Universal scaling dynamics at non-thermal fixed points in multi-component Bose gases far from equilibrium

Far from equilibrium, comparatively little is known about the possibilities nature reserves for the structure and states of quantum many-body systems. A potential scenario is that these systems can approach a non-thermal fixed point and show universal scaling dynamics. The associated spatio-temporal self-similar evolution of correlations is characterized by universal scaling functions and scaling exponents. In this thesis, we investigate the universal scaling behavior of multi-component bosonic quantum gases from a theoretical point of view. In particular, we perform numerical simulations of spin-1 Bose gases in one and two spatial dimensions. To enable universal scaling dynamics, we prepare far-from-equilibrium initial configurations by making use of instabilities arising from a parameter quench between different phases of the spin-1 model. The subsequent universal scaling at the non-thermal fixed point is driven by the annihilation and dissolution of (quasi)topological excitations. In addition, we make analytical predictions for the non-thermal fixed point scaling of $U(N)$-symmetric models which we corroborate with numerical simulations of a $U(3)$-symmetric Bose gas in three spatial dimensions. We find that the scaling behavior at the fixed point is dominated by the conserved redistribution of collective excitations. Furthermore, we introduce prescaling as a generic feature of the evolution of a quantum many-body system towards a non-thermal fixed point. During the prescaling evolution, some well-measurable properties of spatial correlations already scale with the universal exponents of the fixed point while others still show scaling violations. We illustrate the existence of prescaling by means of numerical simulations of a three-dimensional $U(3)$-symmetric Bose gas. The research presented in this thesis contributes to a deeper understanding of universal scaling dynamics far from equilibrium. In particular, it unravels important key aspects for establishing out-of-equilibrium universality classes. Furthermore, the introduced concept of prescaling allows bridging the gap in the time evolution from the initial state to the associated non-thermal fixed point

a comparison of approaches for the estimation of equivalence scales using German expenditure data

Equivalence scales are routinely applied to adjust the income of households of different sizes and compositions. Because of their practical importance for the measurement of inequality and poverty, a large number of methods for the estimation of equivalence scales have been proposed. Until now, however, no comprehensive comparison of current methods has been conducted. In this paper, we employ German household expenditure data to estimate equivalence scales using several parametric, semiparametric, and nonparametric approaches. Using a single dataset, we find that some approaches yield more plausible results than others while implausible scales are mostly based on linear Engel curves. The results we consider plausible are close to the modified OECD scale, and to the square root scale for larger households

Problem-solving in virtual environment simulations prior to direct instruction for differential diagnosis in medical education: An experimental study

Background: Despite acquiring vast content knowledge about the functioning of the human body through university teaching, medical students struggle to transfer that knowledge to one of the core disciplinary practices - differential diagnosis. The authors aimed to overcome this problem by implementing computer-based virtual environment simulations in medical education courses. Methods: In an experimental study, the authors compared problem-solving in medical computer-based virtual environment simulations prior to instruction with an instruction-first approach. They compared the effects on isomorphic testing and transfer performance of clinical knowledge and clinical reasoning skills as well as evoked learning mechanisms. The study took place in spring 2021 with undergraduate medical students in the scope of a medical trajectory course. Due to Corona-Virus-19 measures participants completed all study activities remotely from home. Results: The authors did not find any learning activity sequence to be superior to the other. However, when looking at the two learning activities individually, they found that problem-solving in computer-based virtual environment simulations and direct instruction might be equally effective for learning content knowledge. Nevertheless, problem-solving in computer-based virtual environment simulations with formative feedback might be more effective for learning clinical reasoning skills than mere instruction. Conclusions: The findings indicate that problem-solving in computer-based virtual environment simulations might be more effective for learning clinical reasoning skills than mere theoretical instruction. The present study has a high level of ecological validity because it took place in a realistic setting where students had to perform all learning and testing tasks autonomously