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In this work I investigate two different systems - spin systems and charge-density-waves. The same theoretical method is used to investigate both types of system. My investigations are motivated by experimental investigations and the goal is to describe the experimental results theoretically. For this purpose I formulate kinetic equations starting from the microscopical dynamics of the systems.
First of all, a method is formulated to derive the kinetic equations diagrammatically. Within this method an expansion in equal-time connected correlation functions is carried out. The generating functional of connected correlations is employed to derive the method.
The first system to be investigated is a thin stripe of the magnetic insulator yttrium-iron-garnet (YIG). Magnons are pumped parametrically with an external microwave field. The motivation of my theoretical investigations is to explain the experimental observations. In a small parameter range close to the confluence field strength where confluence processes of two parametrically pumped magnons with the same wave vector becomes kinematically possible the efficiency of the pumping is reduced or enhanced depending on the pumping field strength. Because it is expected that that confluence and splitting processes of magnons are essential for the experimental observations I go beyond the kinetic theories that are conventionally applied in the context of parametric excitations in YIG and investigate the influence of cubic vertices on the parametric instability of magnons in YIG.
Furthermore, the influence of phonons is investigated. Usually in the literature these are taken into account as heat bath. Here, I want to explain experiments where an accumulation of magnetoelastic bosons - magnon-phonon-quasi-particles - has been observed. I employ the method of kinetic equations to investigate this phenomenon theoretically. The kinetic theory is able to reproduce the experimental observations and it is shown that the accumulation of magnetoelastic bosons is purely incoherent.
Finally, charge-density waves (CDW) in quasi-one-dimensional materials will be investigated. Charge-density waves emerge from a Peierls-instability and are a prime example for spontaneous symmetry breaking in solids. Again, the motivation for my theoretical investigations are an experiment where the spectrum of amplitude and phase phonon modes has been measured. Starting from the Fröhlich-Hamiltonian I derive kinetic equations and from these kinetic equations the equations of motion for the CDW order parameter can be derived. The frequencies and damping rates of amplitude and phase phonon modes will be derived from the linearized equations of motion. I compare my theory with existing methods. Furthermore, I also investigate the influence of Coulomb interaction.
This thesis investigates exotic phases within effective models for strongly interacting matter.
The focus lies on the chiral inhomogeneous phase (IP) that is characterized by a spontaneous breaking of translational symmetry and the moat regime, which is a precursor phenomenon exhibiting a non-trivial mesonic dispersion relation.
These phenomena are expected to occur at non-zero baryon densities, which is a parameter region that is mostly non-accessible to first-principle investigations of Quantum chromodynamics (QCD).
As an alternative approach, we consider the Gross-Neveu (GN) and Nambu-Jona-Lasinio (NJL) model within the mean-field approximation, which can be regarded as effective models for QCD.
We focus on two aspects of the moat regime and the IP in these models.
First, we investigate the influence of the employed regularization scheme in the (3+1)-dimensional NJL model, which is nonrenormalizable, i.e., the regulator cannot be removed.
We find that the moat regime is a robust feature under change of regularization scheme, while the IP is sensitive to the specific choice of scheme.
This suggests that the moat regime is a universal feature of the phase diagram of the NJL model, while the IP might only be an artifact of the employed regulator.
Second, we study the influence of the number of spatial dimensions on the emergence of the IP.
To this end, we investigate the GN model in noninteger spatial dimensions d.
We find that the IP and the moat regime are present for d < 2, while they are absent for d > 2.
This demonstrates the central role of the dimensionality of spacetime and illustrates the connection of previously obtained results in this model in integer number of spatial dimensions.
Moreover, this suggests that the occurrence of these phenomena in three spatial dimensions is solely caused by the finite regulator.
In summary, this thesis contributes to advancing our understanding of the phase structure of QCD, particularly regarding the existence and characteristics of inhomogeneous phases and the moat regime.
Even though the investigations are performed within effective models, they provide valuable insight into the aspects that are crucial for the formation of an inhomogeneous chiral condensate in fermionic theories.
In this thesis, we present a detailed consideration of both qualitative and quantitative properties of static spherically symmetric solutions of the Einstein equations with self-interacting scalar fields. Our focus is on solutions with naked singularities. We study the qualitative properties of the solutions of the Einstein equations with real static self-interacting $N$ scalar fields, making some assumptions on self-interaction. We provide a rigorous proof that the corresponding solutions will be regular up to $r=0$. Furthermore, we find the rigorous form of asymptotic solutions near the singularity and at spatial infinity. We construct some examples of spherical-like naked singularities at $r=r_s\neq0$ in curvature coordinates.
We analyze the stability of the previously considered solutions against odd-parity gravitational perturbations and also examine the fundamental quasi-normal modes spectra. For the general class of the self-interaction potential, we demonstrate well-posedness of the initial problem and stability for positively defined potentials. As an example, we numerically study the case of the scalar field with power-law self-interaction potential and find the fundamental quasi-normal modes frequencies. We demonstrate that they differ from the standard Schwarzschild black hole case.
We study in detail the motion of particles in the vicinity of previously considered solutions. Mainly, we are interested in considering properties of the distribution of stable circular orbits around the corresponding configurations and images of the accretion disk for a distant observer. For all cases, we find possible types of stable circular orbit distributions and domains of parameters where they are realized.
We also demonstrate that the presence of self-interaction can lead to a new type of circular orbit distributions, which is absent in the linear massless scalar field case. We build Keplerian disk images in the plane of a distant observer and demonstrate the possibility to mimic the shadows of black holes.
By combining two unique facilities at the Gesellschaft fuer Schwerionenforschung (GSI), the Fragment Separator (FRS) and the Experimental Storage Ring (ESR), the first direct measurement of a proton capture reaction of stored radioactive isotopes was accomplished. The combination of well-defined ion energy, an ultra-thin internal gas target, and the ability to adjust the beam energy in the storage ring enables precise, energy-differentiated measurements of the (p,gamma) cross sections. The new setup provides a sensitive method for measuring (p,gamma) reactions relevant for nucleosynthesis processes in supernovae, which are among the most violent explosions in the universe and are not yet well understood. The cross sections of the 118Te(p,gamma) and 124Xe(p,gamma) reactions were measured
at energies of astrophysical interest. The heavy ions were stored with energies of 6 MeV/nucleon and 7 MeV/nucleon and interacted with a hydrogen gas-jet target.
The produced proton-capture products were detected with a double-sided silicon strip detector. The radiative recombination process of the fully stripped ions and electrons from the hydrogen target was used as a luminosity monitor.
Additionally, post-processing nucleosynthesis simulations within the NuGrid [1] research platform have been performed. The impact of the new experimental results on the p-process nucleosynthesis around 124Xe and 118Te in a core-collapse supernova was investigated. The successful measurement of the proton capture cross sections of radioactive isotopes rises the motivation to proceed with experiments in lower energy regions.
[1] M. Pignatari and F. Herwig, “The nugrid research platform: A comprehensive simulation approach for nuclear astrophysics,” Nuclear Physics News, vol. 22, no. 4, pp. 18–23, 2012.
In this thesis, the early time dynamics in a heavy ion collision of Pb-Nuclei at LHC center-of-mass energies of 5 TeV is studied. Right after the collision the system is out-of-equilibrium and essentially gluon dominated, with their density saturating at a specific momentum scale Q_s. Based on a separation of scales for the soft and hard gluonic degrees of freedom, the initial state is given from an effective model, known as the Color Glass Condensate. Within this model, the soft gluons behave classical to leading order, making it possible to study their dynamics in gauge invariant fashion on a three dimensional lattice, solving Hamiltonian field equations of motion, keeping real time. Quark-Antiquark pairs are produced in the gluonic medium, known as the Glasma and manifest themselves as a source of quantum fluctuations.
They enter the dynamics of the gluons as a current, making the system semi-classical. In lattice simulations, the non-equilibrium system is tested for pressure isotropization, which is a necessary ingredient to reach a local thermal equilibrium (LTE), making a hydrodynamical description at a later stage possible. In addition, the occupation of energy modes is studied with its implications on thermalization and classicality.
Das Experiment ALICE (A Large Ion Collider Experiment) am CERN (Conseil Européen pour la Recherche Nucléaire) LHC (Large Hadron Collider) fokussiert sich auf die Untersuchung stark wechselwirkender Materie unter extremen Bedingungen. Solche Bedingungen existierten wenige Mikrosekunden nach dem Urknall, als die Temperaturen so hoch waren, dass Partonen (Quarks und Gluonen) nicht zu farbneutralen Hadronen gebunden waren. In solch einem Quark-Gluon-Plasma können sich die Partonen frei bewegen, wobei sie allerdings mit anderen Partonen aus dem Medium stark wechselwirken. Am LHC werden Bleikerne auf ultra-relativistische Energien von bis zu 2.68 TeV beschleunigt und zur Kollision gebracht, wobei für weniger als 10 fm/c ein QGP entsteht, das schnell expandiert. Die Partonen hadronisieren, wenn das QGP sich auf Temperaturen von weniger als der Phasenübergangstemperatur von ≈155MeV abkühlt. Die finalen Teilchen- und Impulsverteilungen werden werden vom ALICE Detektor gemessen und geben Aufschluss auf elementare Prozesse im QGP.
Die TPC (Time Projection Chamber ) ist eines der wichtigsten Detektorsysteme von ALICE. Sie trägt maßgeblich zur Rekonstruktion von Teilchenspuren und zur Identifikation der Teilchensorten bei mittleren Rapiditäten bei. Die TPC ist eine große zylindrische Spurendriftkammer und besteht aus einem 88mˆ3 großen Gasvolumen, das von der zentralen Hochspannungselektrode in zwei Seiten geteilt wird. Durchquert ein Teilchen das Gasvolumen, ionisiert es entlang seiner Spur eine spezifische Menge von Gasatomen. Die Ionisationselektronen driften entlang des extrem homogenen elektrischen Feldes zu den Auslesekammern an den Endkappen auf beiden Seiten der TPC. Die Messung der Position und der Menge der Ionisationselektronen erlaubt die Rekonstruktion der Teilchenspur sowie, in Kombination mit der Impulsmessungen über die Krümmung der Teilchenspur im Magnetfeld, die Bestimmung der Teilchensorte über den spezifischen Energieverlust pro Wegstrecke im Gas. Das Gasvolumen der TPC war in LHC Run 1 (2010–2013) mit Ne-CO_2 (90-10) gefüllt. Die Gasmischung wurde zu Ar-CO_2 (88-12) für Run 2 (2015–2018) geändert. Als Auslesekammern wurden Vieldrahtproportionalkammern verwendet, die aus einer segmentierten Ausleseebene, einer Anodendrahtebene, einer Kathodendrahtebene und einem Gating-Grid (GG) bestehen. Das GG is eine zusätzliche Drahtebene, die durch zwei verschiedene Spannungseinstellungen transparent oder undurchlässig für Elektronen und positive Ionen geschaltet werden kann.
In den ersten Daten von Run 2 bei hohen Interaktionsraten wurden große Verzerrungen der gemessenen Spurpunkte beobachtet, die auf Grund von Verzerrungen des Driftfeldes auftreten und nicht von Daten aus Run 1 bekannt waren. Diese Verzerrungen treten nur sehr lokal an den Grenzen von manchen der inneren Auslesekammern (IROCs) auf. Zudem wurden auch große Verzerrungen in einer (C06) der äußeren Auslesekammern (OROCs) festgestellt, die sich bei einem bestimmten Radius über die ganze Breite der Kammer erstrecken. Die Ergebnisse dieser Arbeit befassen sich mit der Untersuchung jener Verzerrungen und ihrer Ursache, sowie mit der Entwicklung von Strategien um die Verzerrungen zu minimieren.
Messungen der Verzerrungen in den IROCs und Vergleiche mit Simulationen lassen darauf schließen, dass die Verzerrungen von positiver Raumladung hervorgerufen werden, die durch Gasverstärkung an sehr begrenzten Regionen der Auslesekammern entsteht und sich durch das Driftvolumen bewegt. Es werden charakteristische Abhängigkeiten von der Interaktionsrate sowie systematische Veränderungen bei Umkehrung der Orientierung des Magnetfeldes gemessen. Eine erneute Analyse von Run 1 Daten mit den Methoden aus Run 2 zeigt, dass die Verzerrungen bereits in Run 1 auftraten, jedoch durch die Ne-Gasmischung und niedrigere Interaktionsraten um eine Größenordnung kleiner waren. Neue Daten aus Run 2, für die die Gasmischung zeitweise wieder von Ar-CO_2 zu Ne-CO_2- N_2 geändert wurde, bestätigen die Ergebnisse der Run 1 Datenanalyse. Der Ursprung der Raumladung wird systematisch eingegrenzt. Es werden einzelne IROCs identifiziert, an deren Anodendrähten die Raumladung entsteht. Physikalische Modelle ermöglichen es, die Entstehung der Raumladung auf das Volumen zurückzuführen, das sich zwischen zwei IROCs befindet. Damit besteht die Vermutung, dass einzelne Spitzen von Anodendrähten am äußeren Rand dieser IROCs in das Gasvolumen hineinragen und somit hohe elektrische Felder erzeugen, an denen Gasverstärkung stattfindet. Die positiven Ionen können dann ungehindert in das Driftvolumen gelangen. Um diesen Effekt zu unterdrücken, wird das Potential der Cover-Elektroden angepasst, die sich auf den Befestigungsvorrichtungen der Drahtebenen an den Kammerrändern befinden. Dadurch kann die Menge von Ionisationselektronen, die in das Volumen zwischen zwei IROCs hineindriftet und vervielfacht wird, eingeschränkt werden. Über elektro-statische Simulationen und Messungen wird eine Einstellung für das Cover-Elektroden-Potential gefunden, mit der die Verzerrungen auf 30 % reduziert werden können. Die Verzerrungen in OROC C06 entstehen durch positive Ionen, die aus der Verstärkungsregion in das Driftvolumen gelangen, da an dieser bestimmten Stelle zwei aufeinanderfolgende GG-Drähte den Kontakt verloren haben. Die Verzerrungen werden um mehr als einen Faktor 3 reduziert, indem die Hochspannung der Anodendrähte um 50 V und somit der Gasverstärkungsfaktor um einen Faktor 2 verringert wird und indem das Potential der noch funktionierenden GG-Drähte erhöht wird.
Zusammenfassend konnten die lokalen Raumladungsverzerrungen für die letzte Pb−Pb Strahlzeit von Run 2 auf weniger als 1cm bei den höchsten Interaktionsraten verringert werden. Zudem wurde der Anteil des von Raumladungsverzerrungen betroffenen Volumens der TPC signifikant verringert, sodass die ursprüngliche Auflösung der Spurrekonstruktion wieder erreicht werden konnte.
Terahertz (THz) radiation lies between the micro and far-infrared range in the electromagnetic spectrum. Compared with microwave and millimeter waves, it has a larger signal bandwidth and extremely narrow antenna beam. Thus, it is easier to achieve high-resolution for imaging and detection applications. The unique properties, such as penetration for majority non-polar materials, non-ionizing characteristic and the spectral fingerprint of materials, makes THz imaging an appealing artifice in the military, biomedical, astronomical communications, and other areas. However, THz radiation’s current low power level and detection sensitivity block THz imaging system from including fewer optical elements than the visible or infrared range. This leads to imaging resolution, contrast, and imaging field of view degenerate and makes the aberration more serious. THz imaging based on the space Fourier spectrum detection is developed in this thesis to achieve high-quality imaging. The main concept of Fourier imaging is by recording the field distribution in the Fourier plane (focal plane) of the imaging system; the information of the target is obtained. The numerical processing method is needed to extract the amplitude and phase information of the imaged target. With additional process, three-dimensional (3D) information can be obtained based on the phase information. The novel recording and reconstructing ways of the Fourier imaging system enables it to have a higher resolution, better contrast, and broader field of view than conventional imaging systems such as microscopy and plane to plane telescopic imaging system.
The work presented in this thesis consists of two imaging systems, one is working at 300 GHz based on the fundamental heterodyne detection of the THz radiation, the other is operated at 600 GHz by utilizing the sub harmonic heterodyne detection technique. The realization and test of the heterodyne detection are based on the THz antenna-coupled field-effect transistor (TeraFET) detector developed by Dr. Alvydas Lisauskas. Both systems use two synchronized electronic multiplier chains to radiate the THz waves. One radiation works as the local oscillator (LO), the other works as illumination with a slight frequency shift, the radiations are mixed on the detector scanning in the Fourier plane to record the complex Fourier spectrum of the imaged target. The LO has the same frequency range as the illuminating radiation for fundamental heterodyne detection but half the frequency range for the sub-harmonic heterodyne detection. The 2-mm resolution, 60-dB contrast, and 5.5-cm diameter imaging area at 300 GHz and the of 500-μm resolution, 40-dB contrast, and 3.5-cm diameter imaging area at 600 GHz are achieved (the 300-GHz illuminating radiation has the approximate power of 600 μW , the 600-GHz illuminating radiation has the approximate power of 60 μW ).
The thesis consists of 6 parts. After the introduction, the second chapter expands on the topic of Fourier optics from a theoretical point of view and the simulations of the Fourier imaging system. First, the theory of the electromagnetic field propagation in free space and through an optical system are investigated to elicit the Fourier transform function of the imaging system. The simulation is used for theoretical considerations and the implementation of a Fourier optic script that allows for numerical investigations on reconstruction. The preliminary imaging field of view and resolution are also demonstrated. The third chapter describes the Fourier imaging system at 300 GHz based on the fundamental heterodyne detection, including the experimental setup, the 2D, and 3D imaging results. The following fourth chapter reports the integration of the TeraFET detector with two substrate lenses (one is a Si lens on the back-side Si substrate, the other is a wax/PTFE lens on the front side containing the bonding wires) for sub-harmonic heterodyne detection at 600 GHz. The characteristic of the wax/PTFE lens at THz range is presented. After that, the compared imaging results between the detector with and without the wax/PTFE lens are shown. The fifth chapter extends the demonstration on the lateral and depth resolution of the Fourier imaging system in detail and uses the experimental results at 600 GHz to validate the analytical predictions. The comparison of the resolution between the Fourier imaging system and the conventional microscopy system proves that the Fourier imaging system has better imaging quality under the same system configuration. The last chapter in this thesis concludes on the findings of the THz Fourier imaging and gives an outlook for the enhancement of the Fourier imaging system at THz range.
This thesis provides a detailed derivation of dissipative spin hydrodynamics from quantum field theory for systems composed of spin-0, spin-1/2, or spin-1 particles.
The Wigner function formalism is introduced for quantum fields in the respective representations of the Poincaré group, and the conserved currents, i.e., the energy-momentum tensor and the total angular momentum tensor, in various so-called pseudogauges are derived. An expansion around the semiclassical limit in powers of the Planck constant is performed.
Subsequently, kinetic equations are obtained for binary elastic scattering, using both the de Groot-van Leeuwen-van Weert and Kadanoff-Baym method, with the latter retaining the effect of quantum statistics. The resulting collision term features both local and nonlocal contributions, with the latter providing a relaxation mechanism for the spin degrees of freedom of the quasiparticles. The local-equilibrium distribution function is derived from the requirement that the local part of the collision term vanishes.
From quantum kinetic theory, dissipative spin hydrodynamics is then constructed via the method of moments, extended to particles with spin. The system of moment equations is closed via the Inverse-Reynolds Dominance (IReD) approach, resulting in a set of equations of motion describing the evolution of both ideal and dissipative degrees of freedom. The application to polarization phenomena relevant to heavy-ion collisions is discussed.
This thesis aims to investigate the properties of hadronic matter by analyzing fluctuations of conserved charges. A transport model (SMASH) is used for these studies to achieve this. The first part of this thesis focuses on examining transport coefficients, specifically the diffusion coefficients of conserved charges and the shear viscosity. The second part investigates equal-time correlations of particle numbers in the form of cumulants. The last chapter studies different aspects of the isobar collision systems Ru and Zr.
As a first step, the hadronic medium and interactions between its constituents are introduced, and simultaneously, their impact on transport coefficients is investigated. The methodology is verified by comparing the results of SMASH with Chapman-Enskog calculations, followed by examining 3-to-1 multi-particle reactions, revealing their influence on shear viscosity and electrical diffusion. The analysis of the full hadron gas considers angle-dependent cross-sections and additional elastic cross-sections via the AQM description, showing significant impacts on transport coefficients. The dependency on the number of degrees of freedom is explored, with noticeable effects on diffusion coefficients but a smaller influence on the shear viscosity. At non-zero baryon chemical potential, the diffusion coefficients are strongly influenced, while the shear viscosity remains unaffected. Overall, the study underscores the importance of individual cross-sections and the modeling of interactions on transport coefficients.
The following chapter explores fluctuations of conserved charges, crucial for understanding phase transitions in heavy-ion collision from the quark-gluon plasma to the hadronic phase. Using SMASH, the impact of global charge conservation on particle number cumulants in subvolumes of boxes simulating infinite matter is studied. Comparisons with simpler systems highlights the influence of hadronic interactions on cumulants, especially via charge annihilation processes and the results from SMASH shows agreement with analytical calculations. Calculations at finite baryon chemical potential reveals a transition from a Poisson to Skellam distribution within the net proton cumulants. It is shown that an unfolding procedure to obtain the net baryon fluctuations from the net proton ones deviates from the actual net baryon result, particularly in larger volumes. Finally, net proton correlations at vanishing baryon chemical potential align with ALICE measurements and the net proton cumulants are unaffected by deuteron formation.
In the next step, the goal is to investigate critical fluctuations in the hadronic medium. Therefore, the hadronic system is initialized with critical equilibrium fluctuations by coupling the hadron resonance gas with the 3D Ising model. The single-particle probability distributions are derived from the principle of maximum entropy. Evolving these distributions in SMASH, their development in an expanding sphere adjusted to experimental conditions can be analyzed. It reveals resonance decay and formations as the primary source that affects the particle cumulants. Because of isospin randomization processes, critical fluctuations are better preserved in net nucleon numbers. However, for the strongest coupling investigated in this work, correlations of the critical field are still present in the final state of the evolution in the net proton fluctuations. Examining cumulant dependence on rapidity windows shows a non-monotonic trend.
In the third part, collisions involving the isobars Ru and Zr are studied at a center-of-mass energy of 200 GeV. Initially, SMASH is used to study the initial conditions to hydrodynamical simulations, emphasizing the importance of the nuclear structure of isobars on the geometry of the collision area. It is found that the deformation parameters notably influence the initial state. Correlations between nucleon-nucleon pairs on eccentricity fluctuations yield no significant effect. Subsequently, the hydrodynamic model vHLLE evolves the previously explored initial conditions and for the transition between the hydrodynamic and kinetic descriptions, the Cooper-Frye formula is used. Usage of the canonical ensemble ensures the exact conservation of the conserved charges B, Q, and S. The neutron skin effect, which changes the charge distribution within Ru nuclei, is additionally considered. Fluctuations are assessed, revealing suppression in large rapidity windows due to global charge conservation. The hadronic phase modifies fluctuations of net pions, net kaons, and net protons via annihilation processes, yet fluctuations remain unaffected by the neutron skin effect.
The core of this work is represented by the investigation of the chiral phase transition, using Monte Carlo simulations and unimproved staggered fermions, both in the weak and strong coupling regimes of Quantum Chromodynamics. Based on recent results from Monte Carlo simulations, both using unimproved staggered fermions and Wilson fermions, the chiral phase transition in the continuum and chiral limit shows compatibility with a second-order phase transition for Nf (number of flavours) in range [2:7], at zero baryon chemical potential. This achievement relies on the analytic continuation of Nf to non-integer values on the lattice, which allows to make use of extrapolation techniques to the chiral limit, where simulations are not possible. Furthermore, these results provide a resolution to the ambiguous scenario for Nf = 2 in the chiral limt. The first part of this thesis is devoted to the investigation of the chiral phase transition when a non-zero imaginary baryon chemical potential is involved, whose value corresponds to the 81% of the Roberge-Weiss one. Using the same extrapolation techniques aforementioned, the order of the chiral phase transition in the continuum and chiral limit shows compatibility with a second-order phase transition for Nf in range [2:6], highlighting a lack of dependence of the order of the chiral phase transition on the imaginary baryon chemical potential value. The second part of this thesis is about the study of the extension of the first-order chiral region in the strong coupling regime, at zero baryon chemical potential. Using Monte Carlo techniques, this can be done by investigating the Z2 boundary on a coarse lattice, whose temporal extent reads Nt = 2, and simulations are realised for Nf = 4, 8. The results in the weak coupling regime show, for $Nt = 8, 6, 4 and fixed Nf value, an inflating first-order chiral region. As in the strong coupling limit a second-order chiral phase transition is expected, the first-order chiral region has to shrink as the strong coupling regime is approached, resulting in a non-monotonic behaviour of the Z2 boundary. For Nf = 8, a critical mass on the Z2 boundary has been obtained, confirming the expected non-monotonic behaviour. For Nf = 4 the results do not provide a unique conclusion: Either a Z2 boundary at extremely low bare quark mass or a second-order chiral phase transition in the O(2) universality class in the chiral limit can take place. In addition to the two main topics, the performances of the second-order minimum norm integrator (2MN) and the fourth-order minimum norm integrator (4MN) have been compared, after implementing the 4MN one in the CL2QCD code used to realise our simulations. The 2MN integrator had already been implemented in the code since the first version was released. The two integrators belong to the class of symplectic integrators and represent an essential component of the RHMC algorithm, involved in our investigation. This step is extremely important, in order to guarantee the best quality when collecting data from simulations, and the results of the comparison suggested to favor the 2MN integrator, for both the topics.
Neutron stars are unique laboratories for the investigation of the high density properties of bulk matter. In this work, the astrophysical constraints for a phase transition from hadronic matter to deconfined quark matter are examined thoroughly. A scheme for relating known astrophysical observables such as mass, radius and tidal deformability to the parameter space of such a transition is devised and applied to the set of data currently available.
In order to span a wide parameter space, a highly parameterizable relativistic mean field equation in compliance with chiral effective field theory results is used, where the stiffness of the equation of state can be varied via the effective mass at saturation density. The phase transitions are modelled using a Maxwell construction and assumed to be of first order, with a constant speed of sound quark matter model. The resulting equations of state are analyzed and divided into four categories, which can be used to constrain the parameter space that allows phase transition. It is highlighted, that a subset of this parameter space would even be detectable without the need of higher precision measurements. A phase transition at high densities is shown to be particularly promising in this regard. Finally, the groundwork is laid to apply the equation of state used in this work for supernova or merger simulations, by extending it to non-zero temperatures.
This thesis deals with several aspects of non-perturbative calculations in low-dimensional quantum field theories. It is split into two main parts:
The first part focuses on method development and testing. Using exactly integrable QFTs in zero spacetime dimensions as toy models, the need for non-perturbative methods in QFT is demonstrated. In particular, we focus on the functional renormalization group (FRG) as a non-perturbative exact method and present a novel fluid-dynamic reformulation of certain FRG flow equations. This framework and the application of numerical schemes from the field of computational fluid dynamics (CFD) to the FRG is tested and benchmarked against exact results for correlation functions. We also draw several conclusions for the qualitative understanding and interpretation of renormalization group (RG) flows from this fluid-dynamic reformulation and discuss the generalization of our findings to realistic higher-dimensional QFTs.
The topics discussed in the second part are also manifold. In general, the second part of this thesis deals with the Gross-Neveu (GN) model, which is a prototype of a relativistic QFT. Even though being a model in two spacetime dimensions, it shares many features of realistic models and theories for high-energy particle physics, but also emerges as a limiting case from systems in solid state physics. Especially, it is interesting to study the model at non-vanishing temperatures and densities, thus, its thermodynamic properties and phase structure.
First, we use this model to test and apply our findings of the first part of this thesis in a realistic environment. We analyze how the fluid-dynamic aspects of the FRG realize themselves in the RG flow of a full-fledged QFT and how we profit from this numeric framework in actual calculations. Thereby, however, we also aim at answering a long-standing question: Is there still symmetry breaking and condensation at non-zero temperatures in the GN model, if one relaxes the commonly used approximation of an infinite number of fermion species and works with a finite number of fermions? In short: Is matter (in the GN model) in a single spatial dimension at non-zero temperature always gas-like?
In general, we also use the GN model to learn about the correct description of QFTs at non-zero temperatures and densities. This is of utmost relevance for model calculations in low-energy quan- tum chromodynamics (QCD) or other QFTs in medium and we draw several conclusions for the requirements for stable calculations at non-zero chemical potential.
Precise intensity monitoring at CRYRING@ESR: on designing a Cryogenic Current Comparator for FAIR
(2023)
In the field of today’s beam intensity diagnostic there is a significant gap in the non-interceptive, calibrated measurement of the absolute intensity of continuous (unbunched) dc beams with current amplitudes below 1 μA. At the Facility for Antiproton and Ion Research (FAIR) low-intensity DC beams will occur during slow extraction from the synchrotrons as well as for coasting beams of highly-charged or exotic nuclei in the storage rings. The lack of adequate beam instrumentation limits the experimental program as well as the accuracy of experimental results.
The Cryogenic Current Comparator (CCC) can close the diagnostic gap with a high-precision dc current reading independent of ion-species and of beam parameters. However, the established detector design based on a core with high magnetic permeability and on a radial shield geometry has well-known weaknesses concerning magnetic shielding efficiency and intrinsic current noise. To eliminate these weaknesses, a novel coreless CCC with a co-axial shield was constructed and combined with a high-performance SQUID contributed by the Leibniz-Institute of Photonic Technology (Leibniz-IPHT Jena). The new axial CCC model was compared to a radial CCC with the established design provided by the Friedrich-Schiller-University Jena. According to numerical simulations prepared at TU Darmstadt and test measurements of the detectors in the laboratory, the new design offered a significant improvement of the shielding factor – from 75dB to 207dB at the required dimensions – and eliminated all noise contributions from the core material, promising an improved current resolution. Although the lower inductance of the pickup coil reduced the coupling to the beam significantly, the noise properties of the new CCC type were comparable to the classical version with a high-permeability core. However, the expected decrease of the low-frequency noise and thus an increase of the current resolution could not be observed at this stage of development.
Consequently, the classical CCC based on the radial shielding and high-permeability core had to be installed in CRYRING@ESR to provide best possible intensity measurements for the upcoming experimental campaign. In CRYRING the CCC was operated with beam currents between 1nA and 20μA and with different ion species (H, Ne, O, Pb, U). It was shown that the CCC provides a noise-limited current resolution of better than 3.2 nArms at a bandwidth of 200 kHz as well as a noise level below 40 pA/√Hz above 1 kHz. During the operation, the main noise sources of the accelerator environment had to be identified and suitable mitigation strategies were developed. Temperature and pressure fluctuations were suppressed with a newly-designed cryogenic support system based on a 70 l helium bath cryostat, developed and built in collaboration with the Institut für Luft- und Kältetechnik Dresden, in combination with a helium re-liquefier. The cryogenic operating time was restricted to around 7 days, which must be expanded significantly in the future. Digital filters were developed to remove the perturbations of the helium liquefier and of the neighboring dipole magnets. Given the promising results the CCC system can be considered as a prototype for future CCCs at FAIR.
Precise tune determination and split beam emittance reconstruction at the CERN PS synchrotron
(2023)
In accelerator physics, the need to improve the performance and better control the operating point of an accelerator has become, year after year, an increasingly important need in order to achieve higher energies and brightness, as well as point-like particle beams. If this involves increasingly advanced technological developments (in terms, for example, of materials for more intense superconducting magnets), it can not take place in the absence of targeted studies of linear and non-linear beam dynamics. In the context of this Ph.D. thesis in physics, linear and non-linear dynamics of charged particles in circular accelerators is the topic that will be discussed and treated in detail. In particular, the presentation and discussion of the results will be divided in two main topics: the need to know the physical properties of a proton beam; and the development of innovative methods to determine and study the accelerator’s working point. With regard to the first topic, an innovative procedure will be presented to determine the transverse size of the PS beam in the beam extraction phase. Among the different ways the extraction occurs at the PS, the analysed one is based on the transverse splitting of the beam by means of non-linear fields. Thus, the knowledge of the transverse beam size is not trivial since resonant linear and non-linear beam structures (namely, core and islands) arise and, for each of them, the beam size has to be quantified. This parameter is crucial for two main reasons: the accelerator that will receive the beam exiting the upstream accelerator may have restrictions (physical or magnetic) that involve a partial or total loss of the incoming beam; and any experiments located downstream of the considered accelerator may need a beam with a transversal size as constant as possible; consequently, its monitoring and control are essential. The second topic concerns the accurate determination of the working point of an accelerator, defined as the number of transverse oscillations the particle beam travels per unit of accelerator circumference, both horizontally and vertically. This quantity is called horizontal and vertical tune, respectively. Their knowledge is also crucial to understand whether the beam will be stable or unstable. In fact, not all tune values are acceptable, as there are particular values that bring the beam into resonance. In this configuration, the amplitude of the transverse oscillations of the particles increases in an uncontrolled manner and leads to the loss of all or part of the beam. Note that, in particular operating conditions, the resonant conditions are sought and desired to model, in a suitable way, the transversal shape of the beam, such as the above mentioned PS extraction scheme. It is even clearer how much the determination of the machine working point is essential to determine the operating conditions of an accelerator. In this context, several methods (also taken from the field of applied mathematics) to calculate the tune will be demonstrated and tested numerically on different types of synthetic signals. At the end of this description, the use of experimental data will allow to obtain the benchmark of a new method for the direct calculation of some characteristic quantities of non-linear beam dynamics (namely, the amplitude detuning, i.e. the variation of tune as a function of intensity of the perturbation provided to the beam.
Investigation of the kinematics involved in compton scattering and hard X-ray photoabsorption
(2023)
The present work investigates the kinematics of Compton scattering at gaseous, internally-cool helium and molecular nitrogen targets in the high- and the low-energy regime. Additionally, photoionization at molecular nitrogen with high-energy photons is investigated. These exeprimental regimes were previously inaccessible due to the extremely small cross sections involved. Nowadays, the third- and fourth-generation synchrotron machines produce sufficient photon flux, enabling the investiagtion of the above processes. The utilized cold-target recoil-ion momentum spectroscopy (COLTRIMS) technique further increases the detection efficiency of the observed processes, since it enables full-solid-angle detection by exploiting momentum conservation.
Compton scattering is investigated at both high (helium and N2) and low (helium) photon energies. In the high-energy regime, the impulse approximation is mostly valid, which is not the case for the low-energy regime. The impulse approximation assumes that the Compton-scattering process takes place at a free electron with a momentum distribution as if it was bound, thus ignoring the binding energy of the system. In the low-energy regime, the impulse approximation is not valid.
Photoionization is investigated at high photon energies, where the linear momentum of the photon cannot be neglected, as is the fashion of the commonly used dipole approximation.
Magnetische Quadrupole und Solenoide sind ein elementarer Bestandteil einer Beschleunigeranlage und begrenzen die transversale Ausdehnung eines Teilchenstrahls durch eine Reflexion der Teilchen in Richtung der Beschleunigerachse. Die konventionelle Bauweise als Elektromagnet besteht aus einem Eisenjoch welches mit Spulen umwickelt ist. In dieser Arbeit werden diese Magnetstrukturen auf Basis von Permanentmagneten designt und hinsichtlich ihrer Qualität zum Strahltransport optimiert, sowie Feldmessungen an permanentmagnetischen Quadrupolen durchgeführt. Diese wurden mit 3D-gedruckten Halterungen aus Kunststoff gefertigt, was eine Vielzahl von Formvariationen ermöglicht. Darauf aufbauend wurde ein im Vakuum befindlicher Aufbau entwickelt, mit welchem die Strahlenvelope im inneren eines permanentmagnetischen Quadrupol Tripletts diagnostiziert werden kann. Dies greift auf ein am Institut für angewandte Physik entwickeltes System zur nicht-invasiven Strahldiagnose mithilfe von Raspberry Pi Einplatinencomputern und Kameras in starken Magnetfeldern zurück.
Die in dieser Arbeit vorgestellte Konfiguration eines PMQ’s ist eine Weiterentwicklung des am CERN im Linac4, einem Alvarez-Driftröhrenbeschleuniger zur Beschleunigung von H– , verwendeten Designs. Bei diesem sind je acht quaderförmige Permanentmagnete aus Samarium Cobalt (SmCo) in die Driftröhren des Beschleunigers integriert.
Darauf aufbauend wurden die geometrischen Designparameter hinsichtlich ihres Einflusses auf die Qualität des Magnetfelds untersucht. In einem magnetischen Quadrupol zur Strahlfokussierung wird dies durch einen linearen Anstieg des Magnetfeldes von Quadrupolachse zu Polflächen charakterisiert. Das Design wurde im Zuge dessen zur Verwendung von industriellen Standardgeometrien von Quadermagneten und der Erhöhung der magnetischen Flussdichte erweitert. Dazu wurde untersucht wie sich das Hinzufügen von zusätzlichen Magneten auswirkt und ob eine bessere Feldqualität durch andere Magnetformen erreicht wird.
Die Kombination mehrerer PMQ in geringem Abstand (<10 mm) führt abhängig von der Geometrie der PMQ-Singlets zu einer erheblichen Verschlechterung der Feldlinearität, was eine Erhöhung des besetzten Phasenraumvolumens der Teilchen nach sich zieht.
Am Beispiel von PMQ-Tripletts werden die zu beachtenden Designparameter analysiert und Lösungsansätze vorgestellt. Die auftretenden Effekte werden anhand von Strahldynamiksimulation veranschaulicht. Für eine Anwendung der vorgestellten Designs wurde eine Magnethülle mit einer Wabenstruktur zur Aufnahme der Einzelmagnete entwickelt. Diese besteht aus zwei Halbschalen, welche jeweils den Kompletteinschluss aller Magnete garantiert und eine einfache Montage um ein Strahlrohr ermöglicht. Diese wurden in der Institutswerkstatt aus Kunststoff via 3D-Druck gefertigt. Aufgrund der höheren erreichbaren Magnetisierung wurden Neodym-Eisen-Bor-Magnete (Nd2F14B, Br =1,36 T) für den Bau der entwickelten Strukturen verwendet. Für eine Magnetfeldmessung zur Bestätigung der magnetostatischen Simulationen und einer Bewertung der Druckqualität wurde eine motorisierte xyz-Stage zur Bewegung einer Hallsonde aufgebaut. Die Messungen zeigen eine gute Zentrierung des Magnetfeldes, sodass PMQ mit einer Kunststoffhalterung eine schnelle und billige Möglichkeit sind, kurzfristig eine Quadrupol-Konfiguration aufzubauen. Die Kosten belaufen sich für einen einzelnen PMQ je nach Länge auf 50€ bis 100€.
Basierend auf der PMQ-Struktur wurde ein PMQ-Triplett in ein Vakuum versetzt und mit Raspberry Pi Kameras im Zwischenraum der Singlets ausgestattet. Dies ermöglichte die Aufnahme der Strahlenvelope innerhalb des Tripletts anhand der durch einen Heliumstrahl induzierten Fluoreszenz und erste Erkenntnisse für notwendige Weiterentwicklungen wurden gesammelt. Auf den genauen technischen Aufbau wird im abschließenden Kapitel der Arbeit detailliert eingegangen.
In der einfachsten Form wird ein PM-Solenoid anhand eines einzelnen axial magnetisierten Hohlzylinders realisiert und erzeugt näherungsweise die Feldverteilung einer Zylinderspule. Durch die radialen Magnetfeldkomponenten an den Rändern des Solenoiden erhalten Teilchen eine tangentiale Geschwindigkeitskomponente und führen eine Gyrationsbewegung entlang der Solenoidachse aus. Diese reduziert den Strahlradius und die Teilchen behalten eine Geschwindigkeitskomponente, welche zur Solenoidachse zeigt. Für eine Maximierung dieser Fokussierung muss das Magnetfeld auf die Zylinderachse konzentriert werden. Insbesondere bei einer Verlängerung des Hohlzylinders wird die Kopplung der Polflächen über das Innenvolumen abgeschwächt. Aufgrund dessen wurde ein Design bestehend aus drei Hohlzylindersegmenten entwickelt. Dieses setzt sich aus zwei radial und einem axial magnetisierten Hohlzylinder zusammen und erhöht die mittlere magnetische Flussdichte für ausgewählte Geometrien um einen Faktor zwei im Vergleich zu einem einzelnen Hohlzylinder gleicher Geometrie. Dies ist gleichzusetzen mit einer Vervierfachung der Fokussierstärke, welche quadratisch mit der mittleren magnetischen Flussdichte skaliert. Die Strahldynamischen Konsequenzen werden anhand von Simulationen mit generierten Magnetfeldverteilungen erläutert. Für eine kostengünstige Bauweise wurde eine Design basierend auf quaderförmigen Magneten entwickelt.
In the framework of the LHC Injectors Upgrade Project (LIU), the CERN Proton Synchrotron Booster (PSB) went through major upgrades resulting in new effects to study, challenges to overcome and new parameter regimes to explore. To assess the achievable beam brightness limit of the machine, a series of experimental and computational studies in the transverse planes were performed. In particular, the new injection scheme induces optics perturbations that are strongly enhanced near the half-integer resonance. In this thesis, methods for dynamically measuring and correcting these perturbations and their impact on the beam performance will be presented. Additionally, the quality of the transverse beam distributions and strategies for improvement will be addressed. Finally, the space charge effects when dynamically crossing the half-integer resonance will be characterized. The results of these studies and their broader significance beyond the PSB will be discussed.
Experiments on Vibrational Energy Transfer (VET) in proteins contribute to our understanding of fundamental biological processes such as allostery, dissipation of excess energy, and possibly enzymatic catalysis. While these processes have been studied for a long time, many questions remain unanswered. The aim of this work was to expand the application of existing spectroscopic techniques to investigate VET, seeking tailored solutions for the diversity of proteins and amino acid environments. Additionally, new target proteins were to be established to broaden the spectrum of VET experiments towards the role of VET and low-frequency protein modes (LFMs).
To test their suitability as VET sensors, the non-canonical amino acids (ncAAs) Azidoalanine (N3Ala), azido-L-Homoalanine (Aha), p-azido-Phenylalanine (N3Phe), p-cyano-Phenylalanine (CNPhe), and 4-cyano-Tryptophan (CNTrp) were coupled to the VET donor β-(1-azulenyl)-L-Alanine (AzAla) in dipeptides. Their spectral properties were compared using FTIR and VET spectra in H2O, dimethyl sulfoxide, and tetrahydrofuran.
The solvent strongly influences the measured VET signals, which can be explained by the direct interaction of the solvent with the dipeptides. Additionally, the peak time within the subgroups of azide and nitrile sensors increased with the size of the side chain, indicating the dependence between peak time and the distance between VET donor and sensor. When incorporated into a protein, solvent interactions are less dominant. Therefore, Aha, N3Phe, and CNPhe were additionally incorporated at two different positions in the PDZ protein domain and investigated. Due to Fermi resonances, signals from azide sensors are challenging to predict, unlike those of the nitrile sensors.
Overall, the experiments showed that nitrile groups can serve well as VET sensors, as their lower extinction coefficient is compensated for by a narrower bandwidth. This expands the number of potential target proteins, and sensor incorporation can be less disruptive at various protein locations.
Since the VET donor AzAla can inject the energy of a photon into a protein as vibrational energy at a specific location, it can also be used for the targeted excitation of LFMs. If these modes are involved in an enzymatic reaction, a direct influence on activity is expected. This hypothesis has long existed but has not been definitively verified. Some studies have found evidence for the involvement of LFMs in formate dehydrogenase (FDH) catalysis. Therefore, FDH was chosen for the investigation of LFMs in enzymes. This specific system additionally allows the use of a natural VET sensor: it forms a stable complex with NAD+ and N3-, an excellent IR marker. Thus, it provided the opportunity to test low-molecular-weight non-covalent ligands as VET sensors.
After ensuring sufficient AzAla supply through the internal establishment of an enzymatic synthesis, AzAla could be incorporated at various positions in FDH. Despite spectral overlap between free and bound N3-, the latter could be identified by its narrower FWHM. For some variants, no binding could be observed. Circular dichroism spectra showed that these variants structurally deviate slightly from other variants and the wild type (WT). VET could be observed over 22 Å from two regions of the protein to the N3- bound in the active center, at protein concentrations of below 2 mM. Unbound N3- did not generate signals, allowing it to be added in excess ensuring the saturation of the protein in VET experiments.
The activity of FDH WT and four AzAla mutants was investigated under substrate saturation without and with AzAla excitation. In these experiments, a slight reduction in activity under illumination was observed, even for the WT, who is not expected to interact with the excitation light. So far, a difference in sample temperature cannot be excluded as the cause for this decline.
The presented experiments with FDH illustrate the potential of low-molecular-weight ligands as VET sensors, with N3- being particularly attractive due to its simple structure (preventing Fermi resonances) and its high extinction coefficient. Its use can add many metalloproteins as potential targets for VET experiments and allows investigation without a VET sensor ncAA. Additionally, initial experiments were conducted to measure light-dependent FDH activity. By specifically exciting protein LFMs, this project could contribute in the future to answering longstanding questions about the extraordinary catalytic efficiency of enzymes.
The Compressed Baryonic Matter (CBM) is one of the core experiments at the future Facility for Anti-proton and Ion Research (FAIR), Darmstadt, Germany. Its goal is to investigate nuclear matter characteristics at high net-baryon densities and moderate temperatures. The Silicon Tracking System (STS) is a central detector system of CBM.
It is placed inside a 1Tm magnet and operated at a temperature of about −10 °C to keep radiation-induced bulk current in the 300μm double-sided microstrip silicon sensors low. The design of the STS aims to minimize the material budget in the detector acceptance (2.5° < θ < 25°). In order to do so, the readout electronics is placed outside the active area, and the analog signals are transported via ultra-thin micro-cables. The STS comprises eight tracking stations with 876 modules. Each module is assembled on a carbon fiber ladder, which is subsequently mounted in the C-shaped aluminum frame.
The scope of the thesis focused on developing a modular control system framework that can be implemented for different sizes of experimental setups. The developed framework was used for setups that required a remote operation, like the irradiation of the powering modules for the front-end electronics (FEE), but also in laboratory-based setups where the automation and archiving were needed (thermal cycling of the STS electronics).
The low voltage powering modules will be placed in the vicinity of the experiment, therefore they will experience a total dose of up to 40mGy over the 10 years of STS lifetime.
To estimate the effects of the radiation on the low-voltage module performance, a dedicated irradiation campaign took place. It aimed at estimating the rate of radiation induced soft errors, that lead to the switch off of the FEE.
Regular power cycles of multiple front-end boards (FEBs) pose a risk to the experiment operation. Firstly, such behavior could negatively influence the physics performance but also have deteriorating effects on the hardware. It was further assessed what are the limitations of the FEBs with respect to the thermal cycling and the mechanical stress. The results served as an indication of possible failure modes of the FEB at the end of STS lifetime. Failure modes after repeated cycles and potential reasons were determined (e.g., Coefficient of Thermal Expansion (CTE) difference between the materials).
Due to the conditions inside the STS efficient temperature and humidity monitoring and control are required to avoid icing or water condensation on the electronics or silicon sensors. The most important properties of a suitable sensor candidate are resilience to the magnetic field, ionizing radiation tolerance, and fairly small size.
A general strategy for ambient parameters monitoring inside the STS was developed, and potential sensor candidates were chosen. To characterize the chosen relative humidity sensors the developed control framework was introduced. A sampling system with a ceramic sensor and Fiber Optic Sensors (FOS) were identified as reliable solutions for the distributed sensing system. Additionally, the industrial capacitive sensors will be used as a reference during the commissioning.
Two different designs of FOS were tested: a hygrometer and 5 sensors multiplexed in an array. The FOS hygrometer turned out to be a more reliable solution. One of the possible reasons for a worse performance is a relatively low distance between the subsequent sensors (15 cm) and a thicker coating. The results obtained from the time response study pointed out that the thinner coating of about 15μm should be a good compromise between the humidity sensitivity and the time response.
The implementation of the containerized-based control system framework for the mSTS is described in detail. The deployed EPICS-based framework proved to be a reliable solution and ensured the safety of the detector for almost 1.5 years. Moreover, the data related to the performance of the detector modules were analyzed and significant progress in the quality of modules was noted. Obtained data was also used to estimate the total fluence, which was based on the leakage current changes.
The developed framework provided a unique opportunity to automate and control different experimental setups which provided crucial data for the STS. Furthermore, the work underlines the importance of such a system and outlines the next steps toward the realization of a reliable Detector Control System for STS.
In this thesis, we use lattice QCD to study a part of the QCD phase diagram, specifically the QCD phase transition at mu=0, where the QCD matter changes from hadron gas to quark-gluon plasma (QGP) with increasing temperature.
This phase transition takes place as a crossover, but when theoretically changing the masses of the quarks, the order of the phase transition changes as well.
We focus on the region of heavy quark masses with Nf=2 flavours, where we investigate the critical quark mass at the second order phase transition in the form of a Z2 point between the first-order and the crossover region.
The first-order region is positioned at infinitely heavy quarks. As the quark masses decrease, the associated Z3 centre symmetry breaks explicitly, causing the first-order phase transition to weaken until it turns into the Z2 point and finally into a crossover.
We study this Z2 point using simulations at Nf=2 and lattices of the sizes Nt = {6, 8, 10, 12}, partially building on previous work, in which the simulations for Nt = {6, 8, 10} were started.
The simulations for Nt=12 are not finished yet though, but we were able to draw some preliminary conclusions. These simulations are run on GPUs and CPUs, using the codes Cl2QCD and open-QCD-FASTSUM, respectively. Afterwards, the data goes through a first analysis step in the form of the Python program PLASMA, preparing it for the two techniques we use to analyse the nature of the phase transition.
As a first, reliable analysis method, we perform a finite size scaling analysis of the data to find the location of the Z2 point. Since we are using lattice QCD, performing a continuum extrapolation is necessary to reach the continuum result.
In regard to this, the finite size scaling analysis method is hampered by the excessive amount of simulated data that is needed regarding statistics and the total number of simulations, which is why this thesis is only an intermediate step towards the continuum limit.
This also leads to the second analysis technique we explore in this thesis.
We start to design a Landau theory which describes the phase boundary for heavy masses at Nf=2 based on the simulated data.
We develop a Landau functional for every Nt we have simulation data for.
Albeit the results are not at the same precision as the ones from the finite size scaling analysis, we are able to reproduce the position of the Z2 point for every Nt.
Even though we are not able to take a continuum extrapolation right now, after more development takes place in future works, this approach might, in the long run, lead to a continuum result that won't need as many simulations as the finite size scaling analysis.