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Particle collisions provide insight into the structure of matter and the interaction of its constituents. Furthermore, they also allow a better understanding of the processes involved in the formation of the universe. To cover these diverse areas, it is necessary to study different observables and collision systems. A particular challenge is to find a suitable measurable observable for a theoretically meaningful variable and to develop a measurement process taking into account the experiment. The analyses of particle collisions in this thesis cover many of the challenges and objectives mentioned above. The focus of the work is the analysis of isolated photons at an energy of √s = 7 TeV. In addition, the work also includes measurements of the average transverse momentum in Pb-Pb collisions at an energy of √s = 2.76 TeV.
Apart from the collision system, the two analyses complement each other in other respects. The measurement of isolated photons represents the first measurement of this observable with ALICE and thus lays the foundation for further measurements at other collision systems and energies. The measurement of the mean transverse momentum, on the other hand, is based on an established measurement and thus allows the comparison of different collision systems. Likewise, the physical processes studied differ. With the measurement of isolated photons, hard scattering processes in the collisions can be investigated, while the average transverse momentum allows a description of the underlying event.
When measuring isolated photons, it should be noted that isolated photons are a measurable observable that cannot be assigned to an explicit physical process. The isolation criterion used in the analysis serves to increase the fraction of prompt photons from 2→2 processes. These photons can contribute to a better understanding of the parton density function (PDF) of gluons, as well as be used as a reference for perturbative QCD calculations.
Of particular importance for the analysis are the cluster shape and the energy within a certain radius around the potential photon. The combination of these two quantities allows determining the background using the ABCD method established by CDF and ATLAS. The result obtained in this way extends the previous measurements of the cross-section of isolated photons at the LHC to lower transverse momenta. Similarly, the previous measurements of the cross-section as a function of the scale variable xT are extended to lower values.
The main focus of the measurement of the average transverse momentum of charged particles ⟨pT⟩ is to compare the measurement for the pp, p-Pb, and Pb-Pb collision systems. To obtain a direct comparison between the different collision systems, ⟨pT ⟩ is measured against the true multiplicity nch. Since the multiplicity range of pp and p-Pb collisions is limited, the analysis in Pb-Pb collisions is restricted to nch = 100. This range corresponds to peripheral Pb-Pb collisions. A particular focus of the analysis is the determination and reduction of the electromagnetic background in peripheral Pb-Pb collisions and the determination of nch based on the measured multiplicity nacc . The different collision systems show similar behavior with increasing multiplicity. The steepest increase occurs at low multiplicities and changes for all collision systems at nch = 14. With higher multiplicities, the slope reduces further, with the effect being most pronounced in Pb-Pb collisions.
In this thesis we investigate the thermodynamic and dynamic properties of the D-dimensional quantum Heisenberg ferromagnet within the spin functional renormalization group (FRG); a
formalism describing the evolution of the system’s observables as the magnetic exchange inter-action is artificially deformed. Following an introduction providing a self contained summary of the conceptual and mathematical background, we present the spin FRG as developed by Krieg and Kopietz in references [1] and [2] in chapter two. Thereto, the generating functional of the imaginary time-spin correlation functions and its exact flow equation describing the deformation process of the exchange interaction are introduced. In addition, it is highlighted that - in contrast to conventional field-theoretic FRG approaches - the related Legendre trans-formed functional cannot be defined if the exchange interaction is initially switched off. Next, we show that this limitation can be circumvented within an alternativ hybrid approach, which treats transverse and longitudinal spin fluctuations differently. The relevant functionals are introduced and the relations of the corresponding functional Taylor coefficients with the spin correlation functions are discussed. Lastly, the associated flow equations are derived and the possibility of explicit or spontaneous symmetry breaking is taken into account.
In chapter three, we benchmark the hybrid formalism against a calculation of the thermo-dynamic properties of the one and two-dimensional Heisenberg model at low temperatures T and finite magnetic field H. For this purpose, we devise an anisotropic deformation scheme of the exchange interaction which allows for a controlled truncation of the infinite hierarchy of FRG flow equations. Thereby, contact with mean-field and spin-wave theory is made and the violation of the Mermin-Wagner theorem is discussed. To fulfill the latter, the truncation scheme is then complemented by a Ward identity relating the transverse self-energy and the magnetization. The resulting magnetization M (H, T ) and isothermal susceptibility χ(H, T ) are in quantitative agreement with the literature and the established behavior of the transverse correlation length and the zero-field susceptibility close to the critical point is qualitatively reproduced in the limit H → 0.
Finally, we investigate the longitudinal dynamics at low temperatures. To this end, the hierarchy of flow equations is solved within the same anisotropic deformation scheme complemented by an expansion in the inverse interaction range, and the resulting longitudinal dynamic structure factor is calculated within a low-momentum expansion. In D = 3, the large phase space accessible for the decay into transverse magnons yields only a broad hump centered at zero frequency whose width scales linearly in momentum. In contrast, at low temperatures and in a certain range of magnetic fields, a well-defined quasiparticle peak with linear dispersion emerges in D ≤ 2, which we identify as zero-magnon sound. Sound velocity and damping are discussed as a function of temperature and magnetic field, and the relevant momentum-frequency window is estimated and compared to the hydrodynamic
second-magnon regime.
Ziel dieser Dissertation ist es, die Gleichgewichts- und Nichtgleichgewichts-Eigenschaften des stark wechselwirkenden QGP-Mediums nahe dem Phasenübergang unter extremen Bedingungen von hohen T und hohen Baryonendichten mit Hilfe der kinetischen Theorie im Rahmen von effektiven Modellen zu untersuchen. Wir werden zunächst die thermodynamischen und Transporteigenschaften des QGPs in der Nähe des Gleichgewichts auf der Basis des DQPM im Bereich moderater chemischer Baryonenpotentiale μB ≥ 0.5 GeV untersuchen. Insbesondere werden die EoS und die Schallgeschwindigkeit sowie die Transportkoeffizienten des QGP auf der Grundlage des DQPM bei endlichen T und μB berechnet. Transportkoeffizienten sind besonders interessant, da sie Informationen über die Wechselwirkungen im Medium erlauben, das im Gleichgewicht durch eine Temperatur T und ein chemisches Potential μB charakterisiert werden kann. Unter Berücksichtigung der Transportkoeffizienten und der EoS der QGP-Phase vergleichen wir unsere Ergebnisse mit verschiedenen Resultaten aus der Literatur, in denen Transportkoeffizienten des QGPs auf Basis von effektiven Modellen vorwiegend bei Null oder kleinem chemischen Potentialen untersucht wurden.
Darüber hinaus werden in Kapitel 3 die Gleichgewichtseigenschaften des QGPs und insbesondere die Auswirkungen der μB-Abhängigkeit der thermodynamischen und Transporteigenschaften des QGPs im Rahmen des erweiterten PHSD-Transportansatzes untersucht, der die vollständige Entwicklung des Systems einschließlich der partonischen Phase umfasst. Die Entwicklung des PHSD-Transportansatzes wird in der partonischen Phase erweitert, indem explizit die gesamt- und differentiellen partonischen Streuquerschnitte auf der Grundlage des DQPM berechnet und bei der tatsächlichen Temperatur T und dem baryonischen chemischen Potential μB in jeder einzelnen Raum-Zeit-Zelle, in der die partonische Streuung stattfindet, ausgewertet werden.
Um die Spuren der μB-Abhängigkeit des QGPs in den Observablen zu untersuchen, werden die Ergebnisse von PHSD5.0 (mit μB-Abhängigkeiten) mit den Ergebnissen von PHSD5.0 für μB = 0 sowie mit PHSD4.0, in dem die Massen/Breiten der Quarks und Gluonen sowie deren Wechselwirkungsquerschnitte nur von T abhängen, verglichen. Wir diskutieren die PHSD-Ergebnisse für verschiedene Observablen: (i) Rapiditäts- und pT -Verteilungen von identifizierten Hadronen für symmetrische Au+Au- und Pb+Pb- Kollisionen bei Energien von 30 AGeV (zukünftige NICA-Energie) sowie für die RHIC-Spitzenenergie von √sNN = 200 GeV; (ii) gerichteter Fluss v1 von identifizierten Hadronen für Au + Au bei invarianter Energie √sNN = 27 GeV und 200 GeV; (iii) elliptischer Fluss v2 der identifizierten Hadronen für Au+Au bei invarianten Energien √sNN = 27 und 200 GeV. Der Vergleich der "Bulk"-Observablen für Au+Au-Kollisionen innerhalb der drei PHSD-Einstellungen hat gezeigt, dass sie eine recht geringe Empfindlichkeit gegenüber den μB -Abhängigkeiten der Partoneigenschaften (Massen und Breiten) und ihrer Wechselwirkungsquerschnitte aufweisen, sodass die Ergebnisse von PHSD5.0 mit und ohne μB sehr nahe beieinander liegen. Nur im Fall von Kaonen, Antiprotonen ̄p und Antihyperonen ̄Λ + ̄Σ0 konnte ein kleiner Unterschied zwischen PHSD4.0 und PHSD5.0 bei den höchsten SPS- und RHIC-Energien festgestellt werden.
Wir finden nur geringe Unterschiede zwischen den Ergebnissen von PHSD4.0 und PHSD5.0 für die hier betrachteten hadronischen Observablen sowohl bei hohen als auch bei mittleren Energien. Dies hängt damit zusammen, dass bei hohen Energien, wo die Materie vom QGP dominiert wird, ein sehr kleines chemisches Baryonenpotential μB in zentralen Kollisionen bei mittlerer Rapidität gemessen wird, während mit abnehmender Energie und größerem μB der Anteil des QGPs rapide abnimmt, sodass die endgültigen Beobachtungswerte insgesamt von den Hadronen dominiert werden, die an der hadronischen Rückstreuung teilgenommen haben, und somit die Information über ihren QGP-Ursprung verwaschen oder verloren geht.
In Kapitel 4 betrachten wir die Transportkoeffizienten von QGP-Materie im erweiterten Polyakov-NJL-Modell entlang der Übergangslinie für moderate Werte des chemischen Baryonenpotenzials 0 ≤ μB ≤ 0.9 GeV sowie in der Nähe des kritischen Endpunkts(CEP) und bei großem chemischen Baryonenpotenzial μB = 1.2 GeV, wo ein Phasenübergang erster Ordnung stattfindet. Wir untersuchen, wie die Natur der Freiheitsgrade die Transporteigenschaften des QGPs beeinflusst. Darüber hinaus demonstrieren wir die Auswirkungen des Phasenübergangs erster Ordnung und des CEP auf die Transportkoeffizienten im dekonfinierten QCD-Medium.
Darüber hinaus wird in Kapitel 5 eine phänomenologische Erweiterung des DQPM auf große baryonchemische Potentiale μB einschließlich der Region mit einem möglichen CEP und späterem Phasenübergang erster Ordnung betrachtet. Eines der wichtigsten Merkmale des Modells ist das Auftreten einer ’kritischen‘ Skalierung in der Nähe des CEP. Das Hauptziel des vorgestellten Modells besteht darin, die mikroskopischen und makroskopischen Eigenschaften der partonischen Freiheitsgrade für den Bereich des Phasendiagramms bereitzustellen, der durch moderates T und moderates oder hohes μB gekennzeichnet ist.
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The putative effects of dark matter are most easily explained by a collisionless fluid on cosmological scales and by Modified Newtonian Dynamics (MOND) on galactic scales. Hybrid MOND dark matter models combine the successes of dark matter on cosmological scales and those of MOND on galactic scales. An example of such a model is superfluid dark matter (SFDM) which postulates that this differing behavior with scale is caused by a single underlying substance with two phases. In this thesis, I highlight successful observational tests of SFDM regarding strong lensing and the Milky Way rotation curve. I also discuss three problems due to the double role of the aforementioned single underlying substance and show how these may be avoided. Finally, I introduce a novel Cherenkov radiation constraint for hybrid MOND dark matter models. This constraint is different from standard modified gravity Cherenkov radiation constraints because such hybrid models allow even non-relativistic objects like stars to emit Cherenkov radiation.
The realization of a fast and robust closed orbit feedback (COFB) system for the on-ramp orbit correction at SIS18 synchrotron of FAIR project is reported in this thesis. SIS18 has some peculiar behaviors including on-ramp optics variation, very short lengths of the ramps (200 ms to 1 s) and a cycle-to-cycle variation of beam parameters. The realized fast COFB system being robust against above mentioned features of SIS18 is a first of its kind and the course to its realization led to some novel contributions in the field of closed orbit correction. A new method relying on the discrete Fourier transform (DFT)-based decomposition of the orbit response matrix (ORM) has been introduced, exploiting the symmetry in the arrangement of beam position monitors (BPMs) and the corrector magnets in the synchrotrons. A nearest-circulant approximation has also been introduced for synchrotrons having slight deviation from the symmetry, making the method applicable to a vast majority of synchrotrons. Moreover, the performance and the stability analysis of COFB systems in the presence of ORM mismatch between the synchrotron and the feedback controller is presented. The COFB systems are divided into slow and fast regimes and a new stability criterion consistent with measurements, is introduced. The practicality of the criterion is verified experimentally at COSY Jülich and is used for the analysis of various sources of ORM mismatch at SIS18. The commissioning of the SIS18 COFB system is also reported in detail which relies on Libera Hadron as the main hardware resource for the controller implementation. The on-ramp orbit correction is demonstrated for the horizontal plane of SIS18, for the disturbance rejection up to 600 Hz.
The present research in high energy physics as well as in the nuclear physics requires the use of more powerful and complex particle accelerators to provide high luminosity, high intensity, and high brightness beams to experiments. With the increased technological complexity of accelerators, meeting the demand of experimenters necessitates a blend of accelerator physics with technology. The problem becomes severe when optimization of beam quality has to be provided in accelerator systems with thousands of free parameters including strengths of quadrupoles, sextupoles, RF voltages, etc. Machine learning methods and concepts of artificial intelligence are considered in various industry and scientific branches, and recently, these methods are used in high energy physics mainly for experiments data analysis.
In Accelerator Physics the machine learning approach has not found a wide application yet, and in general the use of these methods is carried out without a deep understanding on their effectiveness with respect to more traditional schemes or other alternative approaches. The purpose of this PhD research is to investigate the methods of machine learning applied to accelerator optimization, accelerator control and in particular on optics measurements and corrections. Optics correction, maximization of acceptance, and simultaneous control of various accelerator components such as focusing magnets is a typical accelerator scenario. The effectiven- ess of machine learning methods in a complex system such as the Large Hadron Collider, which beam dynamics exhibits nonlinear response to machine settings is the core of the study. This work presents successful application of several machine learning techniques such as clustering, decision trees, linear multivariate models and neural networks to beam optics measurements and corrections at the LHC, providing the guidelines for incorporation of machine learning techniques into accelerator operation and discussing future opportunities and potential work in this field.
Classical light microscopy is one of the main tools for science to study small things. Microscopes and their technology and optics have been developed and improved over centuries, however their resolution is ultimately restricted physically by the diffraction of light based on its wave nature described by Maxwell’s equations. Hence, the nanoworld – often characterized by sub-100-nm structural sizes – is not accessible with classical far-field optics (apart from special x-ray laser concepts) since its lateral resolution scales with the wavelength.
It was not until the 20th century that various technologies emerged to circumvent the diffraction limit, including so-called near-field microscopy. Although conceptually based on Maxwell’s long known equations, it took a long time for the scientific community to recognize its powerful opportunities and the first embodiments of near-field microscopes were developed. One representative of them is the scattering-type Scanning Near-field Optical Microscope (s-SNOM). It is a Scanning Probe Microscope (SPM) that enables imaging and spectroscopy at visible light frequencies down to even radio waves with a sub-100-nm resolution regardless of the wavelength used. This work also reflects this wide spectral range as it contains applications from near-infrared light down to deep THz/GHz radiation.
This thesis is subdivided into two parts. First, new experimental capabilities for the s-SNOM are demonstrated and evaluated in a more technical manner. Second, among other things, these capabilities are used to study various transport phenomena in solids, as already indicated in the title.
On the technical side, preliminary studies on the suitability of the qPlus sensor – a novel scanning probe technology – for near-field microscopy are presented.
The scanning head incorporating the qPlus sensor–named TRIBUS – is originally intended and built for ultra-high vacuum, low temperature, and high resolution applications. These are desirable environments and properties for sensitive nearfield measurements as well. However, since its design was not planned for near-field measurements, several special technical and optical aspects have to be taken into account, among others the scanning tip design and a spring suspended measurement head.
In addition, in this thesis field-effect transistors are used as THz detectors in an s-SNOM for the first time. Although THz s-SNOM is already an emerging technology, it still suffers from the requirements of sophisticated and specialized infrastructure on both the detector and laser side. Field-effect transistors offer an alternative that is flexible, cost-efficient, room-temperature operating, and easy to handle. Here, their suitability for s-SNOM measurements, which in general require very sensitive and fast detectors, is evaluated.
In the scientific part of this thesis, electromagnetic surface waves on silver nanowires and the conductivity/charge carrier density in silicon are investigated. Both are completely different concepts of transport phenomena, but this already shows the general versatility of the s-SNOM as it can enter both fields. Silver nanowires are analysed by means of near-infrared radiation. Their plasmonic behaviour in this spectral region is studied complementing other simulations and studies in literature performed on them using for example far-field optics.
Furthermore, the surface wave imaging ability of the s-SNOM in the near-infrared regime is thoroughly investigated in this thesis. Mapping surface waves in the mid-infrared regime is widespread in the community, however for much smaller wavelengths there are several important aspects to be considered additionally, such as the smaller focal spot size.
After that, doped and photo-excited silicon substrates are investigated. As the characteristic frequencies of charge carriers in semiconductors – described by the plasma frequency and the Drude model – are within the THz range, the THz s-SNOM is very well suited to probe their behaviour and to reveal contrasts, which has already been shown qualitatively by numerous literature reports. Here, the photo-excitation enables to set and tune the charge carrier density continuously.
Furthermore, the analysis of all silicon samples focuses on a quantitative extraction of the charge carrier densities and doping levels ...