A long controversy exists about the structure of chromatin. Theoretically, this structure could be resolved by scattering experiments if one determines the scattering function - or equivalently the pair distribution function - of the nucleosomes. Unfortunately, scattering experiments with live cells are very difficult and limited to only a couple of nucleosomes. Nevertheless, new techniques like the high-resolution light microscopy supply a new approach to this problem. In this work we determine the radial pair distribution function of chromatin described by our E2A model and find that the dominant peaks which characterize the chromatin structure are very robust in several ways: They can still be identified in the case of chromatin fibers with reasonable linker histone and nucleosome defect rates as well as in the 2D case after a projection like in most high-res light microscopy experiments. This might initiate new experimental approaches like optical microscopy to finally determine the nanostructure of chromatin. Furthermore, we examine the statistics of random chromatin collisions and compare it with 5C data of a gene desert. We find that only chromatin fibers with histone depletion show a significant amount of contacts on the kbp-scale which play a important role in gene regulation. Therefore, linker histone and nucleosome depletion might not only be chromatin defects but even be necessary to facilitate transcription. PACS codes: 82.35.Pq, 87.16.A-, 87.16.af
We study confinement in quantum chromodynamics via numerical simulations in the framework of lattice gauge theory. In Landau gauge, the mechanism of confinement is related to the infrared behavior of the ghost and gluon propagators via the Gribov-Zwanziger and Kugo-Ojima scenarios. These scenarios entail a scaling behavior. Functional methods in the continuum allow both for this behavior and for decoupling solutions, while lattice simulations in three and four dimensions yield only the latter. A possible explanation for this mismatch is based on limitations of standard lattice gauge fixing methods. Hence, we investigate a number of alternative gauge fixing algorithms in pure SU(2) gauge theory in two, three and four dimensions. We find that stochastic quantization yields an infrared behavior of the propagators in agreement with the results of standard procedures, even though the Faddeev-Popov operator spectrum indicates some different properties. In the strong-coupling limit, our results challenge the standard picture. In particular, we find in a non-perturbative completion of Landau gauge an enormous effect of the Gribov ambiguity. It entails that no subset of infrared solutions can be excluded yet. Moreover, we study the gluon propagator with free boundary conditions. On large lattices, the results mostly show the standard behavior. We also examine non-periodic gauge transformations. Furthermore, we analyze two topics related to the phase diagram of QCD. First, we explore the sign problem for fermions on the lattice by simulating the three-dimensional Thirring model with a complex Langevin equation. The algorithm succeeds in yielding a 'Silver Blaze' behavior of observables, but it does not reliably describe the onset to a phase with non-zero density. Second, we determine properties of the deconfinement phase transition of pure SU(2) gauge theory in 2+1 dimensions, like the critical temperature, by means of the gluon propagator in Landau gauge.
In this thesis, far-from-equilibrium dynamics of fermionic quantum gases is discussed utilising functional quantum field theoretical methods. Employing the Schwinger-Keldysh path integral, real-time Schwinger-Dyson/Kadanoff-Baym dynamic equations for the two-point correlation functions are derived from the two-particle irreducible (2PI) effective action. For two specific models, these dynamic equations are investigated further. (a) For an N-fold spin-degenerate ultra-cold Fermi gas, non-perturbative approximation schemes based on either a loop or a 1/N expansion of the 2PI effective action are presented. Adopting these approximations, the long-time evolution of a homogeneous Fermi gas with N=2 after an initial preparation far from thermal equilibrium is thoroughly studied in one spatial dimension. Depending on the total energy, the gas is found to evolve into thermal as well as non-thermal states, the latter becoming manifest in violating the fluctuation-dissipation relation. (b) A similar 1/N expansion is derived for the SU(N) symmetric Kondo lattice model. At leading order, the mean-field dynamic equations of the U=0 Anderson model are recovered. At next-to-leading order (NLO), both spin-flip and direct interactions between localised atoms and conduction band atoms are taken into account non-perturbatively into the dynamic equations. This allows future studies of possibly existing novel phases in coupling regimes where the Kondo screening and RKKY-type interactions are competing.
Despite its apparent simplicity, the two-dimensional Hubbard model for locally interacting fermions on a square lattice is widely considered as a promising approach for the understanding of Cooper pair formation in the quasi two-dimensional high-Tc cuprate materials. In the present work this model is investigated by means of the functional renormalization group, based on an exact flow equation for the effective average action. In addition to the fermionic degrees of freedom of the Hubbard Hamiltonian, bosonic fields are introduced which correspond to the different possible collective orders of the system, for example magnetism and superconductivity. The interactions between bosons and fermions are determined by means of the method of “rebosonization” (or “flowing bosonization”), which can be described as a continuous, scale-dependent Hubbard-Stratonovich transformation. This method allows an efficient parameterization of the momentumdependent effective two-particle interaction between fermions (four-point vertex), and it makes it possible to follow the flow of the running couplings into the regimes exhibiting spontaneous symmetry breaking, where bosonic fluctuations determine the types of order which are present on large length scales. Numerical results for the phase diagram are presented, which include the mutual influence of different, competing types of order.
In eukaryotischen Zellen bildet das Strukturprotein Aktin Polymernetzwerke aus, die sehr dynamisch und für viele zelluläre Prozesse lebenswichtig sind. In dieser Arbeit werden theoretische Konzepte vorgestellt, um die Eigenschaften komplexer Aktin-Netzwerkstrukturen zu verstehen und mit Messungen mittels Fluoreszenz- und Elektronenmikroskopie zu vergleichen. Ein Großteil der Arbeit behandelt dabei flache vernetzte Aktinstrukturen, die durch gerichtete Polymerisation gegen eine äußere Kraft anwachsen. Dieser Netzwerktyp ist ein wichtiger Bestandteil von sich bewegenden Zellen, wird aber auch von intrazellulären Pathogenen zur Fortbewegung missbraucht. Eine zentrale, experimentell messbare Eigenschaft solcher Netzwerke ist ihre Kraft-Geschwindigkeits-Relation. Verschiedene aktuelle Messungen ergaben hierfür widersprüchlich erscheinende Ergebnisse. In einem relativ einfachen physikalischen Modell wird gezeigt, dass in wachsenden Aktin-Netzwerken zwei stationäre Filament-Orientierungsverteilungen miteinander konkurrieren. Strukturelle Übergänge zwischen den beiden Architekturen werden durch Änderung der Wachstumsgeschwindigkeit des Netzwerks initiiert. Mit zusätzlichen Annahmen zur mechanischen Stabilität einzelner Filamente werden die experimentell gefundenen Eigenarten der Kraft-Geschwindigkeits-Relation (eine Abfolge von konvexen und konkaven Verläufen sowie Hysterese) theoretisch begründet. Das Modell wird zusätzlich auf Aktinwachstum gegen gekrümmte Hindernisse wie intrazelluläre Pathogene erweitert. Um in der Zukunft spezifische Vorhersagen des Modells experimentell zu überprüfen, wurde eine Methode zur automatischen Analyse von Elektronenmikroskopiebildern von Aktin-Netzwerken entwickelt. Erste Ergebnisse lassen eine gute Übereinstimmung erwarten. Des Weiteren wurde eine Methode entwickelt, um Änderungen in der Aktin-Struktur von adhärenten Zellen in einem Hochdurchsatzverfahren mit Fluoreszenzmikroskopie zu bewerten.
This dissertation deals with the equation of state of hot and dense matter in compact stars, with special focus on first order phase transitions. A general classification of first order phase transitions is given and the properties of mixed phases are discussed. Aspects of nucleation and the role of local constraints are investigated. The derived theoretical concepts are applied to matter in neutron stars and supernovae, in the hadron-quark and the liquid-gas phase transition. For the detailed description of the liquid-gas phase transition a new nuclear statistical equilibrium model is developed. It is based on a thermodynamic consistent implementation of relativistic mean-field interactions and excluded volume effects. With this model different equation of state tables are calculated and the composition and thermodynamic properties of supernova matter are analyzed. As a first application numerical simulations of core-collapse supernovae are presented. For the hadron-quark phase transition two possible scenarios are studied in more detail. First the appearance of a new mixed phase in a proto neutron star and the implications on its evolution. In the second scenario the consequences of the hadron-quark transition in core-collapse supernovae are investigated. Simulations show that the appearance of quark matter has clear observable signatures and can even lead to the generation of an explosion.
Motivated by current experiments with ultracold atoms, the study of complex dynamics of Bose-Einstein condensates in optical lattices forms the central subject of this work. A lattice model of interacting bosons under the influence of an external force is motivated and derived from the experimental setup. Several dynamical regimes of this model are discussed in this thesis. In a first part we will develop a new measure for detecting avoided crossings in complex energy spectra and apply it to the quantum chaotic regime of the single-band system. The second and main part of this work is dedicated to the coupling between energy bands described in terms of a two-band model. The complex time evolution is already apparent in the horizontal and vertical population dynamics of the non-interacting problem. We find resonances in the interband transport, and, in a second step, study the effect of inter-particle interactions on these resonant oscillations. We are able to predict all time scales of the complex interband dynamics even in the presence of interactions. This is possible via the introduction of an effective model that is motivated and supported by a multitude of numerical results and proves exactly solvable.
In dieser Arbeit werden mögliche Hochpräzisionsmessungen des g-Faktors von gebundenen 1S Elektronen untersucht und die bedeutendsten systematischen Effekte, die die Hochpr äzisionsspektroskopie im ultravioletten und sichtbaren Spektralband beeinflussen, analysiert. Um den g-Faktor des gebundenen 1S-Elektrons eines in einer Penning-Falle gefangenen 4He Ions zu messen, werden zwei Anregungsschemata, die auf einer doppelresonanten elektronischen Anregung aufbauen, vorgeschlagen. Das erste Anregungsschema beruht auf der Anregung des 1S1/2(mj = +1/2) <-> 2P3/2(mj = +3/2)-Übergangs in einem 4HeIon durch zirkular polarisierte Ultraviolettstrahlung. Der angeregte Zustand 2P3/2(mj = +3/2) geht wegen seiner kurzen Lebenszeit in den Grundzustand über und strahlt dabei ein Fluoreszenzphoton ab. Das Heliumion durchläuft diesen Kreislauf in der Falle und kann dabei jedesmal aufgrund des abgestrahlten Photons nachgewiesen werden. Gleichzeitig löst ein resonantes Mikrowellenfeld eine Umdrehung des Spins aus, was Quantenspr¨unge zwischen 1S1/2(mj = +1/2) und 1S1/2(mj = −1/2) bewirkt und eine Emissionspause des Kreislaufes zur Folge hat. Die Kombination dieser Prozesse ergibt das Resonanzspektrum der Larmorfrequenz und führt zur Messung des g-Faktors des gebundenen 1S-Elektrons eines Heliumions. In dem zweiten Anregungsschema regt UV-Licht ein in einer Penning-Falle gespeichertes Heliumion an. Diese Laseranregung treibt den Zweiphotonen übergang 1S–2S. Bei einem bestimmten Wert des Magnetfelds der Falle werden die Zustände 2S1/2(mj = −1/2) und 2P1/2(mj = 1/2) entartet. Die Anwendung eines zusätzlichen statischen elektrischen Feldes ermöglicht es diese beiden Zustände zu mischen und die Lebenszeit des oberen Zustands 2S1/2(mj = −1/2) zu reduzieren; dies führt zu einem 2S-Elektronenzerfall in den Grundzustand. Der Zweiphotonenübergang zusammen mit dem Mischungsmechanismus bietet einen Kreislauf an und ergibt einen optischen Nachweis des Heliumions in der Falle. Wie im ersten Anregungsschema wird gleichzeitig ein Mikrowellenfeld auf den 1S-Grundzustand eingestrahlt um eine Umdrehung des Spins auszulösen. Dies ergibt das Resonanzspektrum der Larmorfrequenz. Dieses Anregungsschema, das von dem Mischungsmechanismus zusammen mit dem spinumdrehenden Übergang profitiert, f¨uhrt zu der Messung des g-Faktors des gebundenen 1S Elektrons eines Heliumions. Das zweite Angregungsschema wird ebenfalls auf eine Frequenzbestimmung des 1S–2S-Übergangs durch einen dopplerfreien Zweiphotonen¨uebergang in einem Heliumion angewandt. In den obigen Anregungsschemata sind die bedeutendsten systematischen Effekte in Folge der Anwendung dynamischer und statischer elektrischer Felder, das heißt der AC- und der DC-Stark-Effekt, sorgf¨alltig berücksichtigt. Wir verwenden das zweite Anregungsschema und erweitern es auf Rydbergzustände in dem Bereich großer n. Diesbezüglich berechen wir den AC-Stark-Effekt auf Rydbergzust¨ande mit großem n; dies ist der bedeutendste systematische Effekt in der Frequenzbestimmung des 1S–n′S-Übergangs, n′ → ∞. Basierend auf den Ergebnissen dieser Arbeit kann der g-Faktor des gebundenen 1S-Elektrons in 4He Ionen mit einem Genauigkeitsgrad von 10^−12 · · · 10^−13 bestimmt werden.
In this thesis, we study the evolution of energetic partons in hot and cold QCD matter. In both cases, interactions with the medium lead to energy loss of the parton and its transverse momentum broadens. The propagation of partons in cold nuclear matter can be investigated experimentally in deep-inelastic scattering (DIS) on nuclei. We use the dipole model to calculate transverse momentum broadening in DIS on nuclei and compare to experimental data from HERMES. In hot matter, the evolution of the parton shower is strongly modified. To calculate this modification, we construct an additional scattering term in the QCD evolution equations which accounts for scattering of partons in the quark-gluon plasma. With this scattering term, we compute the modified gluon distribution in the shower at small momentum fractions. Furthermore, we calculate the modified fragmentation function of gluons into pions. The scattering term causes energy loss of the parton shower which leads to a suppression of hadrons with large transverse momentum. In the third part of this thesis, we study double dijet production in hadron collisions. This process contains information about the transverse parton distribution of hadrons. As main result, we find that double dijet production will allow for a study of the transverse growth of hadronic wave functions at the LHC.
In this thesis, we investigate the interplay between geometry and temperature in the Casimir effect for the inclined-plates, sphere-plate and cylinder-plate configurations. We use the worldline approach, which combines the string-inspired quantum field theoretical formalism with Monte Carlo techniques. The approach allows the precise computation of Casimir energies in arbitrary geometries. We analyze the dependence of the Casimir energy, force and torque on the separation parameter and temperature T, and find Casimir phenomena which are dominated by long-range fluctuations. We demonstrate that for open geometries, thermal energy densities are typically distributed on scales of thermal wavelengths. As an important consequence, approximation methods for thermal corrections based on local energy-density estimates, such as the proximity-force approximation, are found to become unreliable even at small surface-separations. Whereas the hightemperature behavior is always found to be linear in T, richer power-law behaviors at small temperatures emerge. In particular, thermal forces can develop a non-monotonic behavior. Many novel numerical as well as analytical results are presented.
In this thesis we review data sets available from various SNe groups like SNLS and HSST and utilize them to put constraints the cosmological parameters. We use the software CMBEASY to apply the MCMC method to models like lambdaCDM, Constant Equation of State (EoS) w and Quintessence, with our emphasis being on the IPL and Corasaniti model. We do the analysis using the Riess Gold Set, the SNLS sample and the Union Data Set (with and without systematics). We have extended CMBEASY to include the Union Data Set and hence be up-to-date with latest observations. Our results show that omega m might be smaller than commonly assumed. Further, we find that irrespective of model or data set chosen we get approximately the same value for omega m, whereas this is not the case with w. The work in this thesis indicates that the emphasis in constructing new cosmological models should change from empirical to theoretical motivations.
Genome function in higher eukaryotes involves major changes in the spatial organization of the chromatin fiber. Nevertheless, our understanding of chromatin folding is remarkably limited. Experimental results suggest that chromatin loops not only impact transcriptional regulation but also act as a major epigenetic mechanism, playing a pivotal role in the observed compartmentalization of chromosomes. However, a unified description of chromatin folding comprising various experimental results is still lacking. After showing that the theory of compact polymers is inconsistent with experimental data, we develop a new model for chromatin based on probabilistic formation of loops. This Random-Loop-Model correctly describes folding into a confined sub-space of the nucleus as well as the observed cell-to-cell variation, suggesting a close relation between expression-dependent compaction and local variations in the looping probabilities. We find that formation of loops is highly beneficial for the nucleus to maintain order and to accomplish entropy-driven segregation of chromosomes. A dynamic model is proposed, showing that the formation of loops can be accomplished solely on the basis of diffusional motion without invoking active mechanisms. Such a dynamic model provides a unified explanatory framework of chromatin folding, yielding testable predictions, which for the first time consistently explain many experimental findings.