77 research outputs found
A Bloch-Sphere-Type Model for Two Qubits in the Geometric Algebra of a 6-D Euclidean Vector Space
Geometric algebra is a mathematical structure that is inherent in any metric
vector space, and defined by the requirement that the metric tensor is given by
the scalar part of the product of vectors. It provides a natural framework in
which to represent the classical groups as subgroups of rotation groups, and
similarly their Lie algebras. In this article we show how the geometric algebra
of a six-dimensional real Euclidean vector space naturally allows one to
construct the special unitary group on a two-qubit (quantum bit) Hilbert space,
in a fashion similar to that used in the well-established Bloch sphere model
for a single qubit. This is then used to illustrate the Cartan decompositions
and subalgebras of the four-dimensional special unitary group, which have
recently been used by J. Zhang, J. Vala, S. Sastry and K. B. Whaley [Phys. Rev.
A 67, 042313, 2003] to study the entangling capabilities of two-qubit
unitaries.Comment: 14 pages, 2 figures, in press (Proceedings of SPIE Conference on
Defense & Security
Fermion absorption cross section of a Schwarzschild black hole
We study the absorption of massive spin-half particles by a small
Schwarzschild black hole by numerically solving the single-particle Dirac
equation in Painleve-Gullstrand coordinates. We calculate the absorption cross
section for a range of gravitational couplings Mm/m_P^2 and incident particle
energies E. At high couplings, where the Schwarzschild radius R_S is much
greater than the wavelength lambda, we find that the cross section approaches
the classical result for a point particle. At intermediate couplings we find
oscillations around the classical limit whose precise form depends on the
particle mass. These oscillations give quantum violations of the equivalence
principle. At high energies the cross section converges on the geometric-optics
value of 27 \pi R_S^2/4, and at low energies we find agreement with an
approximation derived by Unruh. When the hole is much smaller than the particle
wavelength we confirm that the minimum possible cross section approaches \pi
R_S^2/2.Comment: 11 pages, 3 figure
Quadratic Lagrangians and Topology in Gauge Theory Gravity
We consider topological contributions to the action integral in a gauge
theory formulation of gravity. Two topological invariants are found and are
shown to arise from the scalar and pseudoscalar parts of a single integral.
Neither of these action integrals contribute to the classical field equations.
An identity is found for the invariants that is valid for non-symmetric Riemann
tensors, generalizing the usual GR expression for the topological invariants.
The link with Yang-Mills instantons in Euclidean gravity is also explored. Ten
independent quadratic terms are constructed from the Riemann tensor, and the
topological invariants reduce these to eight possible independent terms for a
quadratic Lagrangian. The resulting field equations for the parity
non-violating terms are presented. Our derivations of these results are
considerably simpler that those found in the literature
New Techniques for Analysing Axisymmetric Gravitational Systems. 1. Vacuum Fields
A new framework for analysing the gravitational fields in a stationary,
axisymmetric configuration is introduced. The method is used to construct a
complete set of field equations for the vacuum region outside a rotating
source. These equations are under-determined. Restricting the Weyl tensor to
type D produces a set of equations which can be solved, and a range of new
techniques are introduced to simplify the problem. Imposing the further
condition that the solution is asymptotically flat yields the Kerr solution
uniquely. The implications of this result for the no-hair theorem are
discussed. The techniques developed here have many other applications, which
are described in the conclusions.Comment: 30 pages, no figure
Closed Universes, de Sitter Space and Inflation
We present a new approach to constructing inflationary models in closed
universes. Conformal embedding of closed-universe models in a de Sitter
background suggests a quantisation condition on the available conformal time.
This condition implies that the universe is closed at no greater than the 10%
level. When a massive scalar field is introduced to drive an inflationary phase
this figure is reduced to closure at nearer the 1% level. In order to enforce
the constraint on the available conformal time we need to consider conditions
in the universe before the onset of inflation. A formal series around the
initial singularity is constructed, which rests on a pair of dimensionless,
scale-invariant parameters. For physically-acceptable models we find that both
parameters are of order unity, so no fine tuning is required, except in the
mass of the scalar field. For typical values of the input parameters we predict
the observed values of the cosmological parameters, including the magnitude of
the cosmological constant. The model produces a very good fit to the most
recent CMBR data. The primordial curvature spectrum predicts the low-l fall-off
in the CMB power spectrum observed by WMAP. The spectrum also predicts a
fall-off in the matter spectrum at high k, relative to a power law. A further
prediction of our model is a large tensor mode component, with r~0.2.Comment: 38 pages, 25 figure
Span of control in supervision of rail track work
The supervision of engineering work on the railways has received relatively little examination despite being both safety-critical in its own right and having wider implications for the successful running of the railways. The present paper is concerned with understanding the factors that make different engineering works perceived as easier or harder to manage. We describe an approach building on notions of âspan of controlâ, through which we developed the TOECAP inventory (Team, Organisation, Environment, Communication, Activity and Personal). This tool was validated through both interviews and questionnaires. As well as identifying the physical factors involved, the work also emphasised the importance of collaborative and attitudinal factors. We conclude by discussing limitations of the present work and future directions for development
Priority setting in Indigenous health: assessing priority setting process and criteria that should guide the health system to improve Indigenous Australian health
Phylogenetic ctDNA analysis depicts early-stage lung cancer evolution.
The early detection of relapse following primary surgery for non-small-cell lung cancer and the characterization of emerging subclones, which seed metastatic sites, might offer new therapeutic approaches for limiting tumour recurrence. The ability to track the evolutionary dynamics of early-stage lung cancer non-invasively in circulating tumour DNA (ctDNA) has not yet been demonstrated. Here we use a tumour-specific phylogenetic approach to profile the ctDNA of the first 100 TRACERx (Tracking Non-Small-Cell Lung Cancer Evolution Through Therapy (Rx)) study participants, including one patient who was also recruited to the PEACE (Posthumous Evaluation of Advanced Cancer Environment) post-mortem study. We identify independent predictors of ctDNA release and analyse the tumour-volume detection limit. Through blinded profiling of postoperative plasma, we observe evidence of adjuvant chemotherapy resistance and identify patients who are very likely to experience recurrence of their lung cancer. Finally, we show that phylogenetic ctDNA profiling tracks the subclonal nature of lung cancer relapse and metastasis, providing a new approach for ctDNA-driven therapeutic studies
An Evaluation Schema for the Ethical Use of Autonomous Robotic Systems in Security Applications
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