arXiv subjects

Brian O'Sullivan

Publications and source records attributed to Brian O'Sullivan.

6 recordsLinked to original sources

arXiv2021

Quaternions, Spinors and the Hopf Fibration: Hidden Variables in Classical Mechanics

Rotations in 3 dimensional space are equally described by the SU(2) and SO(3) groups. These isomorphic groups generate the same 3D kinematics using different algebraic structures of the unit quaternion. The Hopf Fibration is a projection between the hypersphere $\mathbb{S}^3$ of the quaternion in 4D space, and the unit sphere $\mathbb{S}^2$ in 3D space. Great circles in $\mathbb{S}^3$ are mapped to points in $\mathbb{S}^2$ via the 6 Hopf maps, and are illustrated via the stereographic projection. The higher and lower dimensional spaces are connected via the $\mathbb{S}^1$ fibre bundle which consists of the global, geometric and dynamic phases. The global phase is quantized in integer multiples of $2π$ and presents itself as a natural hidden variable of Classical Mechanics.

physics.gen-ph↗

arXiv2016

Who's afraid of the Unit Quaternion ?

Far from being just a 2-level Quantum system the Qubit is a Unit Quaternion, also known as a Spinor. Therefore it follows that the Qubit is a 4-dimensional vector which traces a path on the surface of the unit 3-sphere. This is the meaning of the global phase.

physics.gen-ph↗

arXiv2015

The Mid-Infrared Instrument for the James Webb Space Telescope, VI: The Medium Resolution Spectrometer

We describe the design and performance of the Medium Resolution Spectrometer (MRS) for the JWST-MIRI instrument. The MRS incorporates four coaxial spectral channels in a compact opto-mechanical layout that generates spectral images over fields of view up to 7.7 X 7.7 arcseconds in extent and at spectral resolving powers ranging from 1,300 to 3,700. Each channel includes an all-reflective integral field unit (IFU): an 'image slicer' that reformats the input field for presentation to a grating spectrometer. Two 1024 X 1024 focal plane arrays record the output spectral images with an instantaneous spectral coverage of approximately one third of the full wavelength range of each channel. The full 5 to 28.5 micron spectrum is then obtained by making three exposures using gratings and pass-band-determining filters that are selected using just two three-position mechanisms. The expected on-orbit optical performance is presented, based on testing of the MIRI Flight Model and including spectral and spatial coverage and resolution. The point spread function of the reconstructed images is shown to be diffraction limited and the optical transmission is shown to be consistent with the design expectations.

astro-ph.IM↗

arXiv2015

The Mid-Infrared Instrument for JWST, II: Design and Build

The Mid-InfraRed Instrument (MIRI) on the James Webb Space Telescope (JWST) provides measurements over the wavelength range 5 to 28.5 microns. MIRI has, within a single 'package', four key scientific functions: photometric imaging, coronagraphy, single-source low-spectral resolving power (R ~ 100) spectroscopy, and medium-resolving power (R ~ 1500 to 3500) integral field spectroscopy. An associated cooler system maintains MIRI at its operating temperature of < 6.7 K. This paper describes the driving principles behind the design of MIRI, the primary design parameters, and their realization in terms of the 'as-built' instrument. It also describes the test program that led to delivery of the tested and calibrated Flight Model to NASA in 2012, and the confirmation after delivery of the key interface requirements.

astro-ph.IM↗

arXiv2015

The Mid-Infrared Instrument for the James Webb Space Telescope, X. Operations and Data Reduction

We describe the operations concept and data reduction plan for the Mid- Infrared Instrument (MIRI) for the James Webb Space Telescope (JWST). The overall JWST operations concept is to use Observation Templates (OTs) to provide a straightforward and intuitive way for users to specify observations. MIRI has four OTs that correspond to the four observing modes: 1.) Imaging, 2.) Coronagraphy, 3.) Low Resolution Spectroscopy, and 4.) Medium Resolution Spectroscopy. We outline the user choices and expansion of these choices into detailed instrument operations. The data reduction plans for MIRI are split into three stages, where the specificity of the reduction steps to the observation type increases with stage. The reduction starts with integration ramps: stage 1 yields uncalibrated slope images; stage 2 calibrates the slope images; and then stage 3 combines multiple calibrated slope images into high level data products (e.g. mosaics, spectral cubes, and extracted source information). Finally, we give examples of the data and data products that will be derived from each of the four different OTs.

astro-ph.IM↗

arXiv2008

Spontaneous Emission in ultra-cold spin-polarised anisotropic Fermi Seas

We examine and explain the spatial emission patterns of ultracold excited fermions in anisotropic trapping potentials in the presence of a spin polarised Fermi sea of ground state atoms. Due to the Pauli principle, the Fermi sea modifies the available phase space for the recoiling atom and thereby modifies its decay rate and the probability of the emitted photon's direction. We show that the spatial anisotropies are due to an intricate interplay between Fermi energies and degeneracy values of specific energy levels and identify a regime in which the emission will become completely directional. Our results are relevant for recent advances in trapping and manipulating cold fermionic samples experimentally and give an example of a conceptually new idea for a directional photon source.

quant-ph↗