Universitätspublikationen
Refine
Year of publication
- 2021 (27) (remove)
Document Type
- Doctoral Thesis (27) (remove)
Has Fulltext
- yes (27) (remove)
Is part of the Bibliography
- no (27)
Keywords
- 2D materials (1)
- ALICE upgrade (1)
- Astrophysics (1)
- Bohmian mechanics (1)
- CBM Experiment (1)
- Color superconductivity (1)
- Control System (1)
- EPICS (1)
- FEBID (1)
- Gravitational Waves (1)
Institute
- Physik (27) (remove)
Terahertz (THz) technology is an emerging field that considers the radiation between microwave and far-infrared regions where the electronic and photonic technologies merge. THz generation and THz sensing technologies should fill the gap between photonics and electronics which is defined as a region where THz generation power and THz sensing capabilities are at a low technology readiness level (TRL). As one of the options for THz detection technology, field-effect transistors with integrated antennae were suggested to be used as THz detectors in the 1990s by M. Dyakonov and M. Shur from where the development of field-effect transistor-based detector began. In this work, various FET technologies are presented, such as CMOS, AlGaN/GaN, and graphene-based material systems and their further sensitivity enhancement in order to reach the performance of well-developed Schottky diode-based THz sensing technology. Here presented FET-based detectors were explored in a wide frequency range from 0.1 THz up to 5 THz in narrowband and broadband configurations.
For proper implementation of THz detectors, the well-defined characterization is of high importance. Therefore, this work overviews the characterization methods, establishes various definitions of detector parameters, and summarizes the state-of-the-art THz detectors. The electrical, optical, and cryogenic characterization techniques are also presented here, as well as the best results obtained by the development of the characterization methods, namely graphene FET stabilization, low-power THz source characterization for detector calibration, and technology development for cryogenic detection.
Following the discussion about the detector characterization, a wide range of THz applications, which were tested during the last four years of Ph.D. and conducted under the ITN CELTA project from HORIZON2020 program, are presented in this work. The studies began with spectroscopy applications and imaging and later developed towards hyperspectral imaging and even passive imaging of human body THz radiation. As various options for THz applications, single-pixel detectors as well as multi-pixel arrays are also covered in this work.
The conducted research shows that FET-based detectors can be used for spectroscopy applications or be easily adapted for the relevant frequency range. State-of-the-art detectors considered in this work reach the resonant performance below 20 pW/√Hz at 0.3 THz and 0.5 THz, as well as 404 pW/√Hz cross-sectional NEP at 4.75 THz. The broadband detectors show NEP as low as 25 pW/√Hz at around 0.6 THz for the best AlGaN/GaN design and 25 pW/√Hz around 1 THz for the best CMOS design. As one of the most promising applications, metamaterial characterization was tested using the most sensitive devices. Furthermore, one of the single-pixel devices and a multi-pixel array were tested as an engineering solution for a radio astronomy system called GREAT in a stratosphere observatory named SOFIA. The exploration of the autocorrelation technique using FET-based devices shows the opportunity to employ such detectors for direct detection of THz pulses without an interferometric measurement setup.
This work also considers imaging applications, which include near-field and far-field visualization solutions. A considerable milestone for the theory of FET technology was achieved when scanning near-field microscopy led to the visualization of plasma (or carrier density) waves in a graphene FET channel. Whereas another important milestone for the THz technology was achieved when a 3D scan of a mobile phone was performed under the far-field imaging mode. Even though the imaging was done through the phone’s plastic cover, the image displayed high accuracy and good feature recognition of the smartphone, inching the FET-based detector technology ever so close to practical security applications. In parallel, the multi-pixel array testing was carried out on 6x7 pixel arrays that have been implemented in configurable-size aperture and imaging configurations. The configurable aperture size allowed the easier detector focusing procedure and a better fit for the beam size of the incident radiation. The imaging has been tested on various THz sources and compared to the TeraSense 16x16 pixel array. The experimental results show the big advantage of the developed multi-pixel array against the used commercial technology.
Furthermore, two ultra-low-power applications have been successfully tested. The application on hyper-frequency THz imaging tested in the specially developed dual frequency comb and our detector system for 300 GHz radiation with 9 spectral lines led to outstanding imaging results on various materials. The passive imaging of human body radiation was conducted using the most sensitive broadband CMOS detector with a log-spiral antenna working in the 0.1 – 1.5 THz range and reaching the optical NEP of 42 pW/√Hz. The NETD of this device reaches 2.1 K and overcomes the performance limit of passive room-temperature imaging of the human body radiation, which was less than 10 K above the room temperature. This experiment opened a completely new field that was explored before only by the multiplier chain-based or thermal detectors.
...
The topic of this thesis is the theoretical description of the hadron gas stages in heavy-ion collisions. The overall addressed question hereby is: How does the hadronic medium evolve i.e. what are the relevant microscopic reaction mechanisms and the properties of the involved degrees of freedom? The main goal is to address this question specifically for hadronic multi-particle interactions. For this goal, the hadronic transport approach SMASH is extended with stochastic rates, which allow to include detailed balance fulfilling multi-particle reactions in the approach. Three types of reactions are newly-accounted for: 3-to-1, 3-to-2 and 5-to-2 reactions. After extensive verifications of the stochastic rates approach, they are used to study the effect of multi-particle interactions, particularly in afterburner calculations.
These studies follow complementary results for the dilepton and strangeness production with only binary reactions, which show that hadronic transport approaches are capable of describing observables when employed for the entire evolution of low-energy heavy-ion collisions. This is illustrated by the agreement of dilepton and strangeness production for smaller systems with SMASH calculations. It is, in particular, possible to match the measured strangeness production of phi and Xi hadrons via additional heavy nucleon resonance decay channels. For larger systems or higher energies, hadronic transport cascade calculations with vacuum resonance properties can point to medium effects. This is demonstrated extensively for the dilepton emission in comparisons to the full set of HADES dielectron data. The dilepton invariant mass spectra are sensitive to a medium modification of the vector meson spectral function for large collision systems already at low beam energies. The sensitivity to medium modifications is mapped out in detail by comparisons to a coarse-graining approach, which employs medium-modified spectral functions and is based on the same evolution.
The theoretical foundation of stochastic rates are collision probabilities derived from the Boltzmann equation's collision term with the assumption of a constant matrix element. This derivation is presented in a comprehensive and pedagogical fashion. The derived collision probabilities are employed for a stochastic collision criterion and various detailed-balance fulfilling multi-particle reactions: the mesonic Dalitz decay back-reaction (3-to-1), the deuteron catalysis (3-to-2) and the proton-antiproton annihilation back-reaction (5-to-2). The introduced stochastic rates approach is extensively verified by studies of the numerical stability and comparisons to previous results and analytic expectations. The stochastic rates results agree perfectly with the respective analytic results.
Physically, multi-particle reactions are demonstrated to be significant for different observables, most notably the yield of the partaking particles, even in the late dilute stage of heavy-ion reactions. They lead to a faster equilibration of the system than equivalent binary multi-step treatments. The difference in equilibration consequently influences the yield in afterburner calculations. Interestingly, the interpretation of results is not dependent on employing multi-particle or multi-step treatments, which a posteriori validates the latter.
As the first test case of multi-particle reactions in heavy-ion reactions, the mesonic 3-to-1 Dalitz decay is found to be dominated by the omega Dalitz decay back-reaction. While the effect on the medium is found to be negligible overall, the regeneration is found to be sizable: up to a quarter of Dalitz decays are regenerated.
Non-equilibrium rescattering effects are shown to be relevant for late collision stages for two particle species: deuteron and protons. In both cases, the relevant rescatterings involve multiple particles.
The deuteron pion and nucleon catalysis reactions equilibrate quickly in the afterburner stage at intermediate energies. The constant formation and destruction keeps the yield constant and microscopically explains the "snowballs in hell"-paradox. The yield is also generated with no d present at early times, which explains why coalescence models can also match the multiplicity.
New is the study of the 5-body back-reaction of proton-antiproton annihilations. This work marks the first realization of microscopic 5-body reactions in a transport approach to fulfill detailed balance for such reactions. A sizable regeneration due to the back-reaction of up to half of the proton-antiproton pairs lost due to annihilations is found. Consequently, both annihilation and regeneration in the late non-equilibrium stage are shown to have a significant effect on the p yield.
Next-generation DIRC detectors, like the PANDA Barrel DIRC, with improved optical designs and better spatial and timing resolution, require correspondingly advanced reconstruction and PID methods. The investigation of the PID performance of two DIRC counters and the evaluation of the reconstruction and PID algorithms form the core of this thesis. Several reconstruction and PID approaches were developed, optimized, and tested using hadronic beam particles, experimental physics events, and Geant simulations. The near-final design of the PANDA Barrel DIRC was evaluated with a prototype in the T9 beamline at CERN in 2018. The analysis finds excellent agreement between the experimental data and the Geant simulations for all reconstruction algorithms. The best PID performance of up to $5.2 \pm 0.2$ s.d. $\pi$/K separation at 3.5 GeV/c, was obtained with a time imaging PID method. The PANDA Barrel DIRC simulation, as well as the reconstruction and PID algorithms, were evaluated using experimental data from the GlueX DIRC as part of the FAIR Phase-0 program. The performance validation was carried out using physics events of the GlueX experiment and simulations. The initial analysis results of the commissioning dataset show a $\pi$/K separation power of up to 3 s.d. at a momentum of 3.0-3.5 GeV/c, obtained using a geometric reconstruction algorithm.
The main subject of this thesis is the study of hadron and photon production in relativistic heavy-ion collisions by means of hydrodynamics+transport approaches. Two different kinds of such hybrid approaches are employed in this work, the SMASH-vHLLE-hybrid and a MUSIC+SMASH hybrid. While the former is capable of simulating heavy-ion collisions covering a wide range of collision energies down to √s = 4.3 GeV, reproducing the correct baryon stopping powers, the latter provides a framework to consistently model photon production in the hadronic stage of high-energy heavy-ion collisions.
The SMASH-vHLLE-hybrid is a novel state-of-the-art hybrid approach whose development constitutes a major contribution to this thesis. It couples the hadronic transport SMASH to the 3+1D viscous hydrodynamics approach vHLLE. Therein, SMASH is employed to provide the fluctuating 3D initial conditions and to model the late hadronic rescattering stage, and vHLLE for the fluid dynamical evolution of the hot and dense fireball. The initial conditions are provided on a hypersurface of constant proper time, and the macroscopic evolution of the fireball is carried out down to an energy density of ecrit = 0.5 GeV/fm3, where particlization occurs. Consistency at the interfaces is verified in view of global, on-average quantum number conservation and the SMASH-vHLLE-hybrid is validated by comparison to SMASH+CLVisc as well as UrQMD+vHLLE hybrid approaches. The establishment of the SMASH-vHLLE-hybrid to theoretically describe heavy-ion collisions at intermediate and high collision energies forms a basis for a range of extensions and future research projects. It is further made available to the heavy-ion community by virtue of being published on Github.
The SMASH-vHLLE-hybrid is applied to simulate Au+Au/Pb+Pb collisions between √s = 4.3 GeV and √s = 200.0 GeV. A good agreement with the experimentally measured rapidity and transverse mass spectra is obtained. In particular the baryon stopping dynamics are well reproduced at low, intermediate, and high collision energies. Excitation functions for the mid-rapidity yield and mean transverse momentum of pions, protons and kaons are demonstrated to agree well with their experimentally measured counterpart. These results further validate the approach and provide a solid baseline for potential future studies. The importance of annihilations and regenerations of protons and anti-protons is additionally investigated in Au+Au/Pb+Pb collisions between √s = 17.3 GeV and √s = 5.02 TeV with the SMASH-vHLLE-hybrid. It is found that, regarding the p + p ̄ ↔ 5 π reaction, 20-50% (depending on the rapidity range) of the (anti-)proton yield lost to annihila- tions in the hadronic rescattering stage is restored owing to the back reaction. The back reaction thus constitutes a non-negligible contribution to the final (anti-)proton yield and should not be neglected when modelling the late rescattering stage of heavy-ion collisions.
The MUSIC+SMASH hybrid is a hybrid approach ideally suited to model the production of photons in relativistic heavy-ion collisions. Therein, the macroscopic production of photons in the hadronic stage in MUSIC relies on the identical effective field theories as the photon cross sections implemented in SMASH for the microscopic production. The MUSIC+SMASH hybrid thus provides the first consistent framework to the end of hadronic photon production. It accounts for 2 → 2 scattering processes of the kind π + ρ → π + γ and pion bremsstrahlung processes π + π → π + π + γ. The MUSIC+SMASH hybrid is employed in an ideal 2D setup to systematically assess the importance of non-equliibrium dynamics in the hadronic rescattering stage on mid-rapidity transverse momentum spectra and elliptic flow of photons at RHIC/LHC energies. This is achieved by comparing the outcome of the MUSIC+SMASH hybrid, involving an out-of-equilibrium late rescattering stage, to macroscopically approximating late stage photon production by means of MUSIC, employed down to temperatures well below the switching temperature. It is found that non-equilibrium dynamics have only minor implications for photon transverse momentum spectra, but significantly enhance the photon elliptic flow. At RHIC energies, an enhancement of up to 70%, and at LHC of up to 65% is observed in the non-equilibrium afterburner as compared to its hydrodynamical counterpart. In combination with the large amount of photons produced above the particlization temperature, these differences are modest regarding the transverse momentum spectra, but a significant enhancement of the elliptic flow is observed at low transverse momenta. Below pT ≈ 1.4 GeV, the combined v2 is enhanced by up to 30% at RHIC, and up to 20% at the LHC within the non-equilibrium setup as compared to its approximation via hydrodynamics. Non-equilibrium dynamics in the hadronic rescattering stage are hence important, especially in view of momentum anisotropies at low transverse momenta. These findings thus contribute to the understanding of low-pT photons produced in heavy-ion collisions at RHIC/LHC energies and the MUSIC+SMASH hybrid employed for this study provides a baseline for additional studies regarding photon production in the future.
To summarize, the approaches and frameworks presented in this thesis provide a good baseline for further extensions and studies in order to improve the understanding of hadron and photon production in relativistic heavy-ion collisions across a wide range of collision energies. More broadly, such future studies of hadrons and photons may contribute to enhance the understandig of the properties of the fundamental building blocks of matter, of which everything that surrounds us is made of.
Bohmian mechanics as formulated originally in 1952, has been useful in the implementation of numerical methods applied to quantum mechanics. The scientific community though has had ever since a critical thought about it. Therefore, there are still points to be clarified and rectified. The two main problems are basically: Bohmian mechanics gives a privilege role to the position representation. Secondly, the current interpretation of Bohmian trajectories has been recently proven wrong.
In this context, in Chapter 2, new complex Bohmian quantities are defined; so that they allow the capacity to formulate Bohmian mechanics in any arbitrary continuous representation, for instance, the momentum representation. This Chapter is fully based on two articles, regarding the proposed complex Bohmian formulation and its extension into momentum space.
Chapter 3 deals with a redefinition and reinterpretation of the Bohmian trajectories from the handling of the continuity equation, this is done without any need of additional postulates or interpretations. Also, it is proved that Bohmian mechanics is actually more than a projective aspect of the Wigner function.
As a third point, Chapter 4 presents a sytematic treatment of the hydrodynamic scheme of Bohmian mechanics. Then, a brief summary of the transport equations in Bohmian mechanics is done. Next, a unified hydrodynamic treatment is found for the Bohmian mechanics. This treatment is useful to sketch, a Bohmian treatment to efficiently find the steady value of the transmission integral.
In Chapter 5 conclusions of this thesis are drawn.
Neurons are cells with a highly complex morphology; their dendritic arbor spans up to thousands of micrometers. This extended arbor poses a challenge for the logistics of neuronal processes: mRNA, proteins, and organelles have to be transported to dendrites, hundreds of micrometers away from the soma. This thesis aims to calculate the minimum number of proteins needed to populate the dendritic trees for different scenarios.
In chapter 2, I analyzed the ability of different mechanisms to populate the dendritic arbor. I started from the solution of the diffusion equation in Sec. 2.1, then I included the contribution of active transport in Sec. 2.2 and showed how it could have either the effect of increasing the effective diffusion coefficient or of introducing a bias in the diffusion process. In Sec. 2.3 I studied the spatial distribution of locally synthesized protein, accordingly with actively and passively transported mRNA. In Sec. 2.5, I derived the boundary condition for branches showing a qualitatively different behavior of surface and cytoplasmic proteins induced by the medium’s dimensionality in which they diffuse.
In chapter 3, I introduced the concept of protein requirement, defined as the minimum number of proteins that the neuron needs to produce to provide at least one protein to each micrometer of the dendritic arbor. In Sec. 3.1, I derived the protein requirement for diffusive proteins for somatic translation and constant translation in the dendritic arbor. In Sec. 3.2, I analyzed numerically the protein requirement in the case of actively transported protein synthesized in the soma, and, in Sec. 3.3, in the case of actively transported proteins synthesized in the dendritic arbor. In Sec. 3.4, I analyzed the protein requirement of protein synthesized in the dendrite accordingly with the distribution of mRNA described in Sec. 3.3 and 3.2. In Sec. 3.5, I derived the protein requirement for a single branch and purely diffusive proteins.
In chapter 4, I analyzed the relation between the radii of the three afferent dendrites in a branch, their length, and the diffusion length of a protein. In Sec. 4.1 I derived the optimal ratio between the radii of the daughter dendrites that minimizes the protein requirement. In Sec. 4.3 I introduced the 3/2− Rall Rule and in Sec. 4.5 its generalization. Finally, I used those rules to estimate the fraction of proteins diffusing away from and toward the soma.
In chapter 5, I analyzed the radii distribution for three categories of neurons: cultured hippocampal neurons in Sec. 5.1, stomatogastric ganglia neuron in Sec. 5.2, and 3DEM reconstructed prefrontal pyramidal neurons in Sec. 5.3. For each of these three classes, I analyzed the distribution of radii, Rall exponents, and the probability ratio. For most of them, I found that the probability of a protein diffusing away from the soma is higher for surface proteins than for cytoplasmic ones. I quantified this with a parameter called surface bias.
In Chapter 6, I analyzed the fluorescent ratio imaged by our collaborators Anne-Sophie Hafner, for a surface protein, GFP::Nlg, and a soluble one, GFP, in cultured hippocampal neurons, and I compared the fluorescent ratio with the probability ratio obtained in 5.1, finding that they are in good agreement.
In chapter 7, I compared the real dendritic morphologies imaged by one of our collaborators Ali Karimi with the optimal branching rule obtained in Sec. 4.1 and I calculated the cost for not having optimal branching radii.
Finally, in Chapter 8, I used the knowledge of the branching statistics gathered in 5.3 to simulate the protein profile on three different classes of neurons: pyramidal neurons, granule neuron, and Purkinje neurons. I compared the protein profile for surface and cytoplasmic neurons for each morphology for two different values of the diffusion length: λ = 109µm and λ = 473µm, both for optimized radii and symmetrical radii. I showed how the radii optimization reduces the protein requirement of a factor 10 4 for pyramidal neurons.
Die vorliegende Dissertation stellt die Strahldynamikdesigns zweier Hochfrequenzquadrupol-Linearbeschleuniger bzw. Radio Frequency Quadrupoles (RFQs) vor: das fur den RFQ des Protonen-Linearbeschleunigers (p-Linac) des FAIR2-Projekts an der GSI3 Darmstadt sowie einen ersten Designentwurf für einen kompakten RFQ, der u.a. zur Erzeugung von Radioisotopen für medizinische Zwecke genutzt werden könnte. Der Schwerpunkt liegt auf dem ersten Design.
Topological phases set themselves apart from other phases since they cannot be understood in terms of the usual Landau theory of phase transitions. This fact, which is a consequence of the property that topological phase transitions can occur without breaking symmetries, is reflected in the complicated form of topological order parameters. While the mathematical classification of phases through homotopy theory is known, an intuition for the relation between phase transitions and changes to the physical system is largely inhibited by the general complexity.
In this thesis we aim to get back some of this intuition by studying the properties of the Chern number (a topological order parameter) in two scenarios. First, we investigate the effect of electronic correlations on topological phases in the Green's function formalism. By developing a statistical method that averages over all possible solutions of the manybody problem, we extract general statements about the shape of the phase diagram and investigate the stability of topological phases with respect to interactions. In addition, we find that in many topological models the local approximation, which is part of many standard methods for solving the manybody lattice model, is able to produce qualitatively correct phase transitions at low to intermediate correlations.
We then extend the statistical method to study the effect of the lattice, where we evaluate possible applications of standard machine learning techniques against our information theoretical approach. We define a measure for the information about particular topological phases encoded in individual lattice parameters, which allows us to construct a qualitative phase diagram that gives a more intuitive understanding of the topological phase.
Finally, we discuss possible applications of our method that could facilitate the discovery of new materials with topological properties.
This dissertation describes the development of the beam dynamics design of a novel superconducting linear accelerator. At a main operating frequency of 216.816 MHz, ions with a mass-to-charge ratio of up to 6 can be accelerated at high duty cycles up to CW operation. Intended for construction at the GSI Helmholtz Centre for Heavy Ion Research in Darmstadt, the focus of the work is on the beam dynamic design of the accelerator section downstream of the high charge injector (HLI) at an injection energy of 1.39 MeV/u. An essential feature of this linear accelerator (Linac) is the use of the EQUUS (Equidistant Multigap Structure) beam dynamics concept for a variably adjustable output energy between 3.5 and 7.3 MeV/u (corresponding to about 12.4 % of the speed of light) with a required low energy spread of maximum 3 keV/u.
The GSI Helmholtz Centre for Heavy Ion Research is a large-scale research facility that uses its particle accelerators to perform basic research with ion beams. Research on super-heavy elements ("SHE") is a major focus. It is expected that their production and research will provide answers to a large number of scientific questions. The production and detection of elements with atomic numbers 107 to 112 (Bohrium, Hassium, Meitnerium, Darmstadtium, Röntgenium and Copernicium) was first achieved at GSI between 1981 and 1996.
Key to this remarkable progress in SHE research were continuous developments and technical innovations. On the one hand, in the field of experimental sensitivity and detection of the nuclear reaction products and, on the other hand, in the field of accelerator technology.
For the acceleration of the projectile beam, the UNILAC (Universal Linear Accelerator), which was put into operation in 1975, has been used at GSI so far. In the course of the reconstruction and expansion of the research infrastructure at GSI, a dedicated new particle accelerator, HELIAC (Helmholtz Linear Accelerator), is now under development to meet the special requirements of the beam parameters for the synthesis of new superheavy elements. Typically, the production rates of super-heavy elements with effective cross sections in the picobarn range are very low. Therefore, a high duty cycle (up to CW operation) is a key feature of HELIAC. Thus, the required beam time for the desired nuclear reactions can be significantly shortened.
Theoretical preliminary work by Minaev et al. and newly created knowledge about design, fabrication, and operation of superconducting drift tube cavities have laid the foundation for this work and thus the development of the HELIAC linear accelerator. It consists of a superconducting and a normal conducting part. Acceleration takes place in the superconducting part in four cryomodules, each about 5 m long. These contain three CH cavities, one buncher cavity, two solenoid magnets for transverse beam focusing, and two beam position monitors (BPMs).
The following 10 m long normal conducting part is primarily used for beam transport and ends with a buncher cavity. This is operated at a halved frequency of 108.408 MHz.
A key feature of this accelerator is the variability of the output energy from 3.5 to 7.3 MeV/u with a small energy uncertainty of ±3 keV/u maximum over the entire output energy range. For the development of HELIAC, the EQUUS beam dynamics concept used combined the advantages of conventional linac designs with the high acceleration gradients of superconducting CH-DTLs. By doubling the frequency (compared to the GSI high charge injector) to 216.816 MHz in the superconducting section and using CH cavities at an acceleration gradient of maximum 7.1 MV/m, an acceleration efficiency with superconducting drift tube structures that is unique in the world is made possible. At the same time, the compact lengths of the CH cavities ensure good handling for both production and operation. EQUUS leads to longitudinal beam stability in all energy ranges of the accelerator with the sliding motion of the synchronous phase within each CH cavity. The rms emittance growth is moderate in all levels. The modular design of the HELIAC with four cryomodules basically allows the Linac to be commissioned starting with the first cryomodule, the so-called Advanced Demonstrator. In the subsequent expansion stage with only the first two cryomodules of HELIAC, the lower limit of the energy range to be provided by HELIAC (3.5 MeV/u) can already be clearly exceeded, so that use in regular beam operation at GSI is already conceivable from here on.
By means of error tolerance studies, the stability of the HELIAC beam dynamics design against possible alignment errors of the magnetic focusing elements and accelerator cavities as well as errors of the electric field amplitudes and phases have been investigated, basically confirmed and critical parameters have been determined. An additional steering concept via dipole correction coils at the solenoid magnets allows transverse beam control as well as diagnostics by means of two BPMs per cryomodule.
With completion of this work in 2021, the CH1 and CH2 cavities have already been built and are in the final preparation and cold test phase. In parallel, the development of the CH cavities CH3-11 has also been started.
For finite baryon chemical potential, conventional lattice descriptions of quantum chromodynamics (QCD) have a sign problem which prevents straightforward simulations based on importance sampling.
In this thesis we investigate heavy dense QCD by representing lattice QCD with Wilson fermions at finite temperature and density in terms of Polyakov loops.
We discuss the derivation of $3$-dimensional effective Polyakov loop theories from lattice QCD based on a combined strong coupling and hopping parameter expansion, which is valid for heavy quarks.
The finite density sign problem is milder in these theories and they are also amenable to analytic evaluations.
The analytic evaluation of Polyakov loop theories via series expansion techniques is illustrated by using them to evaluate the $\SU{3}$ spin model.
We compute the free energy density to $14$th order in the nearest neighbor coupling and find that predictions for the equation of state agree with simulations to $\mathcal{O}(1\%)$ in the phase were the (approximate) $Z(3)$ center symmetry is intact.
The critical end point is also determined but with less accuracy and our results agree with numerical results to $\mathcal{O}(10\%)$.
While the accuracy for the endpoint is limited for the current length of the series, analytic tools provide valuable insight and are more flexible.
Furthermore they can be generalized to Polyakov-loop-theories with $n$-point interactions.
We also take a detailed look at the hopping expansion for the derivation of the effective theory.
The exponentiation of the action is discussed by using a polymer expansion and we also explain how to obtain logarithmic resummations for all contributions, which will be achieved by employing the finite cluster method know from condensed matter physics.
The finite cluster method can also be used to evaluate the effective theory and comparisons of the evaluation of the effective action and a direction evaluation of the partition function are made.
We observe that terms in the evaluation of the effective theory correspond to partial contractions in the application of Wick's theorem for the evaluation of Grassmann-valued integrals.
Potential problems arising from this fact are explored.
Next to next to leading order results from the hopping expansion are used to analyze and compare the onset transition both for baryon and isospin chemical potential.
Lattice QCD with an isospin chemical potential does not have a sign problem and can serve as a valuable cross-check.
Since we are restricted by the relatively short length of our series, we content ourselves with observing some qualitative phenomenological properties arising in the effective theory which are relevant for the onset transition.
Finally, we generalize our results to arbitrary number of colors $N_c$.
We investigate the transition from a hadron gas to baryon condensation and find that for any finite lattice spacing the transition becomes stronger when $N_c$ is increased and to be first order in the limit of infinite $N_c$.
Beyond the onset, the pressure is shown to scale as $p \sim N_c$ through all available orders in the hopping expansion, which is characteristic for a phase termed quarkyonic matter in the literature.
Some care has to be taken when approaching the continuum, as we find that the continuum limit has to be taken before the large $N_c$ limit.
Although we currently are unable to take the limits in this order, our results are stable in the controlled range of lattice spacings when the limits are approached in this order.