Differential Renormalization-Group Approach to the Layered sine-Gordon Model

New qualitative picture of vortex length-scale dependence has been found in recent electrical transport measurements performed on strongly anisotropic BSCCO single crystals in zero magnetic field. This indicates the need for a better description of the 3D/2D crossover in vortex dimensionality. The vortex-dominated properties of high transition temperature superconductors with extremely high anisotropy (layered systems) are reasonably well described in the framework of the layered XY model which can be mapped onto the layered sine-Gordon model. For the latter we derive an exact renormalization group (RG) equation using Wegner's and Houghton's approach in the local potential approximation. The agreement of the UV scaling laws find by us by linearizing the RG equations with those obtained previously in the literature in the dilute gas approximation makes the improvement appearant which can be achieved by solving our RG equations numerically.Comment: 12 pages, no figures, to be published in Philos. Ma

Asymptotic safety in the sine-Gordon model

In the framework of the functional renormalization group method it is shown that the phase structure of the 2-dimensional sine-Gordon model possesses a nontrivial UV fixed point which makes the model asymptotically safe. The fixed point exhibits strong singularity similarly to the scaling found in the vicinity of the infrared fixed point. The singularity signals the upper energy-scale limit to the validity of the model. We argue that the sine-Gordon model with a momentum-dependent wavefunction renormalization is in a dual connection with the massive sine-Gordon model.Comment: 8 pages, 3 figure

Assessment of Design Procedures for Vertical Borehole Heat Exchangers

The use of ground source energy systems is a well-established method to provide low cost heating to buildings, diversify the energy mix and help meeting increasingly stricter sustainability targets. However, considerable uncertainties remain over their efficient design, with several standards, guidelines and manuals being proposed over the last few years. This paper aims at providing insight into the implications to the design of a vertical borehole heat exchanger of the adoption of different design procedures. The hypothetical case of a typical dwelling located in London, UK, is analysed in order to highlight the impact on the final design of the chosen methodology. Moreover, a parametric study using an analytical design procedure was performed to point out the influence of various factors, such as borehole characteristics and thermal properties of the ground. It is shown that there are considerable discrepancies between design methods and that uncertainties in some input parameters, such as the thermal properties of the ground, which for relatively small systems are often selected from tables rather than measured in situ, may have a substantial influence on the length of borehole required

Optimized regulator for the quantized anharmonic oscillator

The energy gap between the first excited state and the ground state is calculated for the quantized anharmonic oscillator in the framework of the functional renormalization group method. The compactly supported smooth regulator is used which includes various types of regulators as limiting cases. It was found that the value of the energy gap depends on the regulator parameters. We argue that the optimization based on the disappearance of the false, broken symmetric phase of the model leads to the Litim's regulator. The least sensitivity on the regulator parameters leads however to an IR regulator being somewhat different of the Litim's one, but it can be described as a perturbatively improved, or generalized Litim's regulator and provides analytic evolution equations, too.Comment: 8 pages, 4 figure

Quantum censorship in two dimensions

It is pointed out that increasingly attractive interactions, represented by partially concave local potential in the Lagrangian, may lead to the degeneracy of the blocked, renormalized action at the gliding cutoff scale by tree-level renormalization. A quantum counterpart of this mechanism is presented in the two-dimensional sine-Gordon model. The presence of Quantum Censorship is conjectured which makes the loop contributions pile up during the renormalization and thereby realize an approximate semiclassical effect.Comment: 12 pages, 4 figures. Final versio

Quantum-classical transition in the Caldeira-Leggett model

The quantum-classical transition in the Caldeira-Leggett model is investigated in the framework of the functional renormalization group method. It is shown that a divergent quadratic term arises in the action due to the heat bath in the model. By removing the divergence with a frequency cutoff we considered the critical behavior of the model. The critical exponents belonging to the susceptibility and the correlation length are determined and their independence of the frequency cutoff and the renormalization scheme is shown.Comment: 8 pages, 4 figure

CLIC Background Studies and optimization of the innermost tracker elements

The harsh machine background at the Compact Linear Collider (CLIC) forms a strong constraint on the design of the innermost part of the tracker. For the CLIC Conceptual Design Report, the detector concepts developed for the International Linear Collider (ILC) were adapted to the CLIC environment. We present the new layout for the Vertex Detector and the Forward Tracking Disks of the CLIC detector concepts, as well as the background levels in these detectors. We also study the dependence of the background rates on technology parameters like thickness of the active layer and detection threshold.Comment: 7 pages, 5 figures, LCWS 201

Contextualising and connecting learning

In this case study, two academics from The Bartlett, UCL’s global faculty of the built environment, think through how two modules can bring together research and teaching in interdisciplinary education. They use ‘real life’ as a resource to bring together a whole range of knowledge and activities by having students explore cities and organizational networks. Assessment is particularly tricky in such courses, as is also argued by Jessop and Hughes in Chapter 5; interdisciplinary learning is messy and complicated, as Davies outlines in Chapter 8; and global perspectives must be embedded for such courses to be meaningful, as Kraska, Bourn and Blum highlight in Chapter 6. The authors turn these challenges into a chance for students to learn not just dry, isolated and theoretical ideas, but rather to engage publicly, for instance through blogs. There are many benefits to such education: the students see the city and organizational networks around them in a new light, and tackle realistic skills such as working in groups along the way

Renormalization group in internal space

Renormalization group in the internal space consists of the gradual change of the coupling constants. Functional evolution equations corresponding to the change of the mass or the coupling constant are presented in the framework of a scalar model. The evolution in the mass which yields the functional generalization of the Callan-Symanzik equation for the one-particle irreducible effective action is given in its renormalized, cutoff-independent form. The evolution of the coupling constant generates an evolution equation for the two-particle irreducible effective action. © 2005 The American Physical Society