Implications of Lorentz covariance for the guidance equation in two-slit quantum interference

It is known that Lorentz covariance fixes uniquely the current and the associated guidance law in the trajectory interpretation of quantum mechanics for spin particles. In the non-relativistic domain this implies a guidance law for the electron which differs by an additional spin-dependent term from that originally proposed by de Broglie and Bohm. In this paper we explore some of the implications of the modified guidance law. We bring out a property of mutual dependence in the particle coordinates that arises in product states, and show that the quantum potential has scalar and vector components which implies the particle is subject to a Lorentz-like force. The conditions for the classical limit and the limit of negligible spin are given, and the empirical sufficiency of the model is demonstrated. We then present a series of calculations of the trajectories based on two-dimensional Gaussian wave packets which illustrate how the additional spin-dependent term plays a significant role in structuring both the individual trajectories and the ensemble. The single packet corresponds to quantum inertial motion. The distinct features encountered when the wavefunction is a product or a superposition are explored, and the trajectories that model the two-slit experiment are given. The latter paths exhibit several new characteristics compared with the original de Broglie-Bohm ones, such as crossing of the axis of symmetry.Comment: 27 pages including 6 pages of figure

Modelling Gaia CCD pixels with Silvaco 3D engineering software

Gaia will only achieve its unprecedented measurement accuracy requirements with detailed calibration and correction for radiation damage. We present our Silvaco 3D engineering software model of the Gaia CCD pixel and two of its applications for Gaia: (1) physically interpreting supplementary buried channel (SBC) capacity measurements (pocket-pumping and first pixel response) in terms of e2v manufacturing doping alignment tolerances; and (2) deriving electron densities within a charge packet as a function of the number of constituent electrons and 3D position within the charge packet as input to microscopic models being developed to simulate radiation damage.Comment: 4 pages, 3 figures, contributed poster, appearing in proceedings of the ELSA conference: Gaia, at the frontiers of astrometry, 7-11 June 2010, S\`evres, Pari

Digging supplementary buried channels: investigating the notch architecture within the CCD pixels on ESA's Gaia satellite

The European Space Agency (ESA) Gaia satellite has 106 CCD image sensors which will suffer from increased charge transfer inefficiency (CTI) as a result of radiation damage. To aid the mitigation at low signal levels, the CCD design includes Supplementary Buried Channels (SBCs, otherwise known as `notches') within each CCD column. We present the largest published sample of Gaia CCD SBC Full Well Capacity (FWC) laboratory measurements and simulations based on 13 devices. We find that Gaia CCDs manufactured post-2004 have SBCs with FWCs in the upper half of each CCD that are systematically smaller by two orders of magnitude (<50 electrons) compared to those manufactured pre-2004 (thousands of electrons). Gaia's faint star (13 < G < 20 mag) astrometric performance predictions by Prod'homme et al. and Holl et al. use pre-2004 SBC FWCs as inputs to their simulations. However, all the CCDs already integrated onto the satellite for the 2013 launch are post-2004. SBC FWC measurements are not available for one of our five post-2004 CCDs but the fact it meets Gaia's image location requirements suggests it has SBC FWCs similar to pre-2004. It is too late to measure the SBC FWCs onboard the satellite and it is not possible to theoretically predict them. Gaia's faint star astrometric performance predictions depend on knowledge of the onboard SBC FWCs but as these are currently unavailable, it is not known how representative of the whole focal plane the current predictions are. Therefore, we suggest Gaia's initial in-orbit calibrations should include measurement of the onboard SBC FWCs. We present a potential method to do this. Faint star astrometric performance predictions based on onboard SBC FWCs at the start of the mission would allow satellite operating conditions or CTI software mitigation to be further optimised to improve the scientific return of Gaia.Comment: Accepted for publication in MNRAS, 16 pages, 19 figure

Modelling electron distributions within ESA's Gaia satellite CCD pixels to mitigate radiation damage

The Gaia satellite is a high-precision astrometry, photometry and spectroscopic ESA cornerstone mission, currently scheduled for launch in 2012. Its primary science drivers are the composition, formation and evolution of the Galaxy. Gaia will achieve its unprecedented positional accuracy requirements with detailed calibration and correction for radiation damage. At L2, protons cause displacement damage in the silicon of CCDs. The resulting traps capture and emit electrons from passing charge packets in the CCD pixel, distorting the image PSF and biasing its centroid. Microscopic models of Gaia's CCDs are being developed to simulate this effect. The key to calculating the probability of an electron being captured by a trap is the 3D electron density within each CCD pixel. However, this has not been physically modelled for the Gaia CCD pixels. In Seabroke, Holland & Cropper (2008), the first paper of this series, we motivated the need for such specialised 3D device modelling and outlined how its future results will fit into Gaia's overall radiation calibration strategy. In this paper, the second of the series, we present our first results using Silvaco's physics-based, engineering software: the ATLAS device simulation framework. Inputting a doping profile, pixel geometry and materials into ATLAS and comparing the results to other simulations reveals that ATLAS has a free parameter, fixed oxide charge, that needs to be calibrated. ATLAS is successfully benchmarked against other simulations and measurements of a test device, identifying how to use it to model Gaia pixels and highlighting the effect of different doping approximations.Comment: 12 pages, 6 figures, appearing in Proc. of SPIE Optics and Photonics Conference (Focal Plane Arrays for Space telescopes IV), 2-6 August 2009, San Diego, US

I-Xe analysis of a magnetic separate from Lodranite GRA95209

I-Xe dating of a magnetic mineral separate from lodranite GRA95209 suggests that peak temperatures (and therefore melt migration) occurred early, at least a few million years before closure of the I-Xe system in phosphates from Acapulco

Proof Theory and Ordered Groups

Ordering theorems, characterizing when partial orders of a group extend to total orders, are used to generate hypersequent calculi for varieties of lattice-ordered groups (l-groups). These calculi are then used to provide new proofs of theorems arising in the theory of ordered groups. More precisely: an analytic calculus for abelian l-groups is generated using an ordering theorem for abelian groups; a calculus is generated for l-groups and new decidability proofs are obtained for the equational theory of this variety and extending finite subsets of free groups to right orders; and a calculus for representable l-groups is generated and a new proof is obtained that free groups are orderable

Search for Q: single grains Xe isotope analysis of carbonaceous residue from Yilmia

We analyse Xe in single grains in HF-HCl residue from Yilmia using RELAX mass spectrometer