Hamilton's Turns for the Lorentz Group

Hamilton in the course of his studies on quaternions came up with an elegant geometric picture for the group SU(2). In this picture the group elements are represented by ``turns'', which are equivalence classes of directed great circle arcs on the unit sphere $S^2$, in such a manner that the rule for composition of group elements takes the form of the familiar parallelogram law for the Euclidean translation group. It is only recently that this construction has been generalized to the simplest noncompact group $SU(1,1) = Sp(2, R) = SL(2,R)$, the double cover of SO(2,1). The present work develops a theory of turns for $SL(2,C)$, the double and universal cover of SO(3,1) and $SO(3,C)$, rendering a geometric representation in the spirit of Hamilton available for all low dimensional semisimple Lie groups of interest in physics. The geometric construction is illustrated through application to polar decomposition, and to the composition of Lorentz boosts and the resulting Wigner or Thomas rotation.Comment: 13 pages, Late

Non-ischaemic cardiomyopathy, sudden death and implantable defibrillators: a review and meta-analysis

Objective: The recent Danish Study to Assess the Efficacy of ICDs in Patients with Non-ischemic Systolic Heart Failure on Mortality (DANISH) trial suggested that implantable cardioverter defibrillators (ICDs) do not reduce overall mortality in patients with non-ischaemic cardiomyopathy (NICM), despite reducing sudden cardiac death. We performed an updated meta-analysis to examine the impact of ICD therapy on mortality in NICM patients. Methods: A systematic search for studies that examined the effect of ICDs on outcomes in NICM was performed. Our analysis compared patients randomised to an ICD with those randomised to no ICD, and examined the endpoint of overall mortality. Results: Six primary prevention trials and two secondary prevention trials were identified that met the pre-specified search criteria. Using a fixed-effects model, analysis of primary prevention trials revealed a reduction in overall mortality with ICD therapy (RR 0.76, 95% CI 0.65 to 0.91). Conclusions: Although our updated meta-analysis demonstrates a survival benefit of ICD therapy, the effect is substantively weakened by the inclusion of the DANISH trial—which is both the largest and most recent of the analysed trials—indicating that the residual pooled benefit of ICDs may reflect the risk of sudden death in older trials which included patients treated sub-optimally by contemporary standards. As such, these data must be interpreted cautiously. The results of the DANISH trial emphasise that there is no ‘one size fits all’ indication for primary prevention ICDs in NICM patients, and clinicians must consider age and comorbidity on an individual basis when determining whether a defibrillator is appropriate

Wigner distributions for finite dimensional quantum systems: An algebraic approach

We discuss questions pertaining to the definition of `momentum', `momentum space', `phase space', and `Wigner distributions'; for finite dimensional quantum systems. For such systems, where traditional concepts of `momenta' established for continuum situations offer little help, we propose a physically reasonable and mathematically tangible definition and use it for the purpose of setting up Wigner distributions in a purely algebraic manner. It is found that the point of view adopted here is limited to odd dimensional systems only. The mathematical reasons which force this situation are examined in detail.Comment: Latex, 13 page

A Typology for Quantum Hall Liquids

There is a close analogy between the response of a quantum Hall liquid (QHL) to a small change in the electron density and the response of a superconductor to an externally applied magnetic flux - an analogy which is made concrete in the Chern-Simons Landau-Ginzburg (CSLG) formulation of the problem. As the Types of superconductor are distinguished by this response, so too for QHLs: a typology can be introduced which is, however, richer than that in superconductors owing to the lack of any time-reversal symmetry relating positive and negative fluxes. At the boundary between Type I and Type II behavior, the CSLG action has a "Bogomol'nyi point," where the quasi-holes (vortices) are non-interacting - at the microscopic level, this corresponds to the behavior of systems governed by a set of model Hamiltonians which have been constructed to render exact a large class of QHL wavefunctions. All Types of QHLs are capable of giving rise to quantized Hall plateaux.Comment: 4 +epsilon pages, 1 figure; v2 has added references and minor changes, version published in Phys. Rev. B. (Rapid Communications

Modelling the spinning dust emission from LDN 1780

We study the anomalous microwave emission (AME) in the Lynds Dark Nebula (LDN) 1780 on two angular scales. Using available ancillary data at an angular resolution of 1 degree, we construct an SED between 0.408 GHz to 2997 GHz. We show that there is a significant amount of AME at these angular scales and the excess is compatible with a physical spinning dust model. We find that LDN 1780 is one of the clearest examples of AME on 1 degree scales. We detected AME with a significance > 20$\sigma$. We also find at these angular scales that the location of the peak of the emission at frequencies between 23-70 GHz differs from the one on the 90-3000 GHz map. In order to investigate the origin of the AME in this cloud, we use data obtained with the Combined Array for Research in Millimeter-wave Astronomy (CARMA) that provides 2 arcmin resolution at 30 GHz. We study the connection between the radio and IR emissions using morphological correlations. The best correlation is found to be with MIPS 70$\mu$m, which traces warm dust (T$\sim$50K). Finally, we study the difference in radio emissivity between two locations within the cloud. We measured a factor $\approx 6$ of difference in 30 GHz emissivity. We show that this variation can be explained, using the spinning dust model, by a variation on the dust grain size distribution across the cloud, particularly changing the carbon fraction and hence the amount of PAHs.Comment: 14 pages, 11 figures, submitted to MNRA

Variation of Molecular Line Ratios and Cloud Properties in the Arp 299 Galaxy Merger

High resolution observations of 12CO (2.''3), 13CO (3.''9), and HCN (5.''4) J=1--0 in the galaxy merger Arp 299 (IC 694 and NGC 3690) show the line ratios vary dramatically across the system. The 12CO/13CO ratio is unusually large, 60 +- 15, at the IC 694 nucleus, where 12CO emission is very strong, and much smaller, 10 +- 3, in the southern extended disk of that galaxy. Elsewhere, the 12CO/13CO line ratio is 5-20, typical of spiral galaxies. The line ratio variation in the overlap between the two galaxies is smaller, ranging from 10 +- 3 in the east to 20 +- 4 in the west. The 12CO/HCN line ratio also varies across Arp 299, although to a lesser degree. HCN emission is bright towards each galaxy nucleus and in the extranuclear region of active star formation; it was not detected in the IC 694 disk, or the eastern part of the overlap region, leading to lower limits of 25 and 20 respectively. By contrast, at the nuclei of IC 694 and NGC 3690 the ratios are 9 +- 1 and 14 +- 3 respectively. In the western part of the overlap region it is 11 +- 3.Comment: 16 pages, 4 postscript figures, to appear in ApJ Letter

Phase-space descriptions of operators and the Wigner distribution in quantum mechanics II. The finite dimensional case

A complete solution to the problem of setting up Wigner distribution for N-level quantum systems is presented. The scheme makes use of some of the ideas introduced by Dirac in the course of defining functions of noncommuting observables and works uniformly for all N. Further, the construction developed here has the virtue of being essentially input-free in that it merely requires finding a square root of a certain N^2 x N^2 complex symmetric matrix, a task which, as is shown, can always be accomplished analytically. As an illustration, the case of a single qubit is considered in some detail and it is shown that one recovers the result of Feynman and Wootters for this case without recourse to any auxiliary constructs.Comment: 14 pages, typos corrected, para and references added in introduction, submitted to Jour. Phys.