Self-energy and critical temperature of weakly interacting bosons

Using the exact renormalization group we calculate the momentum-dependent self-energy Sigma (k) at zero frequency of weakly interacting bosons at the critical temperature T_c of Bose-Einstein condensation in dimensions 3 <= D < 4. We obtain the complete crossover function interpolating between the critical regime k << k_c, where Sigma (k) propto k^{2 - eta}, and the short-wavelength regime k >> k_c, where Sigma (k) propto k^{2 (D-3)} in D> 3 and Sigma (k) \propto ln (k/k_c) in D=3. Our approach yields the crossover scale k_c on the same footing with a reasonable estimate for the critical exponent eta in D=3. From our Sigma (k) we find for the interaction-induced shift of T_c in three dimensions Delta T_c / T_c approx 1.23 a n^{1/3}, where a is the s-wave scattering length and n is the density.Comment: 4 pages,1 figur

Critical behavior of weakly interacting bosons: A functional renormalization group approach

We present a detailed investigation of the momentum-dependent self-energy Sigma(k) at zero frequency of weakly interacting bosons at the critical temperature T_c of Bose-Einstein condensation in dimensions 3<=D<4. Applying the functional renormalization group, we calculate the universal scaling function for the self-energy at zero frequency but at all wave vectors within an approximation which truncates the flow equations of the irreducible vertices at the four-point level. The self-energy interpolates between the critical regime k > k_c, where k_c is the crossover scale. In the critical regime, the self-energy correctly approaches the asymptotic behavior Sigma(k) \propto k^{2 - eta}, and in the short-wavelength regime the behavior is Sigma(k) \propto k^{2(D-3)} in D>3. In D=3, we recover the logarithmic divergence Sigma(k) \propto ln(k/k_c) encountered in perturbation theory. Our approach yields the crossover scale k_c as well as a reasonable estimate for the critical exponent eta in D=3. From our scaling function we find for the interaction-induced shift in T_c in three dimensions, Delta T_c / T_c = 1.23 a n^{1/3}, where a is the s-wave scattering length and n is the density, in excellent agreement with other approaches. We also discuss the flow of marginal parameters in D=3 and extend our truncation scheme of the renormalization group equations by including the six- and eight-point vertex, which yields an improved estimate for the anomalous dimension eta \approx 0.0513. We further calculate the constant lim_{k->0} Sigma(k)/k^{2-eta} and find good agreement with recent Monte-Carlo data.Comment: 23 pages, 7 figure

An analysis of the Research Fellowship Scheme of the Royal College of Surgeons of England.

BACKGROUND: The Research Fellowship Scheme of the Royal College of Surgeons of England commenced in 1993 with the aim of exposing selected surgical trainees to research techniques and methodology, with the hope of having an impact on surgical research and increasing the cadre of young surgeons who might decide to pursue an academic career in surgery. Over 11 million pounds sterling (approximately US 20 million dollars) has been invested in 264 fellowships. The College wished to evaluate the impact of the Scheme on the careers of research fellows, surgical research, and patient care. As the 10th anniversary of the Scheme approached. STUDY DESIGN: Two-hundred and sixty research fellows whose current addresses were available were sent a questionnaire. Two-hundred and thirty-eight (91.5%) responded. RESULTS: Three-quarters of the research fellows conducted laboratory-based research, with most of the remainder conducting patient-based clinical research. One-third of the fellows who have reached consultant status have an academic component to their post. The total number of publications based on fellowship projects was 531, with a median impact factor of 3.5. Almost all fellows had been awarded a higher degree or were working toward this. Half of the fellows received subsequent funding for research, mostly awarded by national or international funding bodies. CONCLUSIONS: The Research Fellowship Scheme of the Royal College of Surgeons of England has successfully supported many trainee surgeons in the initial phase of their research career. It has helped surgical research by increasing the pool of surgeons willing to embark on an academic career. Indirectly, patient care has benefited by promoting an evidence-based culture among young surgeons. Such schemes are relevant to surgical training programs elsewhere if more young surgeons are to be attracted into academic surgery

The Boundary Cosmological Constant in Stable 2D Quantum Gravity

We study further the r\^ole of the boundary operator \O_B for macroscopic loop length in the stable definition of 2D quantum gravity provided by the $[{\tilde P},Q]=Q$ formulation. The KdV flows are supplemented by an additional flow with respect to the boundary cosmological constant $\sigma$. We numerically study these flows for the $m=1$, $2$ and $3$ models, solving for the string susceptibility in the presence of \O_B for arbitrary coupling $\sigma$. The spectrum of the Hamiltonian of the loop quantum mechanics is continuous and bounded from below by $\sigma$. For large positive $\sigma$, the theory is dominated by the `universal' $m=0$ topological phase present only in the $[{\tilde P},Q]=Q$ formulation. For large negative $\sigma$, the non--perturbative physics approaches that of the $[P,Q]=1$ definition, although there is no path to the unstable solutions of the $[P,Q]=1$ $m$-even models.Comment: (Plain Tex, 11pp, 4 figures available on request) SHEP 91/92-2

The Manchester Color Wheel: development of a novel way of identifying color choice and its validation in healthy, anxious and depressed individuals

Abstract Background For the purposes of our research programme we needed a simple, reliable and validated method for allowing choice of a color in response to a series of questions. On reviewing the literature no such instrument was available and this study aimed to rectify this situation. This was achieved by developing a simple method of presenting a series of colors to people validating it in healthy volunteers and in individuals where color choice might be distorted, namely anxiety and depression. Methods A series of different presentations of four shades of eight colors and grey, as well as black and white were evaluated. 'Mood', 'favourite' and 'drawn to' colors were assessed in 105 healthy, 108 anxious and 110 depressed participants. The positive, neutral or negative attribution of these colors was recorded in a further 204 healthy volunteers. Results The circular presentation of colors was most favoured (Color Wheel). Yellow was the most 'drawn to' color and blue the commonest 'favourite' color in all subjects. Yellow was most often associated with a normal mood and grey with an anxious or depressed mood. Different shades of the same color had completely different positive or negative connotations. Reproducibility was exceptionally high when color choice was recorded in positive, neutral or negative terms. Conclusions The Color Wheel could be used to assess health status, mood or even treatment outcome in a variety of clinical situations. It may also have utility in circumstances where verbal communication may not be optimal, such as with children.</p

The genome of Romanomermis culicivorax:revealing fundamental changes in the core developmental genetic toolkit in Nematoda

Background: The genetics of development in the nematode Caenorhabditis elegans has been described in exquisite detail. The phylum Nematoda has two classes: Chromadorea (which includes C. elegans) and the Enoplea. While the development of many chromadorean species resembles closely that of C. elegans, enoplean nematodes show markedly different patterns of early cell division and cell fate assignment. Embryogenesis of the enoplean Romanomermis culicivorax has been studied in detail, but the genetic circuitry underpinning development in this species has not been explored. Results: We generated a draft genome for R. culicivorax and compared its gene content with that of C. elegans, a second enoplean, the vertebrate parasite Trichinella spiralis, and a representative arthropod, Tribolium castaneum. This comparison revealed that R. culicivorax has retained components of the conserved ecdysozoan developmental gene toolkit lost in C. elegans. T. spiralis has independently lost even more of this toolkit than has C. elegans. However, the C. elegans toolkit is not simply depauperate, as many novel genes essential for embryogenesis in C. elegans are not found in, or have only extremely divergent homologues in R. culicivorax and T. spiralis. Our data imply fundamental differences in the genetic programmes not only for early cell specification but also others such as vulva formation and sex determination. Conclusions: Despite the apparent morphological conservatism, major differences in the molecular logic of development have evolved within the phylum Nematoda. R. culicivorax serves as a tractable system to contrast C. elegans and understand how divergent genomic and thus regulatory backgrounds nevertheless generate a conserved phenotype. The R. culicivorax draft genome will promote use of this species as a research model

tDCS-induced alterations in GABA concentration within primary motor cortex predict motor learning and motor memory: A 7T magnetic resonance spectroscopy study

Transcranial direct current stimulation (tDCS) is a non-invasive brain stimulation technique that alters cortical excitability in a polarity specific manner and has been shown to influence learning and memory. tDCS may have both on-line and after-effects on learning and memory, and the latter are thought to be based upon tDCS-induced alterations in neurochemistry and synaptic function. We used ultra-high-field (7 T) magnetic resonance spectroscopy (MRS), together with a robotic force adaptation and de-adaptation task, to investigate whether tDCS-induced alterations in GABA and Glutamate within motor cortex predict motor learning and memory. Note that adaptation to a robot-induced force field has long been considered to be a form of model-based learning that is closely associated with the computation and ‘supervised’ learning of internal ‘forward’ models within the cerebellum. Importantly, previous studies have shown that on-line tDCS to the cerebellum, but not to motor cortex, enhances model-based motor learning. Here we demonstrate that anodal tDCS delivered to the hand area of the left primary motor cortex induces a significant reduction in GABA concentration. This effect was specific to GABA, localised to the left motor cortex, and was polarity specific insofar as it was not observed following either cathodal or sham stimulation. Importantly, we show that the magnitude of tDCS-induced alterations in GABA concentration within motor cortex predicts individual differences in both motor learning and motor memory on the robotic force adaptation and de-adaptation task

Supersymmetry and Gauge Invariance Constraints in a U(1)×\times U(1)′^{\prime }-Higgs Superconducting Cosmic String Model

A supersymmetric extension of the $U(1)\times U(1)^{\prime }$-Higgs bosonic superconducting cosmic string model is considered,and the constraints imposed upon such a model due to renormalizability, supersymmetry, and gauge invariance are examined. For a simple model with a single $U(1)$ chiral superfield and a single $$ chiral superfield, the Witten mechanism for bosonic superconductivity (giving rise to long range gauge fields outside of the string) does not exist. The simplest model that can accommodate the requisite interactions requires five chiral supermultiplets. This superconducting cosmic string solution is investigated.Comment: 17 pages, revtex, no figures; to appear in Phys. Rev.