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