Bose-Einstein condensates with attractive 1/r interaction: The case of self-trapping

Amplifying on a proposal by O'Dell et al. for the realization of Bose-Einstein condensates of neutral atoms with attractive $1/r$ interaction, we point out that the instance of self-trapping of the condensate, without external trap potential, is physically best understood by introducing appropriate "atomic" units. This reveals a remarkable scaling property: the physics of the condensate depends only on the two parameters $N^2 a/a_u$ and $\gamma/N^2$, where $N$ is the particle number, $a$ the scattering length, $a_u$ the "Bohr" radius and $\gamma$ the trap frequency in atomic units. We calculate accurate numerical results for self-trapping wave functions and potentials, for energies, sizes and peak densities, and compare with previous variational results. As a novel feature we point out the existence of a second solution of the extended Gross-Pitaevskii equation for negative scattering lengths, with and without trapping potential, which is born together with the ground state in a tangent bifurcation. This indicates the existence of an unstable collectively excited state of the condensate for negative scattering lengths.Comment: 7 pages, 7 figures, to appear in Phys. Rev.

Development of a behaviour change intervention: a case study on the practical application of theory

BACKGROUND: Use of theory in implementation of complex interventions is widely recommended. A complex trial intervention, to enhance self-management support for people with osteoarthritis (OA) in primary care, needed to be implemented in the Managing Osteoarthritis in Consultations (MOSAICS) trial. One component of the trial intervention was delivery by general practitioners (GPs) of an enhanced consultation for patients with OA. The aim of our case study is to describe the systematic selection and use of theory to develop a behaviour change intervention to implement GP delivery of the enhanced consultation. METHODS: The development of the behaviour change intervention was guided by four theoretical models/frameworks: i) an implementation of change model to guide overall approach, ii) the Theoretical Domains Framework (TDF) to identify relevant determinants of change, iii) a model for the selection of behaviour change techniques to address identified determinants of behaviour change, and iv) the principles of adult learning. Methods and measures to evaluate impact of the behaviour change intervention were identified. RESULTS: The behaviour change intervention presented the GPs with a well-defined proposal for change; addressed seven of the TDF domains (e.g., knowledge, skills, motivation and goals); incorporated ten behaviour change techniques (e.g., information provision, skills rehearsal, persuasive communication); and was delivered in workshops that valued the expertise and professional values of GPs. The workshops used a mixture of interactive and didactic sessions, were facilitated by opinion leaders, and utilised 'context-bound communication skills training.' Methods and measures selected to evaluate the behaviour change intervention included: appraisal of satisfaction with workshops, GP report of intention to practise and an assessment of video-recorded consultations of GPs with patients with OA. CONCLUSIONS: A stepped approach to the development of a behaviour change intervention, with the utilisation of theoretical frameworks to identify determinants of change matched with behaviour change techniques, has enabled a systematic and theory-driven development of an intervention designed to enhance consultations by GPs for patients with OA. The success of the behaviour change intervention in practice will be evaluated in the context of the MOSAICS trial as a whole, and will inform understanding of practice level and patient outcomes in the trial

Exploring disorganized attachment style among Malay mothers in Malaysia: a study using the Attachment Style Interview

This article explores emerging themes involving disorganized attachment style among Malay Muslim mothers using the Attachment Style Interview (ASI). Analysis of the 18 mothers with disorganized attachment style (those with combined anxious and avoidant styles) utilized themes deemed important from the attachment research literature and selected based on a careful reading of the narrative cases. These include more extreme negative interpersonal experiences than found in other insecure attachment style descriptors, and included partner violence and related isolation/social exclusion. It also indicated more complex cognitive-affective disturbance including mixed or contradictory dependency patterns and both angry and fearful attitudes to others. We discuss the concept of disorganized attachment style in relation to abuse, social exclusion, and its implication for psychopathology, intervention, and treatment

Classical, semiclassical, and quantum investigations of the 4-sphere scattering system

A genuinely three-dimensional system, viz. the hyperbolic 4-sphere scattering system, is investigated with classical, semiclassical, and quantum mechanical methods at various center-to-center separations of the spheres. The efficiency and scaling properties of the computations are discussed by comparisons to the two-dimensional 3-disk system. While in systems with few degrees of freedom modern quantum calculations are, in general, numerically more efficient than semiclassical methods, this situation can be reversed with increasing dimension of the problem. For the 4-sphere system with large separations between the spheres, we demonstrate the superiority of semiclassical versus quantum calculations, i.e., semiclassical resonances can easily be obtained even in energy regions which are unattainable with the currently available quantum techniques. The 4-sphere system with touching spheres is a challenging problem for both quantum and semiclassical techniques. Here, semiclassical resonances are obtained via harmonic inversion of a cross-correlated periodic orbit signal.Comment: 12 pages, 5 figures, submitted to Phys. Rev.

Symmetry breaking in crossed magnetic and electric fields

We present the first observations of cylindrical symmetry breaking in highly excited diamagnetic hydrogen with a small crossed electric field, and we give a semiclassical interpretation of this effect. As the small perpendicular electric field is added, the recurrence strengths of closed orbits decrease smoothly to a minimum, and revive again. This phenomenon, caused by interference among the electron waves that return to the nucleus, can be computed from the azimuthal dependence of the classical closed orbits.Comment: 4 page REVTeX file including 5 postscript files (using psfig) Accepted for publication in Physical Review Letters. Difference from earlier preprint: we have discovered the cause of the earlier apparent discrepancy between experiment and theory and now achieve excellent agreemen

Semiclassical mechanics of a non-integrable spin cluster

We study detailed classical-quantum correspondence for a cluster system of three spins with single-axis anisotropic exchange coupling. With autoregressive spectral estimation, we find oscillating terms in the quantum density of states caused by classical periodic orbits: in the slowly varying part of the density of states we see signs of nontrivial topology changes happening to the energy surface as the energy is varied. Also, we can explain the hierarchy of quantum energy levels near the ferromagnetic and antiferromagnetic states with EKB quantization to explain large structures and tunneling to explain small structures.Comment: 9 pages. For related works see "http://www.msc.cornell.edu/~clh/clh.html