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

Generalized Quantum Hall Projection Hamiltonians

Certain well known quantum Hall states -- including the Laughlin states, the Moore-Read Pfaffian, and the Read-Rezayi Parafermion states -- can be defined as the unique lowest degree symmetric analytic function that vanishes as at least p powers as some number (g+1) of particles approach the same point. Analogously, these same quantum Hall states can be generated as the exact highest density zero energy state of simple angular momentum projection operators. Following this theme we determine the highest density zero energy state for many other values of p and g.Comment: 9 page

Comment on ``Evidence for Anisotropic State of Two-Dimensional Electrons in High Landau Levels''

In a recent letter M. Lilly et al [PRL 82, 394 (1999)] have shown that a highly anisotropic state can arise in certain two dimensional electron systems. In the large square samples studied, resistances measured in the two perpendicular directions are found to have a ratio that may be 60 or larger at low temperature and at certain magnetic fields. In Hall bar measurements, the anisotropy ratio is found to be much smaller (roughly 5). In this comment we resolve this discrepancy by noting that the anisotropy of the underlying sheet resistivities is correctly represented by Hall bar resistance measurements but shows up exponentially enhanced in resistance measurements on square samples due to simple geometric effects. We note, however, that the origin of this underlying resistivity anisotropy remains unknown, and is not addressed here.Comment: 1 page, minor calculational error repaire

A nu=2/5 Paired Wavefunction

We construct a wavefunction, generalizing the well known Moore-Read Pfaffian, that describes spinless electrons at filling fraction nu=2/5 (or bosons at filling fraction nu=2/3) as the ground state of a very simple three body potential. We find, analogous to the Pfaffian, that when quasiholes are added there is a ground state degeneracy which can be identified as zero-modes of the quasiholes. The zero-modes are identified as having semionic statistics. We write this wavefunction as a correlator of the Virasoro minimal model conformal field theory M(5,3). Since this model is non-unitary, we conclude that this wavefunction is a quantum critical state. Nonetheless, we find that the overlaps of this wavefunction with exact diagonalizations in the lowest and first excited Landau level are very high, suggesting that this wavefunction may have experimental relevance for some transition that may occur in that regime.Comment: 13 pages, 2 figure

Delivering organisational adaptation through legislative mechanisms: Evidence from the Adaptation Reporting Power (Climate Change Act 2008)

There is increasing recognition that organisations, particularly in key infrastructure sectors, are potentially vulnerable to climate change and extreme weather events, and require organisational responses to ensure they are resilient and adaptive. However, detailed evidence of how adaptation is facilitated, implemented and reported, particularly through legislative mechanisms is lacking. The United Kingdom Climate Change Act (2008), introduced the Adaptation Reporting Power, enabling the Government to direct so-called reporting authorities to report their climate change risks and adaptation plans. We describe the authors' unique role and experience supporting the Department for Environment, Food and Rural Affairs (Defra) during the Adaptation Reporting Power's first round. An evaluation framework, used to review the adaptation reports, is presented alongside evidence on how the process provides new insights into adaptation activities and triggered organisational change in 78% of reporting authorities, including the embedding of climate risk and adaptation issues. The role of legislative mechanisms and risk-based approaches in driving and delivering adaptation is discussed alongside future research needs, including the development of organisational maturity models to determine resilient and well adapting organisations. The Adaptation Reporting Power process provides a basis for similar initiatives in other countries, although a clear engagement strategy to ensure buy-in to the process and research on its long-term legacy, including the potential merits of voluntary approaches, is required

Fe I and Fe II Abundances of Solar-Type Dwarfs in the Pleiades Open Cluster

We have derived Fe abundances of 16 solar-type Pleiades dwarfs by means of an equivalent width analysis of Fe I and Fe II lines in high-resolution spectra obtained with the Hobby - Eberly Telescope and High Resolution Spectrograph. Abundances derived from Fe II lines are larger than those derived from Fe I lines (herein referred to as over-ionization) for stars with Teff < 5400 K, and the discrepancy (deltaFe = [Fe II/H] - [Fe I/H]) increases dramatically with decreasing Teff, reaching over 0.8 dex for the coolest stars of our sample. The Pleiades joins the open clusters M 34, the Hyades, IC 2602, and IC 2391, and the Ursa Major moving group, demonstrating ostensible over-ionization trends. The Pleiades deltaFe abundances are correlated with Ca II infrared triplet and Halpha chromospheric emission indicators and relative differences therein. Oxygen abundances of our Pleiades sample derived from the high-excitation O I triplet have been previously shown to increase with decreasing Teff, and a comparison with the deltaFe abundances suggests that the over-excitation (larger abundances derived from high excitation lines relative to low excitation lines) and over-ionization effects that have been observed in cool open cluster and disk field main sequence (MS) dwarfs share a common origin. Star-to-star Fe I abundances have low internal scatter, but the abundances of stars with Teff < 5400 K are systematically higher compared to the warmer stars. The cool star [Fe I/H] abundances cannot be connected directly to over-excitation effects, but similarities with the deltaFe and O I triplet trends suggest the abundances are dubious. Using the [Fe I/H] abundances of five stars with Teff > 5400 K, we derive a mean Pleiades cluster metallicity of [Fe/H] = +0.01 +/- 0.02.Comment: 32 pages, 7 figures, 7 tables; accepted by PAS