A new hypothesis of matter formation after the big bang based on either particle-wave duality or electric dipole asymmetry. Both assumptions allow to postulate that the probability of matter formation is slightly higher than that of antimatter formation. As a consequence, this difference of probabilities ∆Pp for protons and ∆Pe with regard to electrons avoided complete annihilation in the beginning.

Universiẗat, Diss., 2002--Mainz.

A new hypothesis of matter formation after the big bang based on either particle-wave duality or electric dipole asymmetry. Both assumptions allow to postulate that the probability of matter formation is slightly higher than that of antimatter formation. As a consequence, this difference of probabilities ∆Pp for protons and ∆Pe with regard to electrons avoided complete annihilation in the beginning.

The thesis deals with the development and characterization of new light sources, which are mandatory for applications in atomic and molecular spectroscopy, medical and biological imaging or industrial production. For that purpose, the employment of interactions of high intensity ultra-short laser pulses with gaseous media offers a rich variety of physical effects which can be exploited. The effects are characterized by a nonlinear dependency on the present light fields. Therefore, accurate modeling of the nonlinearities of the gas is crucial. In general, the nonlinearities are due to the electronic response of the gas atoms to the light field and one distinguishes between the response of bound and ionized electrons. The first part investigates laser pulse self compression, where the consideration of a purely bound electron response is sufficient. We apply an exotic setup with an negative Kerr nonlinearity in order to avoid spatial collapse of the beam on the cost of dealing with an highly dispersive nonlinearity. Analytical analysis and numerical simulations prove the possibility of laser pulse compression in such setups and reveals a new compression scheme, where the usually disturbing dispersion of the nonlinaerity is responsible for compression. Dealing with tera-Hertz generation by focusing an ionizing two-color laser pulse into gas, the second part exploits a medium nonlinearity caused by ionized electrons. We reveal in a mixed analytical and numerical analysis the underlying physical mechanism for THz generation: ionized electrons build up a current, which radiates. Thereby, the the two-color nature of the input laser is crucial for the emitted radiation to be in the tera-Hertz range. Combining this physical model with a pulse propagation equation allows us to achieve remarkable agreement with experimental measurements. Finally, the third part deals with nonlinearities from bound as well from ionized electrons on a fundamental level. We advance beyond phenomenological models for responses of bound and ionized electrons and quantum mechanically model the interaction of an ultra-short laser pulse with a gas. Already the simplest case of one dimensional hydrogen reveals basic features. For low intensities, the Kerr nonlinearity excellently describes the response of bound electrons. For increasing intensity, ionization becomes important and the response from ionized electrons is the governing one for high intensities. This quantum mechanical correct modeling allows us to explain saturation and change of sing of the nonlinear refractive index and to deduce suited approximate models for optical nonlinearities.

Active matter describes systems that convert energy from their environment into directed motion. Therefore, these systems are in intrinsic nonequilibrium, unlike their passive counterparts. From a theoretical point of view, such active systems have been modeled by agent-based models, as well as hydrodynamic approaches, which allowed for the investigation of a wide range of observed collective phenomena characterizing active matter. In this thesis we develop a microscopic field-theoretical approach to describe generic properties of active systems. This description combines the phase field crystal model with a polar order parameter and a self-propulsion term. First, we validate this approach by reproducing results obtained with corresponding agent-based models, such as binary collisions, collective migration and vortex formation. We also perform a direct comparison between our model and a microscopic phase field description of active matter. Next, we use this continuum approach to simulate some larger active systems and to analyze the coarsening process in active crystals, as well as the mechanisms leading to mobile clusters. We show the generality of our approach by extending it to binary mixtures of interacting active and passive particles. Also in this case, we first validate the model by reproducing known results, such as enhanced crystallization via active doping and the suppression of collective migration in an active bath in the presence of fixed obstacles. Interestingly, for the regime of mobile passive particles in an active bath a laning state is found, which is characterized by an alignment of the active particles that is globally nematic, but polar within each lane. This state represents a theoretical prediction feasible to be validated experimentally. Finally, we explore the field of topological active matter. We develop an agent-based model to describe self-propelled particles on curved surfaces and study the complex spatiotemporal patterns that emerge. / Aktive Materie beschreibt Systeme, die Energie aus ihrer Umgebung in gerichtete bewegung umwandeln. Im Gegensatz zur passiven Materie befinden sich diese Systeme nie im physikalischen Gleichgewicht und offenbaren dadurch interessante physikalische Phänomene. Vom theoretischen Standpunkt her wurde aktive Materie bereits simuliert, typischerweise durch agenten-basierte Modelle oder hydrodynamische Ansätze, die es ermöglichen eine Vielzahl der auftretenden kollektiven Bewegungsprinzipien zu untersuchen. In dieser Doktorarbeit entwickeln wir einen mikroskopischen Kontinuumsansatz um die generischen Eigenschaften von aktiven Systemen zu untersuchen. Unsere Beschreibung kombiniert das Phasenfeld-Kristall Modell mit einem polaren Ordnungsparameter und einem Antriebsterm. Zuerst validieren wir den Ansatz durch Reproduktion bekannter Ergebnisse agenten-basierter Modelle, wie binäre Kollisionen, kollektive Bewegung und Wirbelformationen. Des Weiteren führen wir einen direkten Vergleich zwischen unserem Modell und einer mikroskopischen Phasenfeldbeschreibung aktiver Materie durch. Danach nutzen wir den kontinuierlichen Ansatz um große aktive Systeme zu simulieren und analysieren den Vergröberungsprozess in aktiven Kristallen und Mechanismen der mobilen Aggregatbildung. Wir illustrieren die Allgemeingültigkeit unseres Simulationsansatzes durch die Erweiterung auf binäre Systeme, in denen sowohl aktive als auch passive Partikel enthalten sind. Auch in diesem Fall validieren wir das Modell durch Vergleiche mit bekannten Resultaten, wie zum Beispiel die verstärkte Kristallisation durch aktives Doping oder die Unterdrückung kollektiver Bewegung durch die Einführung von Hindernissen in einem aktiven Bad. Interessanterweise finden wir bei der Präsenz mobiler passiver Partikel in einem aktiven Bad einen Fahrspur-Zustand, in welchem die aktiven Partikel nematische Fahrspuren bilden und sich nur jeweils innerhalb einer Fahrspur nematisch polar anordnen. Dieser bisher unbekannte Zustand stellt eine theoretische Vorhersage dar, die experimentell geprüft werden kann. Schließlich begeben wir uns auf das Gebiet der topologischen aktiven Materie. Wir entwickeln ein agenten-basiertes Modell um selbst-angetriebene Partikel auf gekrümmten Oberflächen zu beschreiben und untersuchen die dabei auftretenden zeitlich und räumlich komplexen Muster.%, die dabei auftreten.

Hard-core bosons are versatile and useful in describing several physical systems due to their one-to-one mapping with spin-1/2 operators. We propose two frameworks where hard-core boson mapping not only reduces the complexity of the original problem, but also captures important features of the physics of the original system that would have implied high-computational procedures with not much profound insight in the mechanisms behind its behavior. The first case study comprising part i is an approach to the description of the phases 2D Lattice Gauge Theories, the Quantum 6-Vertex Model and the Quantum Dimer Model using one fluctuating electric string as an 1D precursor of the whole 2D systems[HAMS19]. Both models and consequently the string are described by the Rokhsar-Kivelson Hamiltonian with parameter v measuring the competition of potential versus kinetic terms. The string can be mapped one-to-one onto a 1D system of hard-core bosons that can be solved exactly for the Quantum 6-Vertex Model, and offers footprints of the phase diagram of the Quantum Dimer Model in the region close to the Rokhsar-Kivelson point v = 1, especially when |v| ≤ 1. The second case study we have discussed in part ii is an extension of higher-dimensional bosonization techniques in Landau Fermi liquids to the case of nodal semimetals where the Fermi surface shrinks to a point, so the description of particle-hole interactions as fluctuations of the Fermi surface is not available [MS20]. Additionaly, we focus our analysis on the Q = 0 sector where the electron and the hole have opposite momenta ±k, so they are mapped into a hard-core boson located at a site k in the reciprocal lattice. To test our extension we calculate nonperturbative corrections to the optical conductivity of 2D Dirac fermions with electron-electron interactins described as a Coulomb potential, obtaining results consistent to the literature and the experimental reports where corrections are small even in strong coupling regimes. Part iii discusses further ideas derived from parts i and ii, including a brief discussion on addressing the weak coupling instability in bilayer graphene using the bosonization extension that offers a picture of hard-core bosons describing Q = 0 excitons that undergo a Bose-Einstein condensation resulting in a ground state adiabatically disconnected from the noninteracting case.:1 Introduction 1 1.1 Quantum link models and fluctuating electric strings 2 1.2 Bosonization of Particle-hole excitations in 2D Dirac fermions 7 1.3 Structure of the document 11 i. Quantum link models and fluctuating electric strings 2. A Brief Introduction to Lattice Gauge Theories 15 2.1 Continuous formulation of U(1) gauge theories 15 2.1.1 Gauge field equations 16 2.1.2 Gauss’ law as generator of the gauge transformations 18 2.2 U(1) gauge theories on a lattice 19 2.2.1 Gauge field Hamiltonian 20 2.2.2 Cylindrical algebra from LGT 20 2.2.3 Generator of gauge transformations 21 2.3 Abelian Quantum Link Model 22 2.3.1 Quantum Link Models (QLMs) with S = 1 / 2 23 2.3.2 ’t Hooft operators and winding number sectors 24 2.3.3 Construction of the QLM Hamiltonian 26 2.4 Conclusions 28 3. Electric string in Q6VM as a XXZ chain 29 3.1 Realization of the Q6VM in the S = 1 / 2 QLM 31 3.2 Mapping the electric string to the XXZ chain 32 3.3 Phases of the electric string from the XXZ chain 33 3.3.1 v > 1: FM insulator 34 3.3.2 v = 1: RK point 36 3.3.3 −1 < v < 1: Gapless phase 36 3.3.4 v ≤ −1: KT transition and AFM insulator 37 3.4 Numerical approach: Drude Weight and system size effects 38 3.5 Summary and Discussion 40 4. Electric line in the QDM as a hard-core boson two-leg ladder 41 4.1 Realization of the QDM in the S = 1/ 2 QLM 42 4.2 Construction of an electric string in the QDM 43 4.3 Mapping the electric string in QDM to a two-leg ladder 45 4.3.1 QLM in a triangular lattice 45 4.3.2 From the triangular lattice to the two-leg ladder 45 4.3.3 Construction of the 1D bosonic Hamiltonian 46 4.4 Phases of the electric string from the bosonic two-leg ladder 48 4.4.1 Left Hand Side (LHS) of the Rokhsar-Kivelson (RK) point: Charge Density Wave (CDW) states 48 4.4.2 Right Hand Side (RHS) of the RK point: phase-separated states 50 4.5 Numerical approach: Drude Weight and system size effects 51 4.6 Summary and Discussion 52 ii Bosonization of particle-hole excitations in 2D Dirac fermions 5 Graphene in a nutshell 57 5.1 Origin of the hexagonal structure 57 5.1.1 Hybrid orbitals in C 58 5.1.2 Honeycomb lattice 60 5.2 Tight-binding approach 61 5.2.1 Hopping and overlapping matrices in Nearest Neighbor (NN) approximation 62 5.2.2 Dispersion relation for π electrons 62 5.3 Effective 2D Dirac Fermion Hamiltonian 64 5.4 Electron-electron interactions 65 6 Bosonization of the Q = 0 continuum of Dirac Fermions 67 6.1 Effective Hamiltonian and Hilbert space 69 6.2 Effective Heisenberg Hamiltonian 70 6.3 Quadratic Bosonic Hamiltonian 71 6.4 Connection to diagramatic perturbation theory 73 6.5 Parametrization of the reciprocal space 74 6.5.1 Coordinate transformation 74 6.5.2 Polar parametrization 75 6.5.3 Angular momentum channels 75 6.6 Discussion and Summary 76 7 Non-perturbative corrections to the Optical Conductivity of 2D Dirac Fermions 77 7.1 Optical Conductivity 79 7.1.1 Bosonized current operator and susceptibility 79 7.1.2 Susceptibility in terms of the eigenstates 80 7.1.3 Regularization of the Lehman representation 81 7.2 Numerical approach: IR regularization and system size effects 82 7.2.1 Discretization size dependence 82 7.2.2 Dependence on the IR cutoff 83 7.2.3 Comparison of numerical results with corrections from first order perturbation theory 84 7.2.4 Optical conductivity for several coupling constants 85 7.3 Discussion and Summary 86 iii Weak coupling instability, New Perspectives & Conclusions 8 Weak coupling instability in bilayer graphene from a bosonization picture 91 8.1 Band structure of Bernal-stacked bilayer graphene 92 8.2 Generalization of the effective Hamiltonian of graphene 93 8.2.1 Density of states in monolayer and bilayer graphene 94 8.2.2 Projection onto Q = 0 sector and effective Heisenberg pseudospin Hamiltonian 95 8.2.3 Zeeman vortex coordinates and HCB operators 95 8.2.4 Bogoliubov-Valatin basis 97 8.3 Interaction potentials 97 8.4 BCS instability in pseudospin picture 99 8.5 Numerical procedure 101 8.5.1 Numerical BCS instability 101 8.5.2 Functional form of the instability 101 8.5.3 Comparison to the instability from BCS theory 105 8.6 Conclusions 105 9 Conclusions 107 iv Appendices A. Yang & Yang’s expressions of ground state energy of XXZ Chain using Bethe Ansatz 115 A.1 Bethe Ansatz 115 A.2 Explicit formulas for f ( ∆, 0 ) 116 B. Kadanoff-Baym (KB) self-consistent Hartree-Fock (SCHF) approximation 119 B.1 Details of connection to perturbation theory 119 B.1.1 Bare and dressed fermion propagators 119 B.1.2 Bethe-Salpeter ladder 120 B.1.3 Particle-hole propagator and comparison to HP boson propagator 121 C, Optical Conductivity from Pseudospin precession 123 C.1 Minimal coupling and band (electron-hole) basis 123 C.2 Equations of motion of charge and pseudospin densities 124 C.3 Optical Conductivity from Fermi-Dirac distributions at finite temperature 124 D. Momentum space reparametrization 127 D.1 General coordinate transformations on the continuum limit 127 D.2 Polar re-discretization 129 D.3 Angular momentum channels 130 D.4 Selection of the radial parametrization 130 Bibliography 133

Scale symmetry is notoriously fickle: even when (approximately) present at the classical level, quantum fluctuations often break it, sometimes rather dramatically. Indeed, contemporary physics encompasses the study of very different phenomena at very different scales, e.g., from the (nominally) meV scale of spin systems, via the eV of electronic band structures, to the GeV of elementary particles, and possibly even the 10¹⁹ GeV of quantum gravity. However, there are often – possibly surprising – analogies between systems across these seemingly disparate settings. Studying the possible emergence of quantum scale symmetry and its breakdown is one way to systematically exploit these similarities, and in fact allows one to make testable predictions within a unified technical framework (viz., the renormalization group). The aim of this thesis is to do so for a few explicit scenarios. In the first four of these, quantum scale symmetry emerges in the long-wavelength limit near a quantum phase transition, over length scales of the order of the correlation length. In the fifth example, quantum scale symmetry is restored at very high energies (i.e., at and above the Planck scale), but severely constrains the phenomenology at 'low' energies (e.g., at accelerator scales), despite scale invariance being badly broken there. We begin with the Gross–Neveu (= chiral) SO(3) transition in D = 2+1 spacetime dimensions, which notably has been proposed to describe the transition of certain spin-orbital liquids to antiferromagnets. The chiral fermions that suffer a spontaneous breakdown of their isospin symmetry in this setting are fractionalized excitations (called spinons), and are as such difficult to observe directly in experiment. However, as gapless degrees of freedom, they leave their imprint on critical exponents, which may hence serve as a diagnostic tool for such unconventional excitations. These may be computed using (comparatively) conventional field-theoretic techniques. Here, we employ three complementary methods: a three-loop expansion in D = 4 - ε spacetime dimensions, a second-next-leading order expansion in large flavour number N , and a non-perturbative calculation using the functional renormalization group in the improved local potential approximation. The results are in fair agreement with each other, and yield combined best-guess estimates that may serve as benchmarks for numerical simulations, and possibly experiments on candidate spin liquids. We next turn our attention to spontaneous symmetry breaking at zero temperature in quasi-planar (electronic) semimetals. We begin with Luttinger semimetals, i.e., semimetals where two bands touch quadratically at isolated points of the Brioullin zone; Bernal-stacked bilayer graphene (BBLG) within certain approximations is one example. Luttinger semimetals are unstable at infinitesimal 4-Fermi interaction towards an ordered state (i.e., the field theory is asymptotically free rather than safe). Nevertheless, since the interactions are marginal, there are several pathologies in the critical behaviour. We show how these pathologies may be understood as a collision between the IR-stable Gaußian fixed point and a critical fixed point distinct from the Gaußian one in d = 2 + ε spatial dimensions. Observables like the order-parameter expectation value develop essential rather than power-law singularities; their exponent, as shown herein by explicit computation for the minimal model of two-component ‘spinors’, is distinct from the mean-field one. More tellingly, although finite critical exponents often default to canonical power-counting values, the susceptibility exponent turns out to be one-loop exact, and, in said minimal model takes the value γ = 2γᵐᵉᵃⁿ⁻ᶠᶦᵉˡᵈ = 2. Such an exact yet non-mean-field prediction can serve as a useful benchmark for numerical methods. We then proceed to scenarios in D = 2 + 1 spacetime dimensions where Dirac fermions can arise from Luttinger fermions due to low rotational symmetry. In BBLG, the 'Dirac from Luttinger' mechanism can occur both due to explicit and spontaneous breaking of rotational symmetry. The explicit symmetry breaking is due to the underlying honeycomb lattice, which only has C₃ symmetry around the location of the band crossings (so-called K points). As a consequence, the quadratic band crossing points each split into four Dirac cones, which is shown explicitly by computing the two-loop self-energy in the 4-Fermi theory. Within our approximations, we can estimate the critical coupling up to which a semimetallic state survives; it is finite (unlike a quadratic band touching point with high rotational symmetry), but significantly smaller than a 'vanilla' Dirac semimetal. Based on the ordering temperature of BBLG, our rough estimate further shows that the (effective) coupling strength in BBLG may be close to the critical value, in sharp contrast to other quasi-planar Dirac semimetals (such as monolayer graphene). Rotational symmetry in BBLG may also be broken spontaneously, i.e., due to the presence of nematic order, whereby a quadratic band crossing splits into two Dirac cones. Such a scenario is also very appealing for BBLG, since the precise nature of the ordered ground state of BBLG has not been established unambiguously: whilst some experiments show an insulating ground state with a full bulk gap, others show a partial gap opening with four isolated linear band crossings. Here, we show within a simplified phenomenological model using mean-field theory that there exists an extended region of parameter space with coexisting nematic and layer-polarized antiferromagnetic order, with a gapless nematic phase on one side and a gapped antiferromagnetic phase on the other. We then show that the nematic-to-coexistence quantum phase transition has emergent Lorentz invariance to one-loop in D = 2 + ε as well as D = 4 - ϵ dimensions, and thus falls into the celebrated Gross-Neveu-Heisenberg universality class. Combining previous higher-order field-theoretic results, we derive best-guess estimates for the critical exponents of this transition, with the theoretical uncertainty coming out somewhat smaller than in the monolayer counterpart due to the enlarged number of fermion components. Overall, BBLG may hence be a promising candidate for experimentally accessible Gross–Neveu quantum criticality in D = 2 + 1 spacetime dimensions. Finally, we turn our attention to the 'low-energy' consequences of transplanckian quantum scale symmetry. Extensions to the Standard Model that tend to lower the Higgs mass have many phenomenologically attractive properties (e.g., it would allow one to accommodate a more stable electroweak vacuum). Dark matter is one well-motivated candidate for such an extension. However, even in the most conservative settings, one usually has to contend with a significantly enlarged number of free parameters, and a concomitant reduction of predictivity. Here, we investigate how asymptotic safety (i.e., imposing quantum scale symmetry at the Planck scale and above) may constrain the Higgs mass in Standard Model (plus quantum gravity) when coupled to Yukawa dark matter via a Higgs portal. Working in a toy version of the Standard Model consisting of the top quark and the radial mode of the Higgs, we show within certain approximations that the Higgs mass may be lowered by the necessary amount if the dark scalar undergoes spontaneous symmetry breaking, as a function of the dark scalar mass, which is the only free parameter left in the theory.:1 Introduction 1.1 Scale invariance – why and where 1.1.1 Fundamental quantum field theories 1.1.2 Universality 1.1.3 Novel phases of matter 1.2 Outline of this thesis 2 Renormalization Group: A Brief Review 2.1 Quantum fluctuations and generating functionals 2.2 Renormalization group flow 2.3 Basic notions 2.4 Scale transformations, scale symmetry and RG fixed points 2.5 Characterization and interpretation of RG fixed points 2.5.1 Formal aspects 2.5.2 Scaling at (quantum) phase transitions 2.5.3 Predictivity in fundamental physics 2.5.4 Effective asymptotic safety in particle physics and condensed matter 3 Gross–Neveu SO(3) Quantum Criticality in 2 + 1 Dimensions 3.1 Effective field theory 3.2 Renormalization and critical exponents 3.2.1 4 - ϵ expansion 3.2.1.1 Method 3.2.1.2 Flow equations 3.2.1.3 Critical exponents 3.2.2 Large-N expansion 3.2.2.1 Method 3.2.2.2 Critical exponents 3.2.3 Non-perturbative FRG 3.2.3.1 Flow equations 3.2.3.2 Representation of the effective potential 3.2.3.3 Choice of regulator 3.2.3.4 Limiting behaviour 3.3 Discussion 3.3.1 General behaviour and qualitative aspects 3.3.2 Quantitative estimates for D = 3 3.4 Summary and outlook 4 Luttinger Fermions in Two Spatial Dimensions 4.1 Introduction 4.2 Action from top-down construction 4.3 Renormalization 4.3.1 4-Fermi formulation 4.3.2 Yukawa formulation 4.4 Fixed-point analysis 4.5 Non-mean-field behaviour 4.5.1 Order-parameter expectation value 4.5.2 Susceptibility exponent 4.6 Bottom-up construction: Spinless fermions on kagome lattice 4.6.1 Tight-binding dispersion 4.6.2 From Hubbard to Fermi 4.6.3 Fate of particle-hole asymmetry 4.7 Discussion 5 Dirac from Luttinger I: Explicit Symmetry Breaking 5.1 From lattice to continuum 5.1.1 Fermions on Bernal-stacked honeycomb bilayer 5.1.2 Continuum limit 5.1.3 Interactions 5.2 Mean-field theory 5.3 Renormalization-group analysis 5.3.1 Flow equations 5.3.2 Basic flow properties 5.3.3 Phase diagrams 5.4 Discussion 5.5 Summary and outlook 6 Dirac from Luttinger II: Spontaneous Symmetry Breaking 6.1 Model 6.2 Phase diagram and transitions 6.3 Emergent Lorentz symmetry 6.3.1 Loop expansion near lower critical dimension 6.3.1.1 Minimal 4-Fermi model 6.3.1.2 Gross–Neveu–Heisenberg fixed point 6.3.1.3 Fate of rotational symmetry breaking 6.3.2 Loop expansion near upper critical dimension 6.3.2.1 Gross–Neveu–Yukawa–Heisenberg model 6.3.2.2 Gross–Neveu–Yukawa–Heisenberg fixed point 6.3.2.3 Fate of rotational symmetry breaking 6.4 Critical exponents 6.5 Discussion 7 Higgs Mass in Asymptotically Safe Gravity with a Dark Portal 7.1 Review: The asymptotic safety scenario for quantum gravity and matter 7.2 Review: Higgs mass, and RG flow in the SM and beyond 7.2.1 Higgs mass in the SM 7.2.2 Higgs mass bounds in bosonic portal models 7.2.3 Higgs mass in asymptotic safety 7.2.4 Higgs Portal and Asymptotic Safety 7.3 Higgs mass in an asymptotically safe dark portal model 7.3.1 The UV regime 7.3.2 Flow towards the IR 7.3.3 Infrared masses 7.3.4 From the UV to the IR – Contrasting effective field theory and asymptotic safety 7.4 Discussion 8 Conclusions Appendices A Position-space propagator for C₃-symmetric QBT B Two-sided Padé approximants for C₃-symmetric QBTs C Corrections to the mean-field nematic order-parameter effective potential due to explicit symmetry breaking D Self-energy in anisotropic Yukawa theory E Master integrals for anisotropic Yukawa theory Bibliography

Erste Anzeichen für die Existenz von Dunkler Materie wurden 1933 entdeckt. Der Astrophysiker Fritz Zwicky beobachtete die Geschwindigkeitsverteilung im Coma Cluster und fand dabei heraus, dass 400 mal mehr Materie im Galaxie Haufen sein muss, damit dieser gravitativ gebunden sein kann oder der Galaxie Haufen würde sich aufösen. Trotz erheblicher Bemühungen über die letzten 80 Jahre ist nicht viel über Dunkle Materie bekannt. Das einzige was man weiÿ ist, dass Dunkle Materie gravitativ aber nicht elektromagnetisch wechselwirkt und Dunkle Materie stellt den gröÿten Bestandteil der Materie im Universum da. Doch derzeitige Experimente die nach Dunkler Materie suchen, sowohl direkte Suchen als auch indirekte, beginnen sensitiv genug zu werden um interessante Parameterbereiche von Dunkle Materie Kandidaten zu untersuchen wie das leichteste Super-symmetrische Teilchen, was bedeutet, dass die Entdeckung von Dunkler Materie in der nahen Zukunft sein könnte. In dieser Arbeit wird eine Signalsummierung von H.E.S.S. Zwerg Galaxien Daten durchgeführt und obere Ausschlussgrenzen berechnet. Weiterhin wird die Leistung einer Dunklen Materie Suche im galaktischen Zentrum durch CTA präsentiert für verschiedene mögliche Teleskop Anordnungen und verschiedene Annihilation Kanäle. Die Ergebnisse werden zeigen, dass CTA in der Lage sein wird geschwindigkeitsgemittelte Annihilations Wirkungsquerschnitte von 3 * 10^-26 cm^3s^1 und geringer, der geschwindigkeitsgemittelte Annihilations Wirkungsquerschnitt der für schwach wechselwirkende Dunkle Materie erwartet wird, in 100 h zu erreichen. Diese Beobachtungszeit kann innerhalb von ein bis zwei Jahren erreicht werden. / First indications for the existence of Dark Matter appeared in 1933. The astrophysicist Fritz Zwicky observed the velocity dispersion of the Coma Cluster and found out that 400 times the visible mass must be contained in the galaxy cluster or the cluster could not be gravitationally bound and would disperse.Despite extensive efforts over the last 80 years not much is known about Dark Matter. The facts known are that Dark Matter interacts via gravitation, does not interact electromagneticly and is the main constituent of matter. But current experiment searching for Dark Matter directly and indirectly begin to reach sensitivities that can probe interesting parameter spaces for Dark Matter candidates like the lightest supersymmetric particle, meaning the first Dark Matter detections could happen in the near future.In this thesis a dwarf stacking analysis for Dark Matter signal search using H.E.S.S. data is performed and a upper limit is calculated. Furthermore the prospect for a Dark Matter search with CTA in the galactic center region of the Milky Way is presented for different candidate arrays and different annihilation channels. The results will show that CTA will be able to reach velocity annihilation below 3 *10^-26 cm^3s^-1, the velocity annihilation crosssection expected for a weakly interacting Dark Matter particle, within 100 h of observation which can reasonably be acquired within one to two years.

Neben ihrer Bedeutung in industriellen Anwendungen dienen Kolloide als Modellsysteme in Experimenten und in der Theorie, um die Struktur und Dynamik von kondensierter Materie zu untersuchen. Kürzlich wurde experimentell gezeigt, dass eine kleine Anisotropie ausreicht, um die viskoelastische Antwort im Vergleich zu harten Kugeln drastisch zu ändern. Die mikroskopischen Ursachen hierfür sind bisher nicht verstanden. In dieser Arbeit werden daher Nichtgleichgewichts-Brownsche-Dynamik-Simulationen (NEBD) von harten kolloidalen Dumbbells in oszillatorischen Scherfeldern entwickelt und eingesetzt, um diese Resultate mit Verbindung zu Rheologie- und Neutronenstreuexperimenten zu erklären. Weiterhin wird die Bedeutung der Anisotropie für Struktur und Dynamik von solchen Suspensionen im Gleichgewicht mit Hilfe von "Linear-Response"-Theorie und Brownsche-Dynamik-Simulationen analysiert. Im linearen Limit zeigt die Scherviskosität bei hohen Packungsdichten einen dramatischen Anstieg jenseits eines kritischen Anisotropieparameters. Dies weist darauf hin, dass schon bei den kleinen Anisotropien kollektive Rotations-Translations-Kopplungen für langsame Zeitskalen verantwortlich sind. Weiterhin wird ein Nichtgleichgewichtsübergang mittels NEBD-Simulationen von Suspensionen harter Dumbbells im PC unter oszillatorischer Scherung ersichtlich. Es wird gezeigt, dass der kontinuierliche Übergang nur für sehr kleine Aspektverhältnisse erhalten bleibt. Oberhalb eines bestimmten Aspektverhältnisses wird der Übergang durch einen ungeordneten Zustand vermittelt. Außerdem wird ein Sliding-Layer Zustand mit kollektiver Ordnung der Teilchenausrichtung bei hohen Scheramplituden beobachtet. Somit zeigt diese Arbeit, dass die NEBD-Simulationen Phänomene in Rheologie- und Streuexperimenten erklären. Angesichts dieser Experimente wird gezeigt, dass der Orientierungsfreiheitsgrad einen starken Einfluss auf den strukturellen Übergang bei steigenden Amplituden hat. / Besides being important for industrial applications, colloidal suspensions have long served as model systems for investigating the structure and dynamics of condensed matter. Recently, it has been demonstrated experimentally that apparently a small particle anisotropy is sufficient to dramatically change the viscoelastic response under external shearing fields, of which the microscopic mechanisms are not yet sufficiently understood. In the present work, NEBD simulations of colloidal hard dumbbells in oscillatory shear fields are developed and employed to elucidate the novel findings in close connection with comprehensive rheology and SANS experiments. Furthermore, by utilising BD simulations and linear response theory, the impact of anisotropy on structure and dynamics of such suspensions in equilibrium is analysed. In the linear response limit, the shear viscosity exhibits a dramatic increase at high packing fractions beyond a critical anisotropy of the particles. This indicates that newly occurring, collective rotational-translational couplings must be made responsible for slow time scales appearing in the PC. Moreover, a non-equilibrium transition emerging at moderate aspect ratios is revealed by NEBD of plastic crystalline suspensions under oscillatory shear. This transition behaviour is systematically studied. It is demonstrated that the continuous nature of the transition is retained for very low aspect ratios only. Above a certain aspect ratio, the transition is mediated by an intermediate disordered state. Furthermore, a partially oriented sliding layer state featuring a finite collective order in the particles'' orientations is observed at high strains. Hence, this thesis demonstrates that the NEBD simulations explain novel phenomena in rheology and scattering experiments. In the light of these experiments, it is shown that the orientational degree of freedom has a vigorous impact on the structural transition under increasing oscillatory shear.

In den Materialwissenschaften läuten Künstliche-Intelligenz Methoden einen Paradigmenwechsel in Richtung Big-data zentrierter Forschung ein. Datenbanken mit Millionen von Einträgen, sowie hochauflösende Experimente, z.B. Elektronenmikroskopie, enthalten eine Fülle wachsender Information. Um diese ungenützten, wertvollen Daten für die Entdeckung verborgener Muster und Physik zu nutzen, müssen automatische analytische Methoden entwickelt werden. Die Kristallstruktur-Klassifizierung ist essentiell für die Charakterisierung eines Materials. Vorhandene Daten bieten vielfältige atomare Strukturen, enthalten jedoch oft Defekte und sind unvollständig. Eine geeignete Methode sollte diesbezüglich robust sein und gleichzeitig viele Systeme klassifizieren können, was für verfügbare Methoden nicht zutrifft. In dieser Arbeit entwickeln wir ARISE, eine Methode, die auf Bayesian deep learning basiert und mehr als 100 Strukturklassen robust und ohne festzulegende Schwellwerte klassifiziert. Die einfach erweiterbare Strukturauswahl ist breit gefächert und umfasst nicht nur Bulk-, sondern auch zwei- und ein-dimensionale Systeme. Für die lokale Untersuchung von großen, polykristallinen Systemen, führen wir die strided pattern matching Methode ein. Obwohl nur auf perfekte Strukturen trainiert, kann ARISE stark gestörte mono- und polykristalline Systeme synthetischen als auch experimentellen Ursprungs charakterisieren. Das Model basiert auf Bayesian deep learning und ist somit probabilistisch, was die systematische Berechnung von Unsicherheiten erlaubt, welche mit der Kristallordnung von metallischen Nanopartikeln in Elektronentomographie-Experimenten korrelieren. Die Anwendung von unüberwachtem Lernen auf interne Darstellungen des neuronalen Netzes enthüllt Korngrenzen und nicht ersichtliche Regionen, die über interpretierbare geometrische Eigenschaften verknüpft sind. Diese Arbeit ermöglicht die Analyse atomarer Strukturen mit starken Rauschquellen auf bisher nicht mögliche Weise. / In materials science, artificial-intelligence tools are driving a paradigm shift towards big data-centric research. Large computational databases with millions of entries and high-resolution experiments such as electron microscopy contain large and growing amount of information. To leverage this under-utilized - yet very valuable - data, automatic analytical methods need to be developed. The classification of the crystal structure of a material is essential for its characterization. The available data is structurally diverse but often defective and incomplete. A suitable method should therefore be robust with respect to sources of inaccuracy, while being able to treat multiple systems. Available methods do not fulfill both criteria at the same time. In this work, we introduce ARISE, a Bayesian-deep-learning based framework that can treat more than 100 structural classes in robust fashion, without any predefined threshold. The selection of structural classes, which can be easily extended on demand, encompasses a wide range of materials, in particular, not only bulk but also two- and one-dimensional systems. For the local study of large, polycrystalline samples, we extend ARISE by introducing so-called strided pattern matching. While being trained on ideal structures only, ARISE correctly characterizes strongly perturbed single- and polycrystalline systems, from both synthetic and experimental resources. The probabilistic nature of the Bayesian-deep-learning model allows to obtain principled uncertainty estimates which are found to be correlated with crystalline order of metallic nanoparticles in electron-tomography experiments. Applying unsupervised learning to the internal neural-network representations reveals grain boundaries and (unapparent) structural regions sharing easily interpretable geometrical properties. This work enables the hitherto hindered analysis of noisy atomic structural data.