Precise numerical results for limit cycles in the quantum three-body problem

The study of the three-body problem with short-range attractive two-body forces has a rich history going back to the 1930's. Recent applications of effective field theory methods to atomic and nuclear physics have produced a much improved understanding of this problem, and we elucidate some of the issues using renormalization group ideas applied to precise nonperturbative calculations. These calculations provide 11-12 digits of precision for the binding energies in the infinite cutoff limit. The method starts with this limit as an approximation to an effective theory and allows cutoff dependence to be systematically computed as an expansion in powers of inverse cutoffs and logarithms of the cutoff. Renormalization of three-body bound states requires a short range three-body interaction, with a coupling that is governed by a precisely mapped limit cycle of the renormalization group. Additional three-body irrelevant interactions must be determined to control subleading dependence on the cutoff and this control is essential for an effective field theory since the continuum limit is not likely to match physical systems ({\it e.g.}, few-nucleon bound and scattering states at low energy). Leading order calculations precise to 11-12 digits allow clear identification of subleading corrections, but these corrections have not been computed.Comment: 37 pages, 8 figures, LaTeX, uses graphic

Few-Body Effects in Cold Atoms and Limit Cycles

Physical systems with a large scattering length have universal properties independent of the details of the interaction at short distances. Such systems can be realized in experiments with cold atoms close to a Feshbach resonance. They also occur in many other areas of physics such as nuclear and particle physics. The universal properties include a geometric spectrum of three-body bound states (so-called Efimov states) and log-periodic dependence of low-energy observables on the physical parameters of the system. This behavior is characteristic of a renormalization group limit cycle. We discuss universality in the three- and four-body sectors and give an overview of applications in cold atoms.Comment: 7 pages, 3 figures, plenary talk at the 18th International IUPAP Conference on Few-Body Problems in Physics (FB18), Santos, Brazil, August 200

Efimov physics in a finite volume

Three bosons with large scattering length show universal properties that do not depend on the details of the interaction at short distances. In the three-boson system, these properties include a geometric spectrum of shallow three-body states called "Efimov states" and log-periodic dependence of scattering observables on the scattering length. We investigate the modification of the Efimov states in a finite cubic box and calculate the dependence of their energies on the box size using effective field theory. We explicitly verify the renormalization of the effective field theory in the finite volume.Comment: 9 pages, 3 figures, sign error corrected, numerical results changed, final versio

IMAGES I. Strong evolution of galaxy kinematics since z=1

(abbreviated) We present the first results of the ESO large program, ``IMAGES'' which aims at obtaining robust measurements of the kinematics of distant galaxies using the multi-IFU mode of GIRAFFE on the VLT. 3D spectroscopy is essential to robustly measure the often distorted kinematics of distant galaxies (e.g., Flores et al. 2006). We derive the velocity fields and $\sigma$-maps of 36 galaxies at 0.4<z<0.75 from the kinematics of the [OII] emission line doublet, and generate a robust technique to identify the nature of the velocity fields based on the pixels of the highest signal-to-noise ratios (S/N). We have gathered a unique sample of 63 velocity fields of emission line galaxies (W0([OII]) > 15 A) at z=0.4-0.75, which are a representative subsample of the population of M_stellar>1.5x10^{10} M_sun emission line galaxies in this redshift range, and are largely unaffected by cosmic variance. Taking into account all galaxies -with or without emission lines- in that redshift range, we find that at least 41+/-7% of them have anomalous kinematics, i.e., they are not dynamically relaxed. This includes 26+/-7% of distant galaxies with complex kinematics, i.e., they are not simply pressure or rotationally supported. Our result implies that galaxy kinematics are among the most rapidly evolving properties, because locally, only a few percent of the galaxies in this mass range have complex kinematics.Comment: 17 pages, 6 figures, Accepted by A&

Nonuniversal Effects in the Homogeneous Bose Gas

Effective field theory predicts that the leading nonuniversal effects in the homogeneous Bose gas arise from the effective range for S-wave scattering and from an effective three-body contact interaction. We calculate the leading nonuniversal contributions to the energy density and condensate fraction and compare the predictions with results from diffusion Monte Carlo calculations by Giorgini, Boronat, and Casulleras. We give a crude determination of the strength of the three-body contact interaction for various model potentials. Accurate determinations could be obtained from diffusion Monte Carlo calculations of the energy density with higher statistics.Comment: 24 pages, RevTex, 5 ps figures, included with epsf.te

The elementary excitations of the exactly solvable Russian doll BCS model of superconductivity

The recently proposed Russian doll BCS model provides a simple example of a many body system whose renormalization group analysis reveals the existence of limit cycles in the running coupling constants of the model. The model was first studied using RG, mean field and numerical methods showing the Russian doll scaling of the spectrum, E(n) ~ E0 exp(-l n}, where l is the RG period. In this paper we use the recently discovered exact solution of this model to study the low energy spectrum. We find that, in addition to the standard quasiparticles, the electrons can bind into Cooper pairs that are different from those forming the condensate and with higher energy. These excited Cooper pairs can be described by a quantum number Q which appears in the Bethe ansatz equation and has a RG interpretation.Comment: 36 pages, 12 figure

More on the infrared renormalization group limit cycle in QCD

We present a detailed study of the recently conjectured infrared renormalization group limit cycle in QCD using chiral effective field theory. It was conjectured that small increases in the up and down quark masses can move QCD to the critical trajectory for an infrared limit cycle in the three-nucleon system. At the critical quark masses, the binding energies of the deuteron and its spin-singlet partner are tuned to zero and the triton has infinitely many excited states with an accumulation point at the three-nucleon threshold. We exemplify three parameter sets where this effect occurs at next-to-leading order in the chiral counting. For one of them, we study the structure of the three-nucleon system in detail using both chiral and contact effective field theories. Furthermore, we investigate the matching of the chiral and contact theories in the critical region and calculate the influence of the limit cycle on three-nucleon scattering observables.Comment: 17 pages, 7 figures, discussion improved, results unchanged, version to appear in EPJ

Vitamin D deficiency is associated with IL-6 levels and monocyte activation in HIV-infected persons

Immune activation plays a key role in HIV pathogenesis. Markers of inflammation have been associated with vitamin D deficiency in the general population. Studies have also demonstrated associations of vitamin D deficiency with increased risk of HIV progression and death. The relationship between persistent inflammation and immune activation during chronic HIV infection and vitamin D deficiency remains unclear.Cryopreserved specimens were analyzed from 663 participants at the time of enrollment from the Study to Understand the Natural History of HIV/AIDS in the Era of Effective Therapy (SUN Study) from 2004 to 2006. Biomarkers of inflammation, atherosclerosis, and coagulation were measured using enzyme-linked immunosorbent assays (ELISAs) and electrochemiluminescence. 25(OH)D, the stable precursor form of vitamin D, was measured using a radioimmunoassay with levels defined as: normal (≥30ng/mL), insufficient (20-29 ng/mL) and deficient (<20 ng/mL). Monocyte phenotypes were assessed by flow cytometry. Linear and logistic regression models were used to determine statistical associations between biomarkers and vitamin D deficiency.25(OH)D levels were deficient in 251 (38%) participants, insufficient in 222 (34%), and normal in 190 (29%). Patients with vitamin D deficiency, when compared to those with insufficient or normal vitamin D levels, had increased levels of IL-6 (23%; p<0.01), TNF-α (21%, p = 0.03), D-dimer (24%, p = 0.01), higher proportions of CD14dimCD16+ (22%, p<0.01) and CX3CR1+ monocytes (48%; p<0.001) and decreased frequency of CCR2+ monocytes (-3.4%, p<0.001). In fully adjusted models, vitamin D associations with abnormal biomarker levels persisted for IL-6 levels and CX3CR1+ and CCR2+ phenotypes.Vitamin D deficiency is associated with greater inflammation and activated monocyte phenotypes. The role of vitamin D deficiency in persistent immune activation and associated complications during chronic HIV disease should be further evaluated as a possible target for intervention