Phasendiagrammen aufgrund unterschiedlicher Ankopplung des baryonischen Dekupletts sowie ein ideales Hadronengas. Bei den niedrigen und mittleren Kollisionsenergien zeigt sich eine verbesserte Beschreibung durch die chiralen Parametersätze im Vergleich zum idealen Hadronengas, besonders deutlich für Parametersätze mit Phasendiagramm ähnlich der Vorhersage aus der Gitter-QCD. Die Wechselwirkung im chiralen Modell führt zu Medium-Modifikationen der chemischen Potentiale und der Hadronenmassen. Die resultierenden Ausfrierparameter mu und T sind deshalb gegenüber dem nichtwechselwirkenden Fall signifikant verändert. An den Ausfrierpunkten zeigen sich deutliche Abweichungen der effektiven Massen von den Vakuummassen (5 bis 15 %) und des effektiven baryo-chemischen Potentials vom ursprünglichen Wert (bis zu 20 %). Ferner werden universelle Kriterien für das Ausfrieren diskutiert und isentrope Expansion zu den Ausfrierpunkten untersucht, wo sich eine starke Abhängigkeit der Trajektorien von der Zustandsgleichung ergibt. Schließlich wird der Einfluss des Dilaton-Felds (Gluonkondensat) auf das Phasenübergangsverhalten bei mu=0 studiert, indem das Gluonkondensat an die Dekuplett-Baryonen gekoppelt wird. Es zeigt sich, dass dadurch eine Restauration der Skaleninvarianz im Modell möglich wird, die gleichzeitig auch eine vollständige Restauration der chiralen Symmetrie bewirkt. Die Restauration der Skaleninvarianz erfolgt erst bei Temperaturen, die oberhalb der chiralen Restauration (im nichtseltsamen Sektor) liegen. Diese Modellerweiterung ermöglicht es, zukünftig das Phasenübergangsverhalten -- Restauration von chiraler Symmetrie und Skaleninvarianz -- auch bei nichtverschwindenden Baryonendichten zu untersuchen. Die Resultate dieser Arbeit zeigen die Wichtigkeit der schweren hadronischen Zustände, der Resonanzen, für das QCD-Phasendiagramm. Für die Zukunft ist eine Ankopplung des gesamten hadronischen Massenspektrums an das Modell erstrebenswert, wie sich sowohl aus der Untersuchung der Modellerweiterung um eine Test-Resonanz als auch aus der Anwendung auf experimentelle Teilchenzahlverhältnisse ergibt.
- Structure of exotic nuclei and superheavy elements in meson field theory (2008)
- In this work the nuclear structure of exotic nuclei and superheavy nuclei is studied in a relativistic framework. In the relativistic mean-field (RMF) approximation, the nucleons interact with each other through the exchange of various effective mesons (scalar, vector, isovector-vector). Ground state properties of exotic nuclei and superheavy nuclei are studied in the RMF theory with the three different parameter sets (ChiM, NL3, NL-Z2). Axial deformation of nuclei within two drip lines are performed with the parameter set (ChiM). The position of drip lines are investigated with three different parameter sets (ChiM, NL3, NL-Z2) and compared with the experimental drip line nuclei. In addition, the structure of hypernuclei are studied and for a certain isotope, hyperon halo nucleus is predicted.
- Chiral symmetry restoration and deconfinement in neutron stars (2009)
- Neutron stars are very dense objects. One teaspoon of their material would have a mass of five billion tons. Their gravitational force is so strong that if an object were to fall from just one meter high it would hit the surface of the respective neutron star at two thousand kilometers per second. In such dense bodies, different particles from the ones present in atomic nuclei, the nucleons, can exist. These particles can be hyperons, that contain non-zero strangeness, or broader resonances. There can also be different states of matter inside neutron stars, such as meson condensates and if the density is height enough to deconfine the nucleons, quark matter. As new degrees of freedom appear in the system, different aspects of matter have to be taken into account. The most important of them being the restoration of the chiral symmetry. This symmetry is spontaneously broken, which is a fact related to the presence of a condensate of scalar quark-antiquark pairs, that for this reason is called chiral condensate. This condensate is present at low densities and even in vacuum. It is important to remember at this point that the modern concept of vacuum is far away from emptiness. It is full of virtual particles that are constantly created and annihilated, being their existence allowed by the uncertainty principle. At very high temperature/density, when the composite particles are dissolved into constituents, the chiral consensate vanishes and the chiral symmetry is restored. To explain how and when chiral symmetry is restored in neutron stars we use a model called non-linear sigma model. This is an effective quantum relativistic model that was developed in order to describe systems of hadrons interacting via meson exchange. The model was constructed from symmetry relations, which allow it to be chiral invariant. The first consequence of this invariance is that there are no bare mass terms in the lagrangian density, causing all, or most of the particles masses to come from the interactions with the medium. There are still other interesting features in neutron stars that cannot be found anywhere else in nature. One of them is the high isospin asymmetry. In a normal nucleus, the amount of protons and neutrons is more or less the same. In a neutron star the amount of neutrons is much higher than the protons. The resulting extra energy (called Fermi energy) increases the energy of the system, allowing the star to support more mass against gravitational collapse. As a consequence of that in early stages of the neutron star evolution, when there are still many trapped neutrinos, the proton fraction is higher than in later stages and consequently the maximum mass that the star can support against gravity is smaller. This, between many other features, shows how the microscopic phenomena of the star can reflect into the macroscopic properties. Another important property of neutron stars is charge neutrality. It is a required assumption for stability in neutron stars, but there are others. One example is chemical equilibrium. It means that the number of particles from each kind is not conserved, but they are created and annihilated through specific reactions that happen at the same rate in both directions. Although to calculate microscopic physics of neutron stars the space-time of special relativity, the Minkowski space, can be used, this is not true for the global properties of the star. In this case general relativity has to be used. The solution of Einstein's equations simplified to static, spherical and isotropic stars correspond to the configurations in which the star is in hydrostatic equilibrium. That means that the internal pressure, coming mainly from the Fermi energy of the neutrons, balances the gravity avoiding the collapse. When rotation is included the star becomes more stable, and consequently, can be more massive. The movement also makes it non-spherical, what requires the metric of the star to also be a function of the polar coordinate. Another important feature that has to be taken into account is the dragging of the local inertial frame. It generates centrifugal forces that are not originated in interactions with other bodies, but from the non-rotation of the frame of reference within which observations are made. These modifications are introduced through the Hartle's approximation that solves the problem by applying perturbation theory. In the mean field approximation, the couplings as well as the parameters of the non-linear sigma model are calibrated to reproduce massive neutron stars. The introduction of new degrees of freedom decreases the maximum mass allowed for the neutron star, as they soften the equation of state. In practice, the only baryons present in the star besides the nucleons are the Lambda and Sigma-, in the case in which the baryon octet is included, and Lambda and Delta-,0,+,++, in the case in which the baryon decuplet is included. The leptons are included to ensure charge neutrality. We choose to proceed our calculations including the baryon octet but not the decuplet, in order to avoid uncertainties in the couplings. The couplings of the hyperons were fitted to the depth of their potentials in nuclei. In this case the chiral symmetry restoration can be observed through the behavior of the related order parameter. The symmetry begins to be restored inside neutron stars and the transition is a smooth crossover. Different stages of the neutron star cooling are reproduced taking into account trapped neutrinos, finite temperature and entropy. Finite-temperature calculations include the heat bath of hadronic quasiparticles within the grand canonical potential of the system. Different schemes are considered, with constant temperature, metric dependent temperature and constant entropy. The neutrino chemical potential is introduced by fixing the lepton number in the system, that also controls the amount of electrons and protons (for charge neutrality). The balance between these two features is delicate and influenced mainly by the baryon number conservation. Isolated stars have a fixed number of baryons, which creates a link between different stages of the cooling. The maximum masses allowed in each stage of the cooling process, the one with high entropy and trapped neutrinos, the deleptonized one with high entropy, and the cold one in beta equilibrium. The cooling process is also influenced by constraints related to the rotation of the star. When rotation is included the star becomes more stable, and consequently, can be more massive. The movement also deforms it, requiring the metric of the star to include modifications that are introduced through the use of perturbation theory. The analysis of the first stages of the neutron star, when it is called proto-neutron star, gives certain constraints on the possible rotation frequencies in the colder stages. Instability windows are calculated in which the star can be stable during certain stages but collapses into black holes during the cooling process. In the last part of the work the hadronic SU(3) model is extended to include quark degrees of freedom. A new effective potential to the order parameter for deconfinement, the Polyakov loop, makes the connection between the physics at low chemical potential and hight temperature of the QCD phase diagram with the height chemical potential and low temperature part. This is done through the introduction of a chemical potential dependency on the already temperature dependent potential. Analyzing the effect of both order parameters, the chiral condensate and the Polyakov loop, we can drawn a phase diagram for symmetric as well as for star matter. The diagram contains a crossover region as well as a first order phase transition line. The new couplings and parameters of the model are chosen mainly to fit lattice QCD, including the position of the critical point. Finally, this matter containing different degrees of freedom (depending on which phase of the diagram we are) is used to calculate hybrid star properties.
- The O(N=2) model in polar coordinates at nonzero temperature (2009)
- Chapter 1 contains the general background of our work. We briefly discuss important aspects of quantum chromodynamics (QCD) and introduce the concept of the chiral condensate as an order parameter for the chiral phase transition. Our focus is on the concept of universality and the arguments why the O(4) model should fall into the same universality class as the effective Lagrangian for the order parameter of (massless) two-flavor QCD. Chapter 2 pedagogically explains the CJT formalism and is concerned with the WKB method. In chapter 3 the CJT formalism is then applied to a simple Z(2) symmetric toy model featuring a one-minimum classical potential. As for all other models we are concerned with in this thesis, we study the behavior at nonzero temperature. This is done in 1+3 dimensions as well as in 1+0 dimensions. In the latter case we are able to compare the effective potential at its global minimum (which is minus the pressure) with our result from the WKB approximation. In chapter 4 this program is also carried out for the toy model with a double-well classical potential, which allows for spontaneous symmetry breaking and tunneling. Our major interest however is in the O(2) model with the fields treated as polar coordinates. This model can be regarded as the first step towards the O(4) model in four-dimensional polar coordinates. Although in principle independent, all subjects discussed in this thesis are directly related to questions arising from the investigation of this particular model. In chapter 5 we start from the generating functional in cartesian coordinates and carry out the transition to polar coordinates. Then we are concerned with the question under which circumstances it is allowed to use the same Feynman rules in polar coordinates as in cartesian coordinates. This question turns out to be non-trivial. On the basis of the common Feynman rules we apply the CJT formalism in chapter 6 to the polar O(2) model. The case of 1+0 dimensions was intended to be a toy model on the basis of which one could more easily explore the transition to polar coordinates. However, it turns out that we are faced with an additional complication in this case, the infrared divergence of thermal integrals. This problem requires special attention and motivates the explicit study of a massless field under topological constraints in chapter 8. In chapter 7 we investigate the cartesian O(2) model in 1+0 dimensions. We compare the effective potential at its global minimum calculated in the CJT formalism and via the WKB approximation. Appendix B reviews the derivation of standard thermal integrals in 1+0 and 1+3 dimensions and constitutes the basis for our CJT calculations and the discussion of infrared divergences. In chapter 9 we discuss the so-called path integral collapse and propose a solution of this problem. In chapter 10 we present our conclusions and an outlook. Since we were interested in organizing our work as pedagogical as possible within the narrow scope of a diploma thesis, we decided to make extensive use of appendices. Appendices A-H are intended for students who are not familiar with several important concepts we are concerned with. We will refer to them explicitly to establish the connection between our work and the general context in which it is settled.
- Mechanisms of nanofractal structure formation and post-growth evolution (2011)
- Nanotechnology is a rapidly developing branch of science, which is focused on the study of phenomena at the nanometer scale, in particular related to the possibilities of matter manipulation. One of the main goals of nanotechnology is the development of controlled, reproducible, and industrially transposable nanostructured materials. The conventional technique of thin-film growth by deposition of atoms, small atomic clusters and molecules on surfaces is the general method, which is often used in nanotechnology for production of new materials. Recent experiments show, that patterns with different morphology can be formed in the course of nanoparticles deposition process on a surface. In this context, predicting of the final architecture of the growing materials is a fundamental problem worth studying. Another factor, which plays an important role in industrial applications of new materials, is the question of post-growth stability of deposited structures. The understanding of the post-growth relaxation processes would give a possibility to estimate the lifetime of the deposited material depending on the conditions at which the material was fabricated. Controllable post-growth manipulations with the architecture of deposited structures opens new path for engineering of nanostructured materials. The task of this thesis is to advance understanding mechanisms of formation and post-growth evolution of nanostructured materials fabricated by atomic clusters deposition on a surface. In order to achieve this goal the following main problems were addressed: 1. The properties of isolated clusters can significantly differ from those of analogous clusters occurring on a solid surface. The difference is caused by the interaction between the cluster and the solid. Therefore, the understanding of structural and dynamical properties of an atomic cluster on a surface is a topic of intense interest from the scientific and technological point of view. In the thesis, stability, energy, and geometry of an atomic cluster on a solid surface were studied using a liquid drop approach which takes into account the cluster-solid interaction. Geometries of the deposited clusters are compared with those of isolated clusters and the differences are discussed. 2. The formation scenarios of patterns on a surface in the course of the process of cluster deposition depend strongly on the dynamics of deposited clusters. Therefore, an important step towards predicting pattern morphology is to study dynamics of a single cluster on a surface. The process of cluster diffusion on a surface was modeled with the use of classical molecular dynamics technique, and the diffusion coefficients for the silver nanoclusters were obtained from the analysis of trajectories of the clusters. The dependence of the diffusion coefficient on the system’s temperature and cluster-surface interaction was established. The results of the calculations are compared with the available experimental results for the diffusion coefficient of silver clusters on graphite surface. 3. The methods of classical molecular dynamics cannot be used for modeling the self-assembly processes of atomic clusters on a surface, because these processes occur on the minutes timescale, what would require an unachievable computer resource for the simulation. Based on the results of molecular dynamics simulations for a single cluster on a surface a Monte-Carlo based approach has been developed to describe the dynamics of the self-assembly of nanoparticles on a surface. This method accounts for the free particle diffusion on a surface, aggregation into islands and detachment from these islands. The developed method is allowed to study pattern formation of structures up to thousands nm, as well as the stability of these structures. Developed method was implemented in MBN Explorer computer package. 4. The process of the pattern formation on a surface was modeled for several different scenarios. Based on the analysis of results of simulations was suggested a criterion, which can be used to distinguish between different patterns formed on a surface, for example: between fractals or compact islands.This criteria can be used to predict the final morphology of a growing structure. 5. The post-growth evolution of patterns on a surface was also analyzed. In particular, attention in the thesis is payed to a systematical theoretical analysis of the post-growth processes occurring in nanofractals on a surface. The time evolution of fractal morphology in the course of the post-growth relaxation was analyzed, the results of these calculations were compared with experimental data available for the post-growth relaxation of silver cluster fractals on graphite substrate. All the aforementioned problems are discussed in details in the thesis.
- Transmission grid extensions in renewable electricity systems (2014)
- The present work deals with the integration of variable renewable energy sources, wind and solar energy into the European and US power grid. In contrast to other networks, such as the gas supply mains, the electricity network is practically not able to store energy. Generation and consumption therefore always have tobe balanced. Currently, the load curve is viewed as a rigid boundary condition, which must be followed by the generation system. The basic idea of the approach followed here is that weather-dependent generation causes a shift of focus of the electricity supply. At high shares of wind and solar generation, the role of the rigid boundary condition falls to the residual load, that is, the remaining load after subtraction of renewable generation. The goal is to include the weather dependence as well as the load curve in the design of the future electricity supply. After a brief introduction, the present work first turns to the underlying weather-, generation and load data, which form the starting point of the analysis. In addition, some basic concepts of energy economics are discussed, which are needed in the following. In the main part of the thesis, several algorithms are developed to determine the load flow in a network with a high share of wind and solar energy and to determine the backup supply needed at the same time. Minimization of the energy needed from controllable power plants, the capacity variable power plants, and the capacity of storing serve as guiding principles. In addition, the optimization problem of grid extensions is considered. It is shown that it can be formulated as a convex optimization problem. It turns out that with an optimized, international transmission network which is about four times the currently available transmission capacity, much of the potential savings in backup energy (about 40%) in Europe can be reached. In contrast, a twelvefold increase the transmission capacity would be necessary for a complete implementation of all possible savings in dispatchable power plants. The reduction of the dispatchable generation capacity and storage capacity, however, presents a greater challenge. Due to correlations in the generation of time series of individual countries, it may be reduced only with difficulty, and by only about 30%. In the following, the influence of the relative share of wind and solar energy is illuminated and examined the interplay with the line capacitance. A stronger transmission network tends to lead to a higher proportion of wind energy being better integrated. With increasing line capacity, the optimal mix in Europe therefore shifts from about 70% to 80% wind. Similar analyses are carried out for the US with comparable results. In addition, the cost of the overall system can be reduced. It is interesting at this point that the advantages for the network integration may outweigh higher production costs of individual technologies, so that it is more favourable from the viewpoint of the entire system to use the more expensive technologies. Finally, attention is given to the flexibility of the dispatchable power plants. Starting from a Fourier-like decomposition of the load curve as it was a few years ago, when hardly renewable generation capacity was present, capacities of different flexibility classes of dispatchable power plant are calculated. For this purpose, it is assumed that the power plant park is able to follow the load curve without significant surplusses or deficits. From this examination, it is derived what capacity must at least be available without having to resort to a detailed database of existing power plants. Assuming a strong European cooperation, with a stronger international transmission network, the dispatchable power capacity can be significantly reduced while maintaining security of supply and generating relatively small surplusses in dispatchable power plants.