Refine
Year of publication
Document Type
- Doctoral Thesis (27)
- Master's Thesis (2)
- Bachelor Thesis (1)
Has Fulltext
- yes (30)
Is part of the Bibliography
- no (30)
Keywords
- Theoretische Physik (2)
- UrQMD (2)
- Artificial Intelligence (1)
- Boltzmann-Gleichung (1)
- Correlations (1)
- Deep Learning (1)
- Dileptonen (1)
- Dileptons (1)
- FAIR (1)
- GPGPU (1)
Institute
- Physik (29)
- Informatik und Mathematik (1)
In this thesis the first fully integrated Boltzmann+hydrodynamics approach to relativistic heavy ion reactions has been developed. After a short introduction that motivates the study of heavy ion reactions as the tool to get insights about the QCD phase diagram, the most important theoretical approaches to describe the system are reviewed. To model the dynamical evolution of the collective system assuming local thermal equilibrium ideal hydrodynamics seems to be a good tool. Nowadays, the development of either viscous hydrodynamic codes or hybrid approaches is favoured. For the microscopic description of the hadronic as well as the partonic stage of the evolution transport approaches have beeen successfully applied, since they generate the full phse-space dynamics of all the particles. The hadron-string transport approach that this work is based on is the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) approach. It constitutes an effective solution of the relativistic Boltzmann equation and is restricted to binary collisions of the propagated hadrons. Therefore, the Boltzmann equation and the basic assumptions of this model are introduced. Furthermore, predictions for the charged particle multiplicities at LHC energies are made. The next step is the development of a new framework to calculate the baryon number density in a transport approach. Time evolutions of the net baryon number and the quark density have been calculated at AGS, SPS and RHIC energies and the new approach leads to reasonable results over the whole energy range. Studies of phase diagram trajectories using hydrodynamics are performed as a first move into the direction of the development of the hybrid approach. The hybrid approach that has been developed as the main part of this thesis is based on the UrQMD transport approach with an intermediate hydrodynamical evolution for the hot and dense stage of the collision. The initial energy and baryon number density distributions are not smooth and not symmetric in any direction and the initial velocity profiles are non-trivial since they are generated by the non-equilibrium transport approach. The fulll (3+1) dimensional ideal relativistic one fluid dynamics evolution is solved using the SHASTA algorithm. For the present work, three different equations of state have been used, namely a hadron gas equation of state without a QGP phase transition, a chiral EoS and a bag model EoS including a strong first order phase transition. For the freeze-out transition from hydrodynamics to the cascade calculation two different set-ups are employed. Either an in the computational frame isochronous freeze-out or an gradual freeze-out that mimics an iso-eigentime criterion. The particle vectors are generated by Monte Carlo methods according to the Cooper-Frye formula and UrQMD takes care of the final decoupling procedure of the particles. The parameter dependences of the model are investigated and the time evolution of different quantities is explored. The final pion and proton multiplicities are lower in the hybrid model calculation due to the isentropic hydrodynamic expansion while the yields for strange particles are enhanced due to the local equilibrium in the hydrodynamic evolution. The elliptic flow values at SPS energies are shown to be in line with an ideal hydrodynamic evolution if a proper initial state is used and the final freeze-out proceeds gradually. The hybrid model calculation is able to reproduce the experimentally measured integrated as well as transverse momentum dependent $v_2$ values for charged particles. The multiplicity and mean transverse mass excitation function is calculated for pions, protons and kaons in the energy range from $E_{\rm lab}=2-160A~$GeV. It is observed that the different freeze-out procedures have almost as much influence on the mean transverse mass excitation function as the equation of state. The experimentally observed step-like behaviour of the mean transverse mass excitation function is only reproduced, if a first order phase transition with a large latent heat is applied or the EoS is effectively softened due to non-equilibrium effects in the hadronic transport calculation. The HBT correlation of the negatively charged pion source created in central Pb+Pb collisions at SPS energies are investigated with the hybrid model. It has been found that the latent heat influences the emission of particles visibly and hence the HBT radii of the pion source. The final hadronic interactions after the hydrodynamic freeze-out are very important for the HBT correlation since a large amount of collisions and decays still takes place during this period.
Artificial intelligence in heavy-ion collisions : bridging the gap between theory and experiments
(2023)
Artificial Intelligence (AI) methods are employed to study heavy-ion collisions at intermediate collision energies, where high baryon density and moderate temperature QCD matter is produced. The experimental measurements of various conventional observables such as collective flow, particle number fluctuations, etc. are usually compared with expensive model calculations to infer the physics governing the evolution of the matter produced in the collisions. Various experimental effects and processing algorithms can greatly affect the sensitivity of these observables. AI methods are used to bridge this gap between theory and experiments of heavy-ion collisions. The problems with conventional methods of analyzing experimental data are illustrated in a comparative study of the Glauber MC model and the UrQMD transport model. It is found that the centrality determination and the estimated fluctuations of the number of participant nucleons suffer from strong model dependencies for Au-Au collisions at 1.23 AGeV. This can bias the results of the experimental analysis if the number of participant nucleons used is not consistent throughout the analysis and in the final model-to-data comparison. The measurable consequences of this model dependence of the number of participant nucleons are also discussed. In this context, PointNet-based AI models are developed to accurately reconstruct the impact parameter or the number of participant nucleons in a collision event from the hits and/or reconstructed track of particles in 10 AGeV Au-Au collisions at the CBM experiment. In the last part of the thesis, different AI methods to study the equation of state (EoS) at high baryon densities are discussed. First, a Bayesian inference is performed to constrain the density dependence of the EoS from the available experimental measurements of elliptical flow and mean transverse kinetic energy of mid rapidity protons in intermediate energy collisions. The UrQMD model was augmented to include arbitrary potentials (or equivalently the EoSs) in the QMD part to provide a consistent treatment of the EoS throughout the evolution of the system. The experimental data constrain the posterior constructed for the EoS for densities up to four times saturation density. However, beyond three times saturation density, the shape of the posterior depends on the choice of observables used. There is a tension in the measurements at a collision energy of about 4 GeV. This could indicate large uncertainties in the measurements, or alternatively the inability of the underlying model to describe the observables with a given input EoS. Tighter constraints and fully conclusive statements on the EoS require accurate, high statistics data in the whole beam energy range of 2-10 GeV, which will hopefully be provided by the beam energy scan programme of STAR-FXT at RHIC, the upcoming CBM experiment at FAIR, and future experiments at HIAF and NICA. Finally, it is shown that the PointNet-based models can also be used to identify the equation of state in the CBM experiment. Despite the uncertainties due to limited detector acceptance and biases in the reconstruction algorithms, the PointNet-based models are able to learn the features that can accurately identify the underlying physics of the collision. The PointNet-based models are an ideal AI tool to study heavy-ion collisions, not only to identify the geometric event features, such as the impact parameter or the number of participant nucleons, but also to extract abstract physical features, such as the EoS, directly from the detector outputs.
Atomistic molecular dynamics approach for channeling of charged particles in oriented crystals
(2015)
Der Gitterführungseffekt ist der Prozess der Ausbreitung von geladenen Teilchen entlang der Ebenen oder Achsen von kristallinen Materialien. Seit den 1960er Jahren ist dieser Effekt weitgehend theoretisch und experimentell untersucht worden. Dieser Effekt wurde für die Manipulation von Hochenergiestrahlen, die Hochpräzisionsstruktur- und -fehleranalyse von kristallinen Medien und die Herstellung von hochenergetischer Strahlung angewendet. Zur Abstimmung der Parameter der Gitterführung und Gitterführungsstrahlung wurde dieser Prozess für den Fall von künstlich nanostrukturierten Materialien, wie gebogenen Kristallen, Nanoröhren und Fullerit, angenommen. In den letzten Jahren wurde das Konzept des kristallinen Undulators formuliert und getestet, das besondere Eigenschaften der Strahlung aufgrund der Gitterführung von Projektilen in regelmäßig gebogenen Kristallen vorhersagt.
In dieser Arbeit werden die Prozesse der Gitterführung von Sub- und Multi-GeV-Elektronen und -Positronen durch den atomistischen Molekulardynamik-Ansatz untersucht. Die Ergebnisse dieser Studien wurden in einer Reihe von Artikeln während meiner Promotion in Frankfurt vorgestellt. Dieser Ansatz ermöglicht die Simulation komplexer Fälle von Gitterführung in geraden, gebogenen und periodisch gebogenen Kristallen aus reinen kristallinen Materialien und von gemischten Materialien wie Si-Ge-Kristallen, in mehrschichtigen und nanostrukturierten kristallinen Systemen. Die Arbeit beschreibt die Methode der Simulationen, stellt Ergebnisse von Simulationen für verschiedene Fälle vor und vergleicht die Ergebnisse von Simulationen mit aktuellen experimentellen Daten. Die Ergebnisse werden mit Schätzungen der dechanneling-Länge verglichen, dem Anteil der gittergeführten Projektile, der Winkelverteilung der ausgehenden Projektile und des Strahlungsspektrums.
Nanomaterials, i.e., materials that are manufactured at a very small spatial scale, can possess unique physical and chemical properties and exhibit novel characteristics as compared to the same material without nanoscale features. The reduction of size down to the nanometer scale leads to the abundance of potential applications in different fields of technology. For instance, tailoring the physicochemical properties of nanomaterials for modification of their interaction with a biological environment has been reflected in a number of biomedical applications.
Strategies to choose the size and the composition of nanoscale systems are often hindered by a limited understanding of interactions that are difficult to study experimentally. However, this goal can be achieved by means of advanced computer simulations. This thesis explores, from a theoretical and a computational viewpoints, stability, electronic and thermo-mechanical properties of nanoscale systems and materials which are related to biomedical applications.
We examine the ability of existing classical interatomic potentials to reproduce stability and thermo-mechanical properties of metal systems, assuming that these potentials have been fitted to describe ground-state properties of the perfect bulk materials.
It is found that existing classical interatomic potentials poorly describe highly-excited vibrational states when the system is far from the potential energy minimum. On the other hand, construction of a reliable computational model is essential for further development of nanomaterials for applications. A new interatomic potential that is able to correctly reproduce both the melting temperature and the ground-state properties of different metals, such as gold, platinum, titanium, and magnesium, by means of classical molecular dynamics simulations is proposed in this work. The suggested modification of a many-body potential has a general nature and can be utilized for similar numerical exploration of thermo-mechanical properties of a broad range of molecular and solid state systems experiencing phase transitions.
The applicability of the classical interatomic potentials to the description of nanoscale systems, consisting of several tens-hundreds of atoms, is also explored in this study. This issue is important, for instance, in the case of nanostructured materials, where grains or nanocrystals have a typical size of about a few nanometers. We validate classical potentials through the comparison with density-functional theory calculations of small
atomic clusters made of titanium and nickel. By this analysis, we demonstrate that the classical potentials fitted to describe ground-state properties of a bulk material can describe the energetics of nanoscale systems with a reasonable accuracy.
In this work, we also analyze electronic properties of nanometer-size nanoparticles made of gold, platinum, silver, and gadolinium; nanoparticles composed of these materials are of current interest for radiation therapy applications. We focus on the production of low-energy electrons, having the kinetic energy from a few electronvolts to several tens of electronvolts. It is currently established that the low-energy secondary electrons of such energies play an important role in the nanoscale mechanisms of biological damage resulting from ionizing radiation. We provide a methodology for analyzing the dynamic response of nanoparticles of the experimentally relevant sizes, namely of about several nanometers, exposed to ionizing radiation. Because of a large number of constituent atoms (about 1000 −10000 atoms) and consequently high computational costs, the electronic properties of such systems can hardly be described by means of ab initio methods based on a quantum-mechanical treatment of electrons, and this analysis should rely on model approaches. By comparing the response of smaller systems (of about 1 nm size) calculated within the ab initio- and the model framework, we validate this methodology and make predictions for the electron production in larger systems.
We have revealed that a significant increase in the number of the low-energy electrons emitted from nanometer-size noble metal nanoparticles arises from collective electron excitations formed in the systems. It is demonstrated that the dominating mechanisms of electron yield enhancement are related to the formation of plasmons excited in a whole system and of atomic giant resonances formed due to excitation of valence d electrons in individual atoms of a nanoparticle. Being embedded in a biological medium, the noble metal nanoparticles thus represent an important source of low-energy electrons, able to produce a significant irrepairable damage in biological systems.
A general methodology for studying electronic properties of nanosystems is used to make quantitative predictions for electron production by non-metal nanoparticles. The analysis illustrates that due to a prominent collective response to an external electric field, carbon nanoparticles embedded in a biological medium also enhance the production of low-energy electrons. The number of low-energy electrons emitted from carbon nanoparticles is demonstrated to be several times higher as compared to the case of liquid water.
Direct photon emission from heavy-ion collisions has been calculated and compared to available experimental data. Three different models have been combined to extract direct photons from different environments in a heavy-ion collision: Thermal photons from partonic and hadronic matter have been extracted from relativistic, non-viscous 3+1-dimensional hydrodynamic calculations. Thermal and non-thermal photons from hadronic interactions have been calculated from relativistic transport theory. The impact of different physics assumptions about the thermalized matter has been studied. In pure transport calculations, a viscous hadron gas is present. This is juxtaposed with ideal gases of hadrons with vacuum properties, hadrons which undergo a chiral and deconfinement phase transition and with a system that has a strong first-order phase transition to a deconfined ideal gas of quarks and gluons in the hybrid model calculations with the various Equations of State. The models used for the determination of photons from both hydrodynamic and transport calculations have been elucidated and their numerical properties tested. The origin of direct photons, itemised by emission stage, emission time, channel and baryon number density, has been investigated for various systems, as have the transverse momentum spectra and elliptic flow patterns of direct photons. The differences of photon emission rates from a thermalized transport box and the hadronic photon emission rates that are used in hydrodynamic calculations are found to be very similar, as are the spectra from calculations of heavy-ion collisions with transport model and hybrid model with hadronic Equation of State. Taking into account the full (vacuum) spectral function of the rho-meson decreases the direct photon emission by approximately 10% at low photon transverse momentum. The numerical investigations show that the parameter with the largest impact on the direct photon spectra is the time at which the hydrodynamic description is started. Its variation shows deviations of one to two orders of magnitude. In the regime that can be considered physical, however, the variation is less than a factor of 3. Other parameters change the direct photon yield by up to approximately 20%. In all systems that have been considered -- heavy-ion collisions at E_lab = 35 AGeV and 158 AGeV, (s_NN)**1/2 = 62.4 GeV, 130 GeV and 200 GeV -- thermal emission from a system with partonic degrees of freedom is greatly enhanced over that from hadronic systems, while the difference between the direct photon yields from a viscous and a non-viscous hadronic system (transport vs. hydrodynamics) is found to be very small. Predictions for direct photon emission in central U+U-collisions at 35 AGeV have been made. Since non-soft photon sources are very much suppressed at this energy, experimental results should very easily be able to distinguish between a medium that is entirely hadronic and a system that undergoes a phase transition from partonic to hadronic matter. In the case of lead-lead collisions at 158 AGeV, the situation is not so clear. In central collisions, the complete direct photon spectra including prompt photons seem to favour hadronic emission sources, while the partonic calculations only slightly overpredict the data. In peripheral collisions at the same energy, the hadronic contribution is more than one order of magnitude smaller than the prompt photon contribution, which fits the available experimental data. A similar picture presents itself at higher energies. At RHIC energies, however, the difference between transport calculations and hadronic hybrid model calculations is largest. Hybrid model calculations with partonic degrees of freedom can describe the experimental results in gold-gold collisions at 200 GeV. The elliptic flow component of direct photon emission is found to be consistently positive at small transverse momenta. This means that the initial photon emission from a non-flowing medium does not completely overshine the emission patterns from later stages. High-pt photons dominantly come from the beginning of a heavy-ion collision and therefore do not carry the directed information of an evolving medium.
Die vorliegende Dissertation untersucht die Nichtgleichgewichtsdynamik von relativistischen Schwerionenkollisionen ausgehend von der anfänglichen Produktion von Teilchen durch den Zerfall von Strings, der Bildung eines Quark-Gluon-Plasmas (QGP), dessen kinetische und chemische Äquilibrierung als Funktion der Zeit sowie seine Transporteigenschaften im Gleichgewicht bei endlicher Temperatur und endlichem chemischen Potential. Ein Verständnis der frühen Phase der Schwerionenkollisionen ist insbesondere von großen Interesse, da letztere eine Verbindung zwischen den ersten Nukleon-Nukleon Kollisionen und der Quark-Gluon-Plasma Phase herstellen, die zu einem späteren Zeitpunkt ein gewisses Maß an Thermalisierung zeigt. Allerdings können nur Nichtgleichgewichts-Theorien eine Verbindung zwischen dem anfänglichen QGP und seiner - zumindest partiellen - Thermalisierung herstellen. Um die Dynamik eines stark wechselwirkenden Mediums wie des Quark-Gluon-Plasmas zu beschreiben, reichen übliche Transportgleichungen (basierend auf der Boltzmann-Gleichung) nicht aus und es müssen komplexere Theorien, die auch für stark korrelierte Medien geeignet sind, angewendet werden. Hier kommen hydrodynamische Simulationen oder Transportrechnungen - basierend auf verallgemeinerten Transportgleichungen - zum Einsatz. Solche verallgemeinerte Transportgleichungen, wie die Kadanoff-Baym-Gleichungen, ergeben sich aus der quantenmechanischen Nichtgleichgewichts-Vielteilchentheorie, in der Green’s- Funktionen in Minkowski Raum-Zeit die interessierenden Größen sind, um die Dynamik des betrachteten Mediums zu beschreiben. Mit geeigneten Näherungen kann man so kinetische Transportgleichungen erhalten, die eine einheitliche Behandlung von stabilen und instabilen Teilchen auch außerhalb des Gleichgewichts ermöglichen. Diese Bestandteile bilden die Basis des Transportmodells Parton-Hadron-String Dynamics (PHSD), welches daher ein geeignetes ’Instrument’ ist um die verschiedenen Phasen einer Schwerionenkollision zu analysieren, egal ob die verschiedenen Formen der Materie im Gleichgewicht sind oder nicht.
In dieser Arbeit wird zunächst die Quantenchromodynamik (QCD) vorgestellt und erklärt, wie diese Theorie im Laufe der Jahre entwickelt wurde um ein wichtiger Bestandteil des Standardmodells der Teilchenphysik zu werden. Wir werden weiterhin die verbleibenden Herausforderungen in unserem Verständnis der QCD vorstellen, die sich primär auf das Phasendiagramm der stark wechselwirkenden Materie konzentrieren.
Im zweiten Kapitel untersuchen wir die Nichtgleichgewichts-Feldtheorie und die damit verbundenen Techniken - wie die Keldysh-Kontur - zur Beschreibung der Green’schen Funktionen als wesentlichen Freiheitsgrade. Wir leiten die Evolutionsgleichung für die Green’schen Funktionen her, d. h. die Kadanoff Baym-Gleichungen am Beispiel einer skalaren Feldtheorie.
Im nächsten Kapitel wird das Transportmodell Parton-Hadron-String Dynamics (PHSD), welches die Anwendung der verallgemeinerten Transportgleichungen zur Beschreibung relativistischer Schwerionenkollisionen darstellt, vorgestellt.
Wir beginnen im Kapitel 4 mit der Untersuchung der Nichtgleichgewichtseigenschaften des Quark-Gluon-Plasmas, welches bei relativistischen Schwerionenkollisionen erzeugt wird. Zu diesem Zweck vergleichen wir die Quark-Gluon-Plasmaentwicklung aus dem PHSD mit einem viskosen hydrodynamischen Modell, bei dem ein lokales kinetisches und chemisches Gleichgewicht angenommen wird.
Im Kapitel 5 konzentrieren wir uns auf das frühe Vorgleichgewichtsstadium ultra-relativistischer Schwerionenkollisionen und insbesondere auf die Freiheitsgrade der QGP-Phase in diesem Stadium. Wir untersuchen die Auswirkungen eines QGP, welches anfänglich entweder aus einem System aus massiven Gluonen (Szenario I) oder alternativ aus Quarks und Antiquarks (Szenario II) besteht. Das nächste Kapitel wird ebenfalls die Produktion von Teilchen im Frühstadium von Schwerionenkollisionen behandeln, jedoch bei niedrigeren Kollisionsenergien. Hier wird eine mikroskopische Beschreibung des K+/pi+-Verhältnisses im Vordergrund stehen, d. h. die Erklärung des Maximums in diesem Verhältnis bei etwa 30 A GeV ("Horn") in zentralen Au+Au (oder Pb+Pb) Kollisionen. Insbesonders werden wir die Modifikation des String-Fragmentierungsprozesses (über den Schwinger-Mechanismus) in einer Umgebung mit hoher hadronischer Dichte aufgrund der teilweisen Wiederherstellung der chiralen Symmetrie untersuchen.
In Kapitel 7 erweitern wir das Parton-Hadron-String Dynamics (PHSD)-Transportmodell im partonischen Sektor, indem wir explizit die totalen und differentiellen partonischen Streuungsquerschnitte als Funktion der Temperatur T und des baryochemischen Potentials μB berechnen auf der Basis der effektiven Propagatoren und Kopplungen des Dynamical QuasiParticle Models (DQPM), welches auch die generelle Zeitentwicklung der partonischen Freiheitsgrade beschreibt. Wir finden nur eine sehr bescheidene Änderung von n/s mit dem baryonchemischen Potential μB in Abhängigkeit von der skalierten Temperatur T/Tc(μB). Dies gilt auch für eine Vielzahl von hadronischen Observablen aus zentralen A+A Kollisionen im Energiebereich von 5 GeV < vsNN < 200 GeV bei der Implementierung der differentiellen Querschnitte in das PHSD-Modell. Da wir in Schwerionen-Observablen nur kleine Spuren einer μB-Abhängigkeit finden - obwohl die effektiven Partonenmassen und Kollisionsbreiten sowie deren Partonenquerschnitte eindeutig von μB abhängen - impliziert dies, dass man eine beträchtliche Partonendichte und ein großes Raum-Zeit-QGP-Volumen zur Untersuchung der Dynamik in der partonischen Phase benötigt. Diese Bedingungen sind nur bei hohen Kollisionsenergien erfüllt, bei denen μB jedoch eher niedrig ist. Wenn andererseits die Kollisionsenergie verringert und somit μB erhöht wird, wird die hadronische Phase dominant und dementsprechend wird es zunehmend schwieriger, Signale aus der Partonendynamik auf der Basis von "Bulk"-Observablen zu extrahieren.
In der vorliegenden Arbeit wurden mikroskopische Studien zur Äquilibrierung von partonischer und hadronischer Materie im Rahmen einer Nichtgleichgewichts-Transporttheorie durchgeführt, die sowohl hadronische als partonische Freiheitsgrade enthält und den Übergang zwischen beiden Phasen dynamisch beschreibt. Des Weiteren wurden die thermischen Eigenschaften des Gleichgewichtszustandes der stark wechselwirkenden Materie untersucht, insbesondere Fluktuationen in der Teilchenzahl wie auch höhere Momente von Observablen und deren Verhältnisse. Besonderes Interesse galt dabei den Transportkoeffizienten wie Scher- und Volumenviskosität sowie der elektrischen Leitfähigkeit.
Die Methode der Nichtgleichgewichts-Green'schen Funktionen - initiiert von Schwinger sowie Kadanoff und Baym - wurde vorgestellt um hochenergetische Kern-Kern Kollisionen zu beschreiben. Weiterhin wurde der Schwinger-Keldysh Formalismus benutzt um im Sinne einer Zweiteilchen-irrediziblen Näherung (2PI) die Dynamik von 'resummierten' Propagatoren und Kopplungen in konsistenter Weise zu beschreiben. Des Weiterhin wurden generalisierte Transportgleichungen auf der Basis der Kadanoff-Baym Gleichungen (in Phasenraumdarstellung) abgeleitet und ein Testteilchenverfahren zur Lösung dieser Gleichungen vorgestellt. Damit wurde der formale Rahmen der Parton-Hadron-String Dynamik (PHSD) abgesteckt.
Das PHSD Transportmodell wurde sodann für die Lösung der expliziten Fragestellungen in dieser Arbeit verwendet. Die 'Eingangsgrößen' des Modells wurden in Kapitel 3 aufgeführt. Weiterhin wurde aufgezeigt, dass das Transportmodell alle Phasen einer relativistischen Schwerionenkollision konsistent beschreibt, d.h. angefangen von den primären harten Stoßprozessen und der Bildung von 'Strings' zur Formierung einer partonischen Phase, den Wechselwirkungen in dieser Phase sowie die
dynamische Beschreibung der Hadronisierung. Weiterhin enthält das Modell zudem die hadronischen Endzustandswechselwirkungen bis zum Ausfrieren der hadronischen Freiheitsgrade bei geringer Dichte. ...
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.