Energies of knot diagrams

We introduce and begin the study of new knot energies defined on knot diagrams. Physically, they model the internal energy of thin metallic solid tori squeezed between two parallel planes. Thus the knots considered can perform the second and third Reidemeister moves, but not the first one. The energy functionals considered are the sum of two terms, the uniformization term (which tends to make the curvature of the knot uniform) and the resistance term (which, in particular, forbids crossing changes). We define an infinite family of uniformization functionals, depending on an arbitrary smooth function $f$ and study the simplest nontrivial case $f(x)=x^2$, obtaining neat normal forms (corresponding to minima of the functional) by making use of the Gauss representation of immersed curves, of the phase space of the pendulum, and of elliptic functions

Cooling dynamics of ultracold two-species Fermi-Bose mixtures

We compare strategies for evaporative and sympathetic cooling of two-species Fermi-Bose mixtures in single-color and two-color optical dipole traps. We show that in the latter case a large heat capacity of the bosonic species can be maintained during the entire cooling process. This could allow to efficiently achieve a deep Fermi degeneracy regime having at the same time a significant thermal fraction for the Bose gas, crucial for a precise thermometry of the mixture. Two possible signatures of a superfluid phase transition for the Fermi species are discussed.Comment: 4 pages, 3 figure

A Chandra Study of the Effects of a Major Merger on the Structure of Abell 2319

We present an analysis of a Chandra observation of the massive, nearby galaxy cluster Abell 2319. A sharp surface brightness discontinuity--suggested by previous, lower angular resolution X-ray imaging--is clearly visible in the ACIS image. This roughly 300kpc feature suggests that a major merger is taking place with a significant velocity component perpendicular to the line of sight. The cluster emission-weighted mean temperature is 11.8+/-0.6kev, somewhat higher than previous temperature measurements. The Chandra temperature map of A2319 reveals substructure resembling that anticipated based on hydrodynamic simulations of cluster mergers. The merger feature shows a pressure change across the surface brightness discontinuity by a factor of <=2.5. The higher density side of the front has a lower temperature, suggesting the presence of a cold front similar to those in many other merging clusters. The velocity of the front is roughly sonic. We compare bulk properties of the ICM and galaxies in A2319 to the same properties in a large sample of clusters as a way of gauging the effects of the major merger. Interestingly, by comparing A2319 to a sample of 44 clusters studied with the ROSAT PSPC we find that the X-ray luminosity, isophotal size, and ICM mass are consistent with the expected values for a cluster of its temperature; in addition, the K-band galaxy light is consistent with the light--temperature scaling relation derived from a sample of about 100 clusters studied with 2MASS. Together, these results indicate either that the merger in A2319 has not been effective at altering the bulk properties of the cluster, or that there are large but correlated displacements in these quantities.Comment: 11 pages, 8 figures, ApJ Submitte

Measurement of the Zero Crossing in a Feshbach Resonance of Fermionic 6-Li

We measure a zero crossing in the scattering length of a mixture of the two lowest hyperfine states of 6-Li. To locate the zero crossing, we monitor the decrease in temperature and atom number arising from evaporation in a CO2 laser trap as a function of magnetic field B. The temperature decrease and atom loss are minimized for B=528(4) G, consistent with no evaporation. We also present preliminary calculations using potentials that have been constrained by the measured zero crossing and locate a broad Feshbach resonance at approximately 860 G, in agreement with previous theoretical predictions. In addition, our theoretical model predicts a second and much narrower Feshbach resonance near 550 G.Comment: Five pages, four figure

Numerical simulation of exciton dynamics in Cu2O at ultra low temperatures within a potential trap

We have studied theoretically the relaxation behaviour of excitons in cuprous oxide (Cu2O) at ultra low temperatures when excitons are confined within a potential trap by solving numerically the Boltzmann equation. As relaxation processes, we have included in this paper deformation potential phonon scattering, radiative and non-radiative decay and Auger decay. The relaxation kinetics has been analysed for temperatures in the range between 0.3K and 5K. Under the action of deformation potential phonon scattering only, we find for temperatures above 0.5K that the excitons reach local equilibrium with the lattice i.e. that the effective local temperature is coming down to bath temperature, while below 0.5K a non-thermal energy distribution remains. Interestingly, for all temperatures the global spatial distribution of excitons does not reach the equilibrium distribution, but stays at a much higher effective temperature. If we include further a finite lifetime of the excitons and the two-particle Auger decay, we find that both the local and the global effective temperature are not coming down to bath temperature. In the first case we find a Bose-Einstein condensation (BEC) to occur for all temperatures in the investigated range. Comparing our results with the thermal equilibrium case, we find that BEC occurs for a significantly higher number of excitons in the trap. This effect could be related to the higher global temperature, which requires an increased number of excitons within the trap to observe the BEC. In case of Auger decay, we do not find at any temperature a BEC due to the heating of the exciton gas

Pure Gas of Optically Trapped Molecules Created from Fermionic Atoms

We report on the production of a pure sample of up to 3x10^5 optically trapped molecules from a Fermi gas of 6Li atoms. The dimers are formed by three-body recombination near a Feshbach resonance. For purification a Stern-Gerlach selection technique is used that efficiently removes all trapped atoms from the atom-molecule mixture. The behavior of the purified molecular sample shows a striking dependence on the applied magnetic field. For very weakly bound molecules near the Feshbach resonance, the gas exhibits a remarkable stability with respect to collisional decay.Comment: 4 pages, 5 figure

Efficient and robust initialization of a qubit register with fermionic atoms

We show that fermionic atoms have crucial advantages over bosonic atoms in terms of loading in optical lattices for use as a possible quantum computation device. After analyzing the change in the level structure of a non-uniform confining potential as a periodic potential is superimposed to it, we show how this structure combined with the Pauli principle and fermion degeneracy can be exploited to create unit occupancy of the lattice sites with very high efficiency.Comment: 4 pages, 3 figure

Qualitative exploration of the Medical Examiner role in identifying problems with the quality of patient care

Objective: A national system of Medical Examiners (MEs) implemented in England and Wales from April 2019 was intended to ensure that every death receives scrutiny from an independent, senior doctor, resulting in early detection of problems in care. The aim of this study was to increase understanding of how the ME role operates to identify problems related to quality of patient care and to explore the potential for development to maximise learning opportunities. Design: A qualitative approach involved the use of semi-structured interviews. Data analysis employed a framework approach. Setting: Study participants were recruited from 11 acute hospitals in England, known to be operating an ME service. Participants: A purposive sample of 20 MEs and one ME officer. Results: MEs brought different perspectives to the role based on their medical background. The process for identifying and acting on quality of care concerns was broadly consistent, with a notable consensus regarding the value of speaking to bereaved relatives. Variation was identified within and between services in relation to how core components are carried out and the perceived salience of information, which appeared to reflect individual and service preferences as well as different organisational pathways. ME services required flexibility to accommodate fluctuating demand, but funding arrangements imposed restrictions. The majority of MEs highlighted limited opportunity for formal team contact and a lack of meaningful feedback as limiting scope for development. Conclusion: Core components of the ME role were being conducted, although individual and systemic variations in practice were identified. The discussion with bereaved relatives is a unique feature of the ME role and was considered highly valuable, both for the organisation and relatives. Further development could consider the impact of the variation identified and address mechanisms for feedback and shared learning

Feshbach resonances in a quasi-2D atomic gas

Strongly confining an ultracold atomic gas in one direction to create a quasi-2D system alters the scattering properties of this gas. We investigate the effects of confinement on Feshbach scattering resonances and show that strong confinement results in a shift in the position of the Feshbach resonance as a function of the magnetic field. This shift, as well as the change of the width of the resonance, are computed. We find that the resonance is strongly damped in the thermal gas, but in the condensate the resonance remains sharp due to many-body effects. We introduce a 2D model system, suited for the study of resonant superfluidity, and having the same scattering properties as the tightly confined real system near a Feshbach resonance. Exact relations are derived between measurable quantities and the model parameters.Comment: 8 pages, 2 figure

Auger decay, Spin-exchange, and their connection to Bose-Einstein condensation of excitons in Cu_2O

In view of the recent experiments of O'Hara, et al. on excitons in Cu_2O, we examine the interconversion between the angular-momentum triplet-state excitons and the angular-momentum singlet-state excitons by a spin-exchange process which has been overlooked in the past. We estimate the rate of this particle-conserving mechanism and find a substantially higher value than the Auger process considered so far. Based on this idea, we give a possible explanation of the recent experimental observations, and make certain predictions, with the most important being that the singlet-state excitons in Cu_2O is a very serious candidate for exhibiting the phenomenon of Bose-Einstein condensation.Comment: 4 pages, RevTex, 1 ps figur