Nonperturbative Condensates in the Electroweak Phase-Transition

We discuss the electroweak phase-transition in the early universe, using non-perturbative flow equations for a computation of the free energy. For a scalar mass above $\sim 70$ GeV, high-temperature perturbation theory cannot describe this transition reliably. This is due to the dominance of three-dimensional physics at high temperatures which implies that the effective gauge coupling grows strong in the symmetric phase. We give an order of magnitude-estimate of nonperturbative effects in reasonable agreement with recent results from electroweak lattice simulations. (Talk given by C. Wetterich at the 3rd Colloque Cosmologie, Paris, June 7-9, 1995, to appear in the proceedings)Comment: 20 pages, LaTeX, 4 figures, Talk given by C. Wetterich at the 3rd Colloque Cosmologie, Paris, June 7-9, 1995, to appear in the proceedings, *** Replaced figure 1 **

PHASE TRANSITION OF N-COMPONENT SUPERCONDUCTORS

We investigate the phase transition in the three-dimensional abelian Higgs model for N complex scalar fields, using the gauge-invariant average action \Gamma_{k}. The dependence of \Gamma_{k} on the effective infra-red cut-off k is described by a non-perturbative flow equation. The transition turns out to be first- or second-order, depending on the ratio between scalar and gauge coupling. We look at the fixed points of the theory for various N and compute the critical exponents of the model. Comparison with results from the \epsilon-expansion shows a rather poor convergence for \epsilon=1 even for large N. This is in contrast to the surprisingly good results of the \epsilon-expansion for pure scalar theories. Our results suggest the existence of a parameter range with a second-order transition for all N, including the case of the superconductor phase transition for N=1.Comment: 30p. with 9 uuencoded .eps-figures appended, LaTe

Evolutionary Models for Signal Enhancement and Approximation

This thesis deals with nature-inspired evolution processes for the purpose of signal enhancement and approximation. The focus lies on mathematical models which originate from the description of swarm behaviour. We extend existing approaches and show the potential of swarming processes as a modelling tool in image processing. In our work, we discuss the use cases of grey scale quantisation, contrast enhancement, line detection, and coherence enhancement. Furthermore, we propose a new and purely repulsive model of swarming that turns out to describe a specific type of backward diffusion process. It is remarkable that our model provides extensive stability guarantees which even support the utilisation of standard numerics. In experiments, we demonstrate its applicability to global and local contrast enhancement of digital images. In addition, we study the problem of one-dimensional signal approximation with limited resources using an adaptive sampling approach including tonal optimisation. We suggest a direct energy minimisation strategy and validate its efficacy in experiments. Moreover, we show that our approximation model can outperform a method recently proposed by Dar and Bruckstein

International Education and Economic Growth

Education, Education, Education. With this slogan the British Prime Minister Tony Blair set out his priorities for office in 2007. Indeed, many governments have now formulated the need for greater education spending and try to facilitate international exchange. The idea is that education is an investment that pays off in the long run through higher economic growth on a path towards a “knowledge society”. Economists, for a long time, have tried to capture the effect of education on growth and introduced the idea into a series of models, which go back to the Solow model. While these models manage to capture a broad range of the features associated with education, such as positive externalities and opportunity costs included in Lucas (1988) or the necessary monetary investment in Mankiw et al. (1992), they have not yet attempted to embrace international education. However, international education has left the ivory tower and is becoming a mass phenomenon which can impact economic growth. Multiple interesting transformations are linked with this development. On the one hand it is engaging to ask whether the productivity of international education is large enough to justify the promotion of exchanges. Here, Economics faces the problem that its standard trade theory seems incompatible with models for international growth. The one casually assumes countries with different factor endowments trading different goods, while the other focuses on the “production” as a whole. More fundamentally, trade theory tends to be static and “non accumulative” and is therefore regarded as part of total factor productivity in growth models. Human Capital, however, is accumulating and should thus be treated differently

Reference-Dependent Preferences in Contests and Non-Cognitive Ability in the Labour Market

The dissertation includes four individual essays that are laid out over four separate chapters. Following a short overall introduction in Chapter 1, Chapter 2 models the strategic interaction between two agents who engage in a game-theoretical contest and hold expectation-based reference-dependent preferences. We show, that agents who find themselves disadvantaged ex ante, in this setting end up as favourites in two out of three possible equilibria. In Chapter 3 we investigate, using field data, whether it is possible to invest in non-cognitive ability through an educational policy. We measure the impact of a study abroad experience on non-cognitive skills and compute its monetary implications using wage data from the German Socio-Economic Panel. The project presented in Chapter 4 is an outcome of initiating the study series Fachkraft 2020 which is, at the moment of writing, the biggest student survey in Germany with more than 40,000 annual participants. Based on about 23,000 student responses we examine whether there is selection and change of non-cognitive abilities in different study tracks of German higher education. We find sizeable selection, but little change. Lastly, Chapter 5 models the impact of the internationalisation of higher education on economic growth in a two country setting. We provide conditions necessary for internationalisation to be beneficent and simulate different growth paths for both countries

Critical exponents from optimised renormalisation group flows

Within the exact renormalisation group, the scaling solutions for O(N) symmetric scalar field theories are studied to leading order in the derivative expansion. The Gaussian fixed point is examined for d>2 dimensions and arbitrary infrared regularisation. The Wilson-Fisher fixed point in d=3 is studied using an optimised flow. We compute critical exponents and subleading corrections-to-scaling to high accuracy from the eigenvalues of the stability matrix at criticality for all N. We establish that the optimisation is responsible for the rapid convergence of the flow and polynomial truncations thereof. The scheme dependence of the leading critical exponent is analysed. For all N > 0, it is found that the leading exponent is bounded. The upper boundary is achieved for a Callan-Symanzik flow and corresponds, for all N, to the large-N limit. The lower boundary is achieved by the optimised flow and is closest to the physical value. We show the reliability of polynomial approximations, even to low orders, if they are accompanied by an appropriate choice for the regulator. Possible applications to other theories are outlined.Comment: 34 pages, 15 figures, revtex, to appear in NP