42,280 research outputs found
Asymptotics of Relativistic Spin Networks
The stationary phase technique is used to calculate asymptotic formulae for
SO(4) Relativistic Spin Networks. For the tetrahedral spin network this gives
the square of the Ponzano-Regge asymptotic formula for the SU(2) 6j symbol. For
the 4-simplex (10j-symbol) the asymptotic formula is compared with numerical
calculations of the Spin Network evaluation. Finally we discuss the asymptotics
of the SO(3,1) 10j-symbol.Comment: 31 pages, latex. v3: minor clarification
Semiclassical Limits of Extended Racah Coefficients
We explore the geometry and asymptotics of extended Racah coeffecients. The
extension is shown to have a simple relationship to the Racah coefficients for
the positive discrete unitary representation series of SU(1,1) which is
explicitly defined. Moreover, it is found that this extension may be
geometrically identified with two types of Lorentzian tetrahedra for which all
the faces are timelike.
The asymptotic formulae derived for the extension are found to have a similar
form to the standard Ponzano-Regge asymptotic formulae for the SU(2) 6j symbol
and so should be viable for use in a state sum for three dimensional Lorentzian
quantum gravity.Comment: Latex2e - 26 pages, 6 figures. Uses AMS-fonts, AMS-LaTeX, epsf.tex
and texdraw. Revised version with improved clarity and additional result
Feynman diagams coupled to three-dimensional quantum gravity
A framework for quantum field theory coupled to three-dimensional quantum
gravity is proposed. The coupling with quantum gravity regulates the Feynman
diagrams. One recovers the usual Feynman amplitudes in the limit as the
cosmological constant tends to zero.Comment: 7 pages. v2: minor corrections, added re
Investigations into a diffusion model of dry heat sterilization Interim report
Diffusion model of dry heat sterilizatio
Design and fabrication of four pin high pressure squib
Development of high pressure squibs for deep space probe vehicle
A superconducting cavity bus for single Nitrogen Vacancy defect centres in diamond
Circuit-QED has demonstrated very strong coupling between individual
microwave photons trapped in a superconducting coplanar resonator and nearby
superconducting qubits. In this work we show how, by designing a novel
interconnect, one can strongly connect the superconducting resonator, via a
magnetic interaction, to a small number (perhaps single), of electronic spins.
By choosing the electronic spin to be within a Nitrogen Vacancy centre in
diamond one can perform optical readout, polarization and control of this
electron spin using microwave and radio frequency irradiation. More
importantly, by utilising Nitrogen Vacancy centres with nearby 13C nuclei,
using this interconnect, one has the potential build a quantum device where the
nuclear spin qubits are connected over centimeter distances via the Nitrogen
Vacancy electronic spins interacting through the superconducting bus.Comment: 4 pages, 6 figure
Electric field formulation for thin film magnetization problems
We derive a variational formulation for thin film magnetization problems in
type-II superconductors written in terms of two variables, the electric field
and the magnetization function. A numerical method, based on this formulation,
makes it possible to accurately compute all variables of interest, including
the electric field, for any value of the power in the power law current-voltage
relation characterizing the superconducting material. For high power values we
obtain a good approximation to the critical state model solution. Numerical
simulation results are presented for simply and multiply connected films, and
also for an inhomogeneous film.Comment: 15 p., submitte
On the causal Barrett--Crane model: measure, coupling constant, Wick rotation, symmetries and observables
We discuss various features and details of two versions of the Barrett-Crane
spin foam model of quantum gravity, first of the Spin(4)-symmetric Riemannian
model and second of the SL(2,C)-symmetric Lorentzian version in which all
tetrahedra are space-like. Recently, Livine and Oriti proposed to introduce a
causal structure into the Lorentzian Barrett--Crane model from which one can
construct a path integral that corresponds to the causal (Feynman) propagator.
We show how to obtain convergent integrals for the 10j-symbols and how a
dimensionless constant can be introduced into the model. We propose a `Wick
rotation' which turns the rapidly oscillating complex amplitudes of the Feynman
path integral into positive real and bounded weights. This construction does
not yet have the status of a theorem, but it can be used as an alternative
definition of the propagator and makes the causal model accessible by standard
numerical simulation algorithms. In addition, we identify the local symmetries
of the models and show how their four-simplex amplitudes can be re-expressed in
terms of the ordinary relativistic 10j-symbols. Finally, motivated by possible
numerical simulations, we express the matrix elements that are defined by the
model, in terms of the continuous connection variables and determine the most
general observable in the connection picture. Everything is done on a fixed
two-complex.Comment: 22 pages, LaTeX 2e, 1 figur
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