5,979 research outputs found

### Lagrange-Poincare field equations

The Lagrange-Poincare equations of classical mechanics are cast into a field
theoretic context together with their associated constrained variational
principle. An integrability/reconstruction condition is established that
relates solutions of the original problem with those of the reduced problem.
The Kelvin-Noether theorem is formulated in this context. Applications to the
isoperimetric problem, the Skyrme model for meson interaction, metamorphosis
image dynamics, and molecular strands illustrate various aspects of the theory.Comment: Submitted to Journal of Geometry and Physics, 45 pages, 1 figur

### Random Hamiltonian in thermal equilibrium

A framework for the investigation of disordered quantum systems in thermal
equilibrium is proposed. The approach is based on a dynamical model--which
consists of a combination of a double-bracket gradient flow and a uniform
Brownian fluctuation--that `equilibrates' the Hamiltonian into a canonical
distribution. The resulting equilibrium state is used to calculate quenched and
annealed averages of quantum observables.Comment: 8 pages, 4 figures. To appear in DICE 2008 conference proceeding

### Hamiltonian statistical mechanics

A framework for statistical-mechanical analysis of quantum Hamiltonians is
introduced. The approach is based upon a gradient flow equation in the space of
Hamiltonians such that the eigenvectors of the initial Hamiltonian evolve
toward those of the reference Hamiltonian. The nonlinear double-bracket
equation governing the flow is such that the eigenvalues of the initial
Hamiltonian remain unperturbed. The space of Hamiltonians is foliated by
compact invariant subspaces, which permits the construction of statistical
distributions over the Hamiltonians. In two dimensions, an explicit dynamical
model is introduced, wherein the density function on the space of Hamiltonians
approaches an equilibrium state characterised by the canonical ensemble. This
is used to compute quenched and annealed averages of quantum observables.Comment: 8 pages, 2 figures, references adde

### Cosmology with positive and negative exponential potentials

We present a phase-plane analysis of cosmologies containing a scalar field
$\phi$ with an exponential potential $V \propto \exp(-\lambda \kappa \phi)$
where $\kappa^2 = 8\pi G$ and $V$ may be positive or negative. We show that
power-law kinetic-potential scaling solutions only exist for sufficiently flat
($\lambda^26$) negative
potentials. The latter correspond to a class of ever-expanding cosmologies with
negative potential. However we show that these expanding solutions with a
negative potential are to unstable in the presence of ordinary matter, spatial
curvature or anisotropic shear, and generic solutions always recollapse to a
singularity. Power-law kinetic-potential scaling solutions are the late-time
attractor in a collapsing universe for steep negative potentials (the ekpyrotic
scenario) and stable against matter, curvature or shear perturbations.
Otherwise kinetic-dominated solutions are the attractor during collapse (the
pre big bang scenario) and are only marginally stable with respect to
anisotropic shear.Comment: 8 pages, latex with revtex, 9 figure

### Testing A (Stringy) Model of Quantum Gravity

I discuss a specific model of space-time foam, inspired by the modern
non-perturbative approach to string theory (D-branes). The model views our
world as a three brane, intersecting with D-particles that represent stringy
quantum gravity effects, which can be real or virtual. In this picture, matter
is represented generically by (closed or open) strings on the D3 brane
propagating in such a background. Scattering of the (matter) strings off the
D-particles causes recoil of the latter, which in turn results in a distortion
of the surrounding space-time fluid and the formation of (microscopic, i.e.
Planckian size) horizons around the defects. As a mean-field result, the
dispersion relation of the various particle excitations is modified, leading to
non-trivial optical properties of the space time, for instance a non-trivial
refractive index for the case of photons or other massless probes. Such models
make falsifiable predictions, that may be tested experimentally in the
foreseeable future. I describe a few such tests, ranging from observations of
light from distant gamma-ray-bursters and ultra high energy cosmic rays, to
tests using gravity-wave interferometric devices and terrestrial particle
physics experients involving, for instance, neutral kaons.Comment: 25 pages LATEX, four figures incorporated, uses special proceedings
style. Invited talk at the third international conference on Dark Matter in
Astro and Particle Physics, DARK2000, Heidelberg, Germany, July 10-15 200

### Regular spherical dust spacetimes

Physical (and weak) regularity conditions are used to determine and classify
all the possible types of spherically symmetric dust spacetimes in general
relativity. This work unifies and completes various earlier results. The
junction conditions are described for general non-comoving (and non-null)
surfaces, and the limits of kinematical quantities are given on all comoving
surfaces where there is Darmois matching. We show that an inhomogeneous
generalisation of the Kantowski-Sachs metric may be joined to the
Lemaitre-Tolman-Bondi metric. All the possible spacetimes are explicitly
divided into four groups according to topology, including a group in which the
spatial sections have the topology of a 3-torus. The recollapse conjecture (for
these spacetimes) follows naturally in this approach.Comment: Minor improvements, additional references. Accepted by GR

### On CPT Symmetry: Cosmological, Quantum-Gravitational and other possible violations and their phenomenology

I discuss various ways in which CPT symmetry may be violated, and their
phenomenology in current or immediate future experimental facilities, both
terrestrial and astrophysical. Specifically, I discuss first violations of CPT
symmetry due to the impossibility of defining a scattering matrix as a
consequence of the existence of microscopic or macroscopic space-time
boundaries, such as Planck-scale Black-Hole (event) horizons, or cosmological
horizons due to the presence of a (positive) cosmological constant in the
Universe. Second, I discuss CPT violation due to breaking of Lorentz symmetry,
which may characterize certain approaches to quantum gravity, and third, I
describe models of CPT non invariance due to violations of locality of
interactions. In each of the above categories I discuss experimental
sensitivities. I argue that the majority of Lorentz-violating cases of CPT
breaking, with minimal (linear) suppression by the Planck-mass scale, are
already excluded by current experimental tests. There are however some
(stringy) models which can evade these constraints.Comment: 27 pages latex, Conference talk Beyond the Desert 200

### Exploring taboo issues in professional sport through a fictional approach

While the need to consider life course issues in elite sport research and practice is increasingly recognised, some experiences still seem to be considered too dangerous to explore. Consequently, stories of these experiences are silenced and the ethical and moral questions they pose fail to be acknowledged, understood or debated. This paper presents an ethnographic fiction through which we explore a sensitive set of experiences that were uncovered during our research with professional sportspeople. Through a multiâlayered reconstruction, the story reveals the complex, but significant, relationships that exist between identity, cultural narratives and embodied experiences. After the telling we consider how the story has stimulated reflective practice among students, researchers and practitioners. While there are risks involved in writing and sharing taboo stories, the feedback we have received suggests that storytelling can be an effective pedagogical tool in education and professional development

### False Vacuum Inflation with a Quartic Potential

We consider a variant of Hybrid Inflation, where inflation is driven by two
interacting scalar fields, one of which has a `Mexican hat' potential and the
other a quartic potential. Given the appropriate initial conditions one of the
fields can be trapped in a false vacuum state, supported by couplings to the
other field. The energy of this vacuum can be used to drive inflation, which
ends when the vacuum decays to one of its true minima. Depending on parameters,
it is possible for inflation to proceed via two separate epochs, with the
potential temporarily steepening sufficiently to suspend inflation. We use
numerical simulations to analyse the possibilities, and emphasise the
shortcomings of the slow-roll approximation for analysing this scenario. We
also calculate the density perturbations produced, which can have a spectral
index greater than one.Comment: 10 pages, RevTeX 3.0, no figure

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