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In this doctoral thesis the transformation from relativistic hydrodynamics to transport and vice versa is studied. Approximations made by hybrid (hydrodynamics + transport) simulations of relativistic heavy ion collisions are discussed and their reliability is assessed at intermediate collision energies. A new method to simulate heavy ion collisions is suggested, based on the forced thermalization in high-density regions.
Compact stars can be treated as the ultimate laboratories for testing theories of dense matter. They are not only extremely dense objects, but they are known to be associated with strong magnetic fields, fast rotation and, in certain cases, with very high temperatures. Here, we present several different approaches to model numerically the signatures and properties of these stars, namely:
•The effects of strong magnetic fields on hybrid stars by using a fully general relativistic approach. We solved the coupled Maxwell-Einstein equations in a self-consistent way, taking into consideration the anisotropy of the energy-momentum tensor due purely to the magnetic field, magnetic field effects on equation of state and the interaction between matter and the magnetic field (magnetization). We showed that the effects of the magnetization and the magnetic field on the equation of state for matter do not play an important role on global properties of neutron stars (only the pure magnetic _eld contribution does). In addition, the magnetic field breaks the spherical symmetry of stars, inducing major changes in the populated degrees of freedom inside these objects and, potentially, converting a hybrid star into a hadronic star over time.
•The effects of magnetic fields and rotation on the structure and composition of proto-neutron stars. We found that the magnetic field not only deforms these stars, but also significantly alters the number of trapped neutrinos in the stellar interior, together with the strangeness content and temperature in each evolution stage from a hot proto-neutron star to a cold neutron star.
•The influence of the quark-hadron phase transitions in neutron stars. In particular, previous calculations have shown that fast rotating neutron stars, when subjected to a quark-hadron phase transition in their interiors, could give rise to the backbending phenomenon characterized by a spin-up era. In this work, we obtained the interesting backbending phenomenon for fast spinning neutron stars. More importantly, we showed that a magnetic field, which is assumed to be axisymmetric and poloidal, can also be enhanced due to the phase transition from normal hadronic matter to quark matter on highly magnetized neutron stars. Therefore, in parallel to the spin-up era, classes of neutron stars endowed with strong magnetic fields may go through a `magnetic-up era' in their lives.
•Finally, we were also able to calculate super-heavy white dwarfs in the presence of strong magnetic fields. White dwarfs are the progenitors of supernova Type Ia explosions and they are widely used as candles to show that the Universe is expanding and accelerating. However, observations of ultraluminous supernovae have suggested that the progenitor of such an explosion should be a white dwarf with mass above the well-known Chandrasekhar limit ~ 1.4 M. In corroboration with other works, but by using a fully general relativistic framework, we obtained also strongly magnetized white dwarfs with masses M ~ 2:0 M.
In April and May 2012 data on Au+Au collisions at beam energies of Ekin = 1.23A GeV were recorded with the High Acceptance Di-Electron Spectrometer, which is located at the GSI Helmholtz Center for Heavy Ion Research in Darmstadt, Germany. At this beam energy all hadrons containing strangeness are produced below their elementary production threshold. The required energy is not available in binary NN collisions but must be provided by the system e.g. through multi-particle interactions or medium effects like a modified in-medium potential (e.g. KN/ΛN potential). Thus, a high sensitivity to these medium effects is expected in the investigated system.
The baryon-dominated systems created in relativistic heavy-ion collisions (HIC) at SIS18 energies reach densities of about 2-3 times ground state density p0 and may be similar to the properties of matter expected in the inner core of neutron stars. It is in particular the behavior of hadrons containing strangeness, i.e. kaons and hyperons, and their potentials in the dense medium which may have severe implications on astrophysical objects and processes. As ab-initio calculations of quantum chromodynamics (QCD) cannot be performed rigorously on the lattice at finite baryo-chemical potentials due to the fermion sign problem, effective descriptions have to be used in order to model properties of dense systems and the involved particles. The only way to access the in-medium potential of strange hadrons above nuclear ground state density p0 is by comparing data from relativistic HIC to such effective microscopic models. Up to now, not much data on neutral kaons and Λ hyperons are available from heavy collision systems close to their NN production threshold. These two electromagnetically uncharged strange hadrons are in particular well suited to study their potential in a dense nucleon-dominated environment as their kinematic spectra are not affected by Coulomb interactions.
In dieser Arbeit wurden thermodynamische Eigenschaften eines chiralen Quark Meson Modelles untersucht. Das chirale Quark Meson Model beschreibt die starke Wechselwirkung über den Austausch von Mesonen und zudem die thermische und dichteabhängige Entwicklung der Quarkmassen im Medium über die chirale Symmetrie.Im SU(2) Model wurde zunächst in mean field approximation gearbeitet, um im Anschluss den divergenten Vakuumterm mit einzubeziehen. Nach eingehender Untersuchung der Ergebnisse, wurden dann die thermischen Mesonenfluktuationen studiert. In beiden Ansätzen verschiebt die Nullpunktsenergie den chiralen Phasenübergang zu höheren Temperaturen, wodurch die Massen bei höheren Temperaturen entarten. Beide Ansätze wurden dann zu einem gemeinsamen Modell kombiniert, um den Einfluss der Mesonenfluktuationen auf Ordnungsparameter, Massen und thermodynamische Grössen zu untersuchen. Als Fazit der Studie kann behauptet werden, dass sich der Einfluss der Mesonenfluktuationen in grösserem Maÿ auf die Thermodynamik, als auf den Ordnungsparameter und die Massen auswirkt. Im SU(3) Modell wurden ebenfalls regularisiert und zudem Vektormesonen mitberücksichtigt, welche die Repulsion zwischen den einzelnen Freiheitsgraden modelliert. Die Zustandsgleichung wird durch den Vakuum Term etwas softer und zeigt ein ähnliches Verhalten im niederen Energiebereich. Untersucht wurde neben der Temperatur T, die Elektron Baryon Rate Ye, die Sigma Meson Masse noch der Einfluss der Vektorkopplung. Aus der Zustandsgleichung konntendann Isentropen im T-mu Phasendiagramm errechnet werden, welche in naher Zukunft Aufschluss über eine dritte Familie von kompakten Sternen in Zusammenhang mit der entsprechenden Supernova Explosion geben könnte. Um die Existenz von kompakten Sternen genauer zu analysieren, wurde das chiraleSU(3) Quark Meson Modell bei T = 0 benutzt, um über die aus dem Formalismusgewonnenen Grössen Druck und Energiedichte die Tolmann-Oppenheimer-Volkoff zu lösen. Diese stellen die Masse-Radius Beziehungen kompakter Objekte dar. Auf der Suche nach Twin Stern Lösungen aus dem chiralen SU(3) Quark Meson Model wurde zunächst ein Modell für Hybridsterne entwickelt. Im untersuchten Parameterbereich fanden wir Hybrid Stern Lösungen, bei welchen der Einfluss der Quarkmaterie auf die Stabilität des Sternes untersucht wurde, denn das Einsetzen des Phasenüberganges übt einen zusätzlichen gravitativen Zug auf die hadronische Kruste aus. Der Stern ist stabil, wenn der Druck der Quarkmaterie diesem zusätzlichen Zug standzuhalten vermag. Für einen zu grossen Sprung in der Energiedichte werden die Lösungen jedoch instabil. Zwillingssterne waren nicht unter den Lösungen, da der Übergangsdruck relativklein sein muss, während der Energiedichtesprung eher gross sein sollte. Das Auftreten zweier stabiler Äste in der Masse Radius Relation kann allerdingsmit dem SU(3) Modell und entsprechendem chiralen Phasenübergang modelliert werden. Für einen gewissen Parameterbereich einhergehend mit kleinem Wert des Vakuum Druckes B konnten Nicht-Linearitäten in der Zustangsgleichungzur Lösung der TOV Gleichung beitragen. Im Weitern ist das Zusammenspiel der Vektorkopplung und der Sigma Mesonen Masse einflussreich auf die Lösungen, welche auf Kausalität, Stabilität und neben der 2 Sonnenmassen Bedingung noch auf Restriktionen vom millisecond pulsar PSR J1748-2446ad untersucht wurden.Mit Weltraummissionen wie etwa NICER (Neutron star Interior CompositionExploreR) sollte die Radiusbestimmung kompakter Objekte in Zukunft bis auf einen Kilometer genau bestimmt werden können. Die Entdeckung von zweiSternen mit der gleichen Masse und unterschiedlichen Radien wäre in der Tat ein Beweis für die Existenz von Zwillingssternen, welche dann die Theorie des Phasenüberganges in dichter Materie untermauern würde. Das Kollaps-Szenario eines Zwillingssternes würde weiteren Aufschluss über Neutrino-Emmissivität, Gamma-ray burster und Gravitationswellen Signale geben können. Dynamische Simulationen in allgemein relativistischem Kontext für compact star merger mit den hier diskutierten Zustandsgleichungen sind bereits in Planung, um Eigenschaftenwie beispielsweise das Temperatur- und Dichteprofil solcher Objekte genauer zu analysieren.
The theory of strong interactions — Quantum Chromodynamics (QCD) — is well-defined mathematically. However, direct applications of this theory to experiment are rather limited due to significant technical obstacles. Even some general features of QCD remain unclear to date.
Hence, phenomenological input is important and needed for practical applications, e.g. for theoretical analysis of the heavy-ion collision experiments. In this thesis the role of hadronic interactions is studied in the hadron resonance gas (HRG) model — a popular model for the confined phase of QCD. The description of hadronic interactions is based on the famous van der Waals (VDW) equation and its quantum statistical generalization. While this is not the conventional choice for nuclear/hadronic physicspplications, the simplicity of the VDW approach makes it extremely useful.
In particular, this framework allows to include the two most basic ingredients of hadron-hadron interaction: the short-range repulsion, modeled by excluded-volume (EV) corrections, and the intermediate range attraction. The first part of the thesis considers just the repulsive EV interactions between hadrons. A hitherto unknown, but surprisingly strong sensitivity of the long known thermal fits to heavy-ion hadron yield data to the choice of hadron eigenvolumes is uncovered. It challenges the robustness of the chemical freeze-out temperature and baryochemical potential determination from the thermal fits. However, at the same time, the extracted value of the entropy per baryon is found to be a robust observable which depends weakly on this systematic uncertainty of the HRG model.
A Monte Carlo procedure to treat EV interactions in HRG is also introduced in this thesis. It allows to study simultaneous effects of EV and of exact charge conservation in HRG for the first time. Generalizations of the classical VDW equation are required for its applications in hadronic physics. he grand canonical ensemble (GCE) formulation of the classical VDW equation is presented. Remarkably, this important aspect of the VDW equation was not discovered before. The GCE formulation yields the analytic structure of the critical fluctuations, both in the vicinity of and far off the critical point. These critical fluctuations are presently actively being used as probes for the QCD critical point. Another extension is the hitherto undiscovered generalization of the VDW equation to include quantum Bose-Einstein and Fermi-Dirac statistics. It is performed for both single-component and multi-component fluids. The Fermi-Dirac VDW equation is applied for the first time. It is used to describe nucleons and basic properties of nuclear matter. The quantum statistical generalization of the VDW equation developed in this work is quite general, and can be applied for any fluid. Thus, its applications are not restricted to QCD physics, but may also find themselves in chemistry and/or industry. The quantum statistical VDW equation is used to describe baryonic interactions in full HRG. The VDW parameters $a$ and $b$ are fixed to the nuclear ground state and the predictions of the model are confronted with lattice QCD calculations. The inclusion of baryonic interactions leads to a qualitatively different behavior of the fluctuations of conserved charges in the crossover region. In many cases it resembles the lattice data. These results suggest that hadrons do not melt quickly with increasing temperature, as one could conclude on the basis of the common simple ideal HRG model. Calculations at finite chemical potentials show that the nuclear liquid-gas transition manifests itself by non-trivial fluctuations of the net baryon number in heavy ion collisions. In the final part of the thesis the pure glue initial scenario for high-energy hadron and heavy-ion collisions is explored. This scenario is shown not to spoil the existing agreement of the hadronic and electromagnetic observables description in Pb+Pb collisions at energies available at the CERN Large Hadron Collider. Hydrodynamic calculations suggest that collisions of small-sized nuclei at lower collision energies available at the BNL Relativistic Heavy Ion Collider are promising in the search for the traces of the chemically non-equilibrium gluon-dominated phase transition.
Im Weltall existieren hunderte sehr helle Objekte, die eine hohe konstante Leuchtkraft im Wellenlängenbereich von Gammastrahlung besitzen. Die konstante Leuchtkraft mancher dieser Objekte wird in regelmäßigen Abständen von starken Ausbrüchen, den sogenannten X-Ray-Bursts, unterbrochen. Hauptenergiequelle dieser X-RayBursts ist der „rapid-proton-capture“-Prozess (rp-Prozess). Dieser zeichnet sich durch eine Abfolge von (p,γ)-Reaktionen und β+-Zerfällen aus, die die charakteristischen Lichtkurven produzieren. Für viele am Prozess beteiligte Reaktionen ist der Q-Wert sehr klein, wodurch die Rate der einzelnen Reaktionen von den resonanten Einfängen in die ungebundenen Zustände dominiert wird. Die Unsicherheiten in der Beschreibung der Lichtkurve sind derzeit aufgrund fehlender kernphysikalischer Informationen von vielen am Prozess beteiligten Isotopen sehr groß. Sensitivitätsstudien zeigen, dass dabei die Unsicherheiten der 23Al(p,γ)24Si-Reaktion eine der größten Auswirkungen auf die Lichtkurve hat. Diese werden durch ungenaue und widersprüchliche Informationen zu den ungebundenen Zuständen im kurzlebigen 24Si hervorgerufen.
Um Informationen über die Kernstruktur von 24Si zu erhalten, wurde am National Superconducting Cyclotron Laboratory (NSCL), Michigan, USA, die 23Al(d,n)24Si Transferreaktion untersucht. Der in dieser Form erstmals umgesetzte Versuchsaufbau bestand aus einem Gammadetektor zur Messung der Übergangsenergien des produzierten 24Si, einem Neutronendetektor zur Messung der Winkelverteilung der emittierten Neutronen und einem Massensprektrometer zur Identifikation des produzierten Isotops. Mit diesem Aufbau, der eine Detektion der kompletten Kinematik der (d,nγ)-Reaktion ermöglichte, konnten folgende Erkentnisse gewonnen werden:
Aus der Energie der nachgewiesenen Gammas konnten die Übergänge zwischen den Kernniveaus von 24Si bestimmt und daraus die Energien der einzelnen Zustände ermittelt werden. Dabei konnte neben dem bereits bekannten gebundenen 2+-Zustand (in dieser Arbeit gemessen bei 1874 ± 2,9keV) und dem ungebundenen 2+-Zustand (3448,8 ± 4,6keV), erstmals ein weiterer ungebundener (4+,0+)-Zustand bei 3470,6 ± 6,2 keV beobachtet werden. Zusätzlich konnte die Diskrepanz, die bezüglich der Energie des ungebundenen 2+-Zustands aufgrund früherer Messungen bestand, beseitigt und die Energieunsicherheit reduziert werden.
Aus der Anzahl der nachgewiesenen Gammas konnten ebenfalls die (d,n)-Wirkungsquerschnitte in die einzelnen Zustände von 24Si bestimmt werden. Unter Verwendung der Ergebnisse von DWBA-Rechnungen konnte mithilfe dieser die spektroskopischen Faktoren berechnet werden. Für die angeregten Zustände musste dabei zwischen verschiedenen Drehimpulsüberträgen unterschieden werden. Mittels der Winkelverteilung der nachgewiesenen Neutronen konnte gezeigt werden, dass die Gewichtung anhand der theoretischen spektroskopischen Faktoren zur Berechnung der Anteile des jeweiligen Drehimpulsübertrags am gesamten Wirkungsquerschnitt für den entsprechenden Zustand gute Ergebnisse liefert. Für eine quantitative Bestimmung der spektroskopischen Faktoren der Zustände anhand der Neutronenwinkelverteilungen in 24Si war allerdings die Statistik zu gering. Für den Fall der deutlich häufiger beobachteten 22Mg(d,n)23Al-Reaktion konnte hingegen ein spektroskopischer Faktor für den 23Al-Grundzustand von 0,29 ± 0,04 bestimmt werden. Abschließend wurden die Auswirkungen der gewonnenen Erkenntnisse zur Kernstruktur von 24Si auf die Rate der 23Al(p,γ)-Reaktion untersucht. Dabei konnte aufgrund der besseren Energiebestimmung zum einen die Diskrepanz zwischen den Raten die auf Grundlage der beiden früheren Untersuchungen berechnet wurden und bis zu einem Faktor von 20 voneinander abweichen, beseitigt werden. Zum anderen konnte aufgrund der kleineren Unsicherheit in der Energiebestimmung der Fehlerbereich der Rate verkleinert werden. Die Untersuchungen zeigen, dass die Unsicherheit in der neuen Rate von der Ungenauigkeit der Massenbestimmung der beiden beteiligten Isotope und damit dem Q-Wert der Reaktion dominiert wird. Durch eine bessere Bestimmung des Q-Werts könnte die Unsicherheit in der Rate aufgrund der neuen experimentellen Ergebnisse auf ein Zehntel gesenkt werden.
Terahertz (THz) physics are an emerging field of research dealing with electromagnetic radiation in the far-infrared to microwave region. The development of innovative technologies for the generation and detection of THz radiation has only in the recent past led to a tremendous rise of both fundamental research as well as investigation of possible fields of application for THz radiation. The most prominent reason has long been the scarce accessibility of the THz region of the electromagnetic spectrum - commonly loosely located between 0.1 and 30 THz - to broad research, and it was mostly limited to astronomy and high energy physics facilities. Over the recent years, numerous novel concepts on both the source and detector side have been proposed and successfully implemented to overcome this so-called THz gap. New technology has become available and paved the way for wide-spread experimental laboratory work and accompanying theoretical investigations. First application studies have emerged and in some cases even commercial development of the field of THz physics is on the rise. Despite these enormous progresses, a continuing demand for more efficient THz detectors still impels current technological research. Relatively low source powers are often a major limiting factor and the request for new detection concepts, their understanding and implementation, as well as the optimization on a device basis has been and still remains in place. One of these concepts is the use of field-effect transistors (FETs) high above their conventional cut-off frequencies as electronic THz detectors. The concept has been proposed in a number of theoretical publications by M. Dyakonov and M. Shur in the early 1990's, who pioneered to show that under certain boundary conditions, non-linear collective excitations of the charge carrier system of a two-dimensional electron gas (2DEG) by incident THz radiation can exhibit rectifying behaviour - a detection principle, which has become known as plasma wave or plasmonic mixing. Up until this day, the concept has been successfully implemented in many device realizations - most advanced in established silicon CMOS technology - and stands on the edge of becoming commercially available on a large scale. The main direction of the work presented in this thesis was the modeling and experimental characterization of antenna-coupled FETs for THz detection - termed TeraFETs in this and the author's previous works - which have been implemented in different material systems. The materials presented in this thesis are AlGaN/GaN HEMTs and graphene FETs. In a number of scientific collaborations, TeraFETs were designed based on a hydrodynamic transport model, fabricated in the respective materials, and characterized mainly in the lower THz frequency region from 0.2 to 1.2 THz. The theoretical description of the plasma wave mixing mechanism in TeraFETs, as initiated by Dyakonov and Shur, was based on a fluid-dynamic transport model for charge carriers in the transistor channel. The THz radiation induces propagating charge density oscillations (plasma waves) in the 2DEG, which via non-linear self-mixing cause rectification of the incident THz signals. Over the course of this work, it became evident in the on-going detector characterization experiments that this original theoretical model of the detection process widely applied in the respective literature does not suffice to describe some of the experimental findings in TeraFET detection signals. Thorough measurements showed signal contributions, which are identified in this work to be of thermoelectric origin arising from an inherent asymmetric local heating of charge carriers in the devices. Depending on the material, these contributions constituted a mere side effect to plasmonic detection (AlGaN/GaN) or even reached a comparable magnitude (graphene FETs). To include these effects in the detector model, the original reduced fluid-dynamic description was extended to a hydrodynamic transport model. The model yields at the current stage a reasonable qualitative agreement to the measured THz detection signals. This thesis presents the formulation of a hydrodynamic charge carrier transport model and its specific implementation in a circuit simulation tool. A second modeling aspect is that the transport equations cover only the intrinsic plasmonic detection process in the active gated part of the TeraFET's transistor channel. In order to model and simulate the behavior of real devices, extrinsic detector parts such as ungated channel regions, parasitic resistances and capacitances, integrated antenna impedance, and others must be considered. The implemented detector model allows to simulate THz detection in real devices with the above influences included. Besides presentation of the detector model, experimental THz characterization of the fabricated TeraFETs is presented in this work. Careful device design yielded record detection performance for detectors in both investigated materials. The respective results are shown and the experimental observations of the thermoelectric effect in TeraFETs are compared to modeling results. It is the goal of this work to provide a framework for further theoretical and experimental studies of the plasmonic and thermoelectric effect in TeraFETs, which could eventually lead to a new type of THz detectors particularly exploiting the thermoelectric effect to enhance the sensitivity of today's plasmonic TeraFETs.
The topic of this thesis is the investigation of scalar tetraquark candidates from lattice QCD. It is motivated by a previous study originating in the twisted mass collaboration. The initial tetraquark candidate of choice is the $a_0(980)$, an isovector in the nonet of light scalars ($J^P=0^+$). This channel is still poorly understood. It displays an inverted mass hierarchy to what is expected from the conventional quark model and the $a_0(980)$ and $f_0(980)$ feature a surprising mass degeneracy. For this reasons the $a_0(980)$ is a long assumed tetraquark candidate in the literature.
We follow a methodological approach by studying the sensitivity of the scalar spectrum with fully dynamical quarks to a large basis of two-quark and four-quark creation operators. Ultimately, the candidate has to be identified in the direct vicinity of two two-particles states, which is understandably inevitable for a tetraquark candidate. To succeed in this difficult task two-meson creation operators are essential to employ in this channel. By localized four-quark operators we intend to probe the Hamiltonian on eigenstates with a closely bound four-quark structure.