We use the functional renormalization group (FRG) to derive analytical expressions for thermodynamic observables (density, pressure, entropy, and compressibility) as well as for single-particle properties (wave-function renormalization and effective mass) of interacting bosons in two dimensions as a function of temperature T and chemical potential μ. We focus on the quantum disordered and the quantum critical regime close to the dilute Bose gas quantum critical point. Our approach is based on a truncated vertex expansion of the hierarchy of FRG flow equations and the decoupling of the two-body contact interaction in the particle-particle channel using a suitable Hubbard-Stratonovich transformation. Our analytic FRG results extend previous analytical renormalization-group calculations for thermodynamic observables at μ=0 to finite values of μ. To confirm the validity of our FRG approach, we have also performed quantum Monte Carlo simulations to obtain the magnetization, susceptibility, and correlation length of the two-dimensional spin-1/2 quantum XY model with coupling J in a regime where its quantum critical behavior is controlled by the dilute Bose gas quantum critical point. We find that our analytical results describe the Monte Carlo data for μ≤0 rather accurately up to relatively high temperatures T0.1J.

The search for renewable energy sources is a wide area in which significant progress is still expected. This paper focuses on an energy system that uses Fresnel lenses to concentrate sunlight on a tubing system to heat up the working fluid. Fresnel lenses are lighter, thinner and cheaper to build than ordinary lenses. The model is designed to be integrated into the façade of a building that will then be heated or cooled using the energy extracted from sunlight. Details of the concept have been given in Tsoutsou et al. (2014) in which the viability of the concept was investigated and its energy saving and economic benefits have been quantified. A prototype façade of 1.5 x 3.6m, with 3 m2 Fresnel lens area, has been constructed as a proto-type and tested in a standard office size of a dummy building. This paper presents the experimental performance of the solar concentrating façade and identifies advantages and disadvantages of the solar system. A model has been developed to predict the effect of design choices. This model is used to identify potential optimization strategies. In addition to the suntracking method, mass flow through the collectors can be adjusted to achieve maximum efficiency of the Fresnel collectors