Derivation of Effective Models using Self-Similar Continuous Unitary Transformations in Real Space

In this thesis the method of self-similar continuous unitary transformations (CUTs) in real space is developed. It is applied to various models from the field of strongly correlated solid state physics and optical lattices. The CUT method maps a given Hamiltonian to an effective Hamiltonian which is in some respect simpler. In a self-similar CUT the truncation scheme relies on the structure of the operators. The real space approach put forward in this thesis truncates the operators according to their extension in real space. We mainly use a MKU generator to derive an effective model which is block-diagonal in the number of quasiparticles. We give a detailed description of the method. The transformation of the Hamiltonian and of the observables is explained. The implementation on a computer and the optimization of the programs are extensively discussed. The first application of the method deals with the fermionic Hubbard model. We derive an effective Hamiltonian, a generalized t-J-model, which conserves the number of doubly occupied sites. The effective model includes beyond the well-known Heisenberg term also further two-spin and four-spin terms. In addition, the charge motion and interaction within the effective model is addressed. In the context of the Hubbard model we discuss the question if an effective model that conserves the number of double occupancies can be derived in principle. The antiferromagnetic spin ladder and spin chain are treated from the viewpoint of a dimerized system. For the spin ladder we calculate the dispersion, the two-particle energies including bound states and the multi-particle continua. The discussion of multi-particle continua shows that the order of the energy levels is important for the convergence of the transformation. For the spin chain the dispersion is calculated. In addition, the transformation of an observable yields the corresponding spectral weights. The spectral weights are compared to results from a perturbative CUT. For the bosonic Hubbard model we calculate the dispersion and determine the phase diagram. The spectral weight of a certain observable is calculated in order to explain the outcome of a recent experiment that measures the spectroscopic response of atoms confined in optical traps. The distribution of spectral weight is analyzed also at finite temperatures. We find evidence for a substantial temperature of the size of the microscopic parameters. This finding is supported by purely thermodynamic considerations

„Ich bin keine Pausenaufsicht, ich bin kein Retter … ich bin Lehrer.“: Eine dokumentarische Analyse zur Rolle von Lehrenden im “home schoolings” der COVID-19-Krise.

Lehrerinnen und Lehrer kamen aufgrund der durch die COVID-19-Krise bedingte Ausnahmesituation und der Umstellung auf “home schooling” nicht nur hinsichtlich des bereits etablierten alltäglichen Unterrichtspraxis, sondern auch bezüglich ihrer hierin eingenommenen Rolle mit gewichtigen Ungewissheiten sowie zahlreichen neuen Anforderungen und Herausforderungen konfrontiert. Einerseits wurden in einem sehr knapp bemessenen Zeitraum sämtliche – dem regulären Unterricht inhärente – Regeln, Routinen und Rituale bzw. das dem gewohnten Unterrichtssetting zugrundeliegende Handlungsprogramm vollkommen außer Kraft gesetzt (vgl. Thiel 2016, S. 109f). Dies führte andererseits wiederum dazu, dass gewisse Verpflichtungen der bzw. die Erwartungen an die Lehrpersonen neu definiert bzw. ausgehandelt wurden. Der Aufsatz thematisiert folglich die Rolle als durch die Institution Schule induzierte Zumutung der Gesellschaft in Zeiten der COVID-19-Krise und deren Einfluss auf die digitalisierte Handlungspraxis von Lehrende im Kontext des von der Regierung verordneten home schoolings.Due to the exceptional situation caused by the COVID 19 crisis and the associated (initial) restrictions imposed by the government, teachers have been or are confronted with significant uncertainties and numerous new demands and challenges, not only with regard to the already established everyday teaching practice, but also with regard to the role they play as teachers. On the one hand, all rules, routines and rituals inherent in regular teaching or the action programme underlying the usual teaching setting were completely overridden within a very short period of time (cf. Thiel 2016, p. 109f). On the other hand, this in turn led to the fact that certain obligations of or expectations towards the teachers were redefined or negotiated. The article therefore deals with the role of the teacher as an imposition of society in times of the COVID-19 crisis and its influence on the digitized practice of teachers in the context of home schooling decreed by the government

Systematic Mapping of the Hubbard Model to the Generalized t-J Model

The generalized t-J model conserving the number of double occupancies is constructed from the Hubbard model at and in the vicinity of half-filling at strong coupling. The construction is realized by a self-similar continuous unitary transformation. The flow equation is closed by a truncation scheme based on the spatial range of processes. We analyze the conditions under which the t-J model can be set up and we find that it can only be defined for sufficiently large interaction. There, the parameters of the effective model are determined.Comment: 16 pages, 13 figures included. v2: Order of sections changed. Calculation and discussion of apparent gap in Section IV.A correcte

Mechanisms behind variation in the Clostridium difficile 16S–23S rRNA intergenic spacer region

Clostridium difficile infection is an increasing problem in hospitals worldwide, mainly due to the recent emergence of a hypervirulent C. difficile strain. C. difficile PCR ribotyping, based on size variation of the 16S–23S rRNA intergenic spacer region (16S–23S ISR), is widely used in Europe for molecular epidemiological investigation. The mechanism underlying the 16S–23S ISR size variations in the genome of C. difficile is currently not completely understood. To elucidate this mechanism, isolates of six different PCR ribotypes were analysed by cloning and sequencing the 16S–23S ISR. A direct repeat, IB, of 9 bp was detected up to five times in the 16S–23S ISR in all 47 clones investigated. Thirty-five clones displayed differences either by ribotype or by nucleotide sequence. The sequences of the 16S–23S ISR of C. difficile showed a uniformly organized structure, composed of a tRNAAla gene and spacers of 33 and 53 bp separated by the 9 bp direct repeat IB. The results of the study support the hypothesis that this composition is responsible for the length variations seen in the 16S–23S ISR, and indicate that these length variations result from slipped-strand mispairing and intra- and possibly interchromosomal homologous recombination

A relationship between three-dimensional surface hydration structures and force distribution measured by atomic force microscopy

Hydration plays important roles in various solid–liquid interfacial phenomena. Very recently, three-dimensional scanning force microscopy (3D-SFM) has been proposed as a tool to visualise solvated surfaces and their hydration structures with lateral and vertical (sub) molecular resolution. However, the relationship between the 3D force map obtained and the equilibrium water density, ρ(r), distribution above the surface remains an open question. Here, we investigate this relationship at an interface of an inorganic mineral, fluorite, and water. The force maps measured in pure water are directly compared to force maps generated using the solvent tip approximation (STA) model and from explicit molecular dynamics simulations. The results show that the simulated STA force map describes the major features of the experimentally obtained force image. The agreement between the STA data and the experiment establishes the correspondence between the water density used as an input to the STA model and the experimental hydration structure and thus provides a tool to bridge the experimental force data and atomistic solvation structures. Further applications of this method should improve the accuracy and reliability of both interpretation of 3D-SFM force maps and atomistic simulations in a wide range of solid–liquid interfacial phenomena

Modulation of Genetic Associations with Serum Urate Levels by Body-Mass-Index in Humans

We tested for interactions between body mass index (BMI) and common genetic variants affecting serum urate levels, genome-wide, in up to 42569 participants. Both stratified genome-wide association (GWAS) analyses, in lean, overweight and obese individuals, and regression-type analyses in a non BMI-stratified overall sample were performed. The former did not uncover any novel locus with a major main effect, but supported modulation of effects for some known and potentially new urate loci. The latter highlighted a SNP at RBFOX3 reaching genome-wide significant level (effect size 0.014, 95% CI 0.008-0.02, P-inter= 2.6 x 10(-8)). Two top loci in interaction term analyses, RBFOX3 and ERO1LB-EDAR-ADD, also displayed suggestive differences in main effect size between the lean and obese strata. All top ranking loci for urate effect differences between BMI categories were novel and most had small magnitude but opposite direction effects between strata. They include the locus RBMS1-TANK (men, Pdifflean-overweight= 4.7 x 10(-8)), a region that has been associated with several obesity related traits, and TSPYL5 (men, Pdifflean-overweight= 9.1 x 10(-8)), regulating adipocytes-produced estradiol. The top-ranking known urate loci was ABCG2, the strongest known gout risk locus, with an effect halved in obese compared to lean men (Pdifflean-obese= 2 x 10(-4)). Finally, pathway analysis suggested a role for N-glycan biosynthesis as a prominent urate-associated pathway in the lean stratum. These results illustrate a potentially powerful way to monitor changes occurring in obesogenic environment.Peer reviewe

Identification of Novel Genetic Loci Associated with Thyroid Peroxidase Antibodies and Clinical Thyroid Disease

Peer reviewe