Single-crystal diamond low-dissipation cavity optomechanics

Single-crystal diamond cavity optomechanical devices are a promising example of a hybrid quantum system: by coupling mechanical resonances to both light and electron spins, they can enable new ways for photons to control solid state qubits. However, realizing cavity optomechanical devices from high quality diamond chips has been an outstanding challenge. Here we demonstrate single-crystal diamond cavity optomechanical devices that can enable photon-phonon-spin coupling. Cavity optomechanical coupling to $2\,\text{GHz}$ frequency ($f_\text{m}$) mechanical resonances is observed. In room temperature ambient conditions, these resonances have a record combination of low dissipation (mechanical quality factor, $Q_\text{m} > 9000$) and high frequency, with $Q_\text{m}\cdot f_\text{m} \sim 1.9\times10^{13}$ sufficient for room temperature single phonon coherence. The system exhibits high optical quality factor ($Q_\text{o} > 10^4$) resonances at infrared and visible wavelengths, is nearly sideband resolved, and exhibits optomechanical cooperativity $C\sim 3$. The devices' potential for optomechanical control of diamond electron spins is demonstrated through radiation pressure excitation of mechanical self-oscillations whose 31 pm amplitude is predicted to provide 0.6 MHz coupling rates to diamond nitrogen vacancy center ground state transitions (6 Hz / phonon), and $\sim10^5$ stronger coupling rates to excited state transitions.Comment: 12 pages, 5 figure

Static Ricci-flat 5-manifolds admitting the 2-sphere

We examine, in a purely geometrical way, static Ricci-flat 5-manifolds admitting the 2-sphere and an additional hypersurface-orthogonal Killing vector. These are widely studied in the literature, from different physical approaches, and known variously as the Kramer - Gross - Perry - Davidson - Owen solutions. The 2-fold infinity of cases that result are studied by way of new coordinates (which are in most cases global) and the cases likely to be of interest in any physical approach are distinguished on the basis of the nakedness and geometrical mass of their associated singularities. It is argued that the entire class of solutions has to be considered unstable about the exceptional solutions: the black string and soliton cases. Any physical theory which admits the non-exceptional solutions as the external vacuua of a collapsing object has to accept the possibility of collapse to zero volume leaving behind the weakest possible, albeit naked, geometrical singularities at the origin.Finally, it is pointed out that these types of solutions generalize, in a straightforward way, to higher dimensions.Comment: Generalize, in a straightforward way, to higher dimension

An exact self-similar solution for an expanding ball of radiation

We give an exact solution of the $5D$ Einstein equations which in 4D can be interpreted as a spherically symmetric dissipative distribution of matter, with heat flux, whose effective density and pressure are nonstatic, nonuniform, and satisfy the equation of state of radiation. The matter satisfies the usual energy and thermodynamic conditions. The energy density and temperature are related by the Stefan-Boltzmann law. The solution admits a homothetic Killing vector in $5D$, which induces the existence of self-similar symmetry in 4D, where the line element as well as the dimensionless matter quantities are invariant under a simple "scaling" group.Comment: New version expanded and improved. To appear in Int. J. Mod. Phys.

New Wrinkles on an Old Model: Correlation Between Liquid Drop Parameters and Curvature Term

The relationship between the volume and surface energy coefficients in the liquid drop A^{-1/3} expansion of nuclear masses is discussed. The volume and surface coefficients in the liquid drop expansion share the same physical origin and their physical connection is used to extend the expansion with a curvature term. A possible generalization of the Wigner term is also suggested. This connection between coefficients is used to fit the experimental nuclear masses. The excellent fit obtained with a smaller number of parameters validates the assumed physical connection.Comment: 6 pages, 2 figure

An exact solution of the five-dimensional Einstein equations with four-dimensional de Sitter-like expansion

We present an exact solution to the Einstein field equations which is Ricci and Riemann flat in five dimensions, but in four dimensions is a good model for the early vacuum-dominated universe.Comment: 6 pages; to appear in Journal of Mathematical Physics; v2: reference 3 correcte

Stability of Transparent Spherically Symmetric Thin Shells and Wormholes

The stability of transparent spherically symmetric thin shells (and wormholes) to linearized spherically symmetric perturbations about static equilibrium is examined. This work generalizes and systematizes previous studies and explores the consequences of including the cosmological constant. The approach shows how the existence (or not) of a domain wall dominates the landscape of possible equilibrium configurations.Comment: 12 pages, 7 figures, revtex. Final form to appear in Phys. Rev.

Adventures in Invariant Theory

We provide an introduction to enumerating and constructing invariants of group representations via character methods. The problem is contextualised via two case studies arising from our recent work: entanglement measures, for characterising the structure of state spaces for composite quantum systems; and Markov invariants, a robust alternative to parameter-estimation intensive methods of statistical inference in molecular phylogenetics.Comment: 12 pp, includes supplementary discussion of example

Practical applications of biomechanical principles in resistance training: moments and moment arms

Exercise professionals routinely prescribe resistance training to clients with varied goals. Therefore, they need to be able to modify the difficulty of a variety of exercises and to understand how such modifications can alter the relative joint loading on their clients so to maximise the potential for positive adaptation and to minimise injury risk. This paper is the first in a three part series that will examine how a variety of biomechanical principles and concepts have direct relevance to the prescription of resistance training for the general and athletic populations as well as for musculoskeletal injury rehabilitation. In this paper, we start by defining the terms moment (torque), moment arms, compressive, tensile and shear forces as well as joint stress (pressure). We then demonstrate how an understanding of moments and moment arms is integral to the exercise professionals’ ability to develop a systematic progression of variations of common exercises. In particular, we examine how a variety of factors including joint range of motion, body orientation, type of external loading, the lifter’s anthropometric proportions and the position of the external load will influence the difficulty of each exercise variation. We then highlight the primary results of several selected studies which have compared the resistance moment arms and joint moments, forces or stresses that are encountered during selected variations of common lower body resistance training exercises. We hope that exercise professionals will benefit from this knowledge of applied resistance training biomechanics and be better able to systematically progress exercise difficulty and to modify joint loading as a result. The two remaining articles in this series will focus on the neuromechanical properties of the human musculoskeletal system and better understanding the biomechanical implications of a variety of alternative resistance training techniques, respectively