Spectra of phase point operators in odd prime dimensions and the extended Clifford group

We analyse the role of the Extended Clifford group in classifying the spectra of phase point operators within the framework laid out by Gibbons et al for setting up Wigner distributions on discrete phase spaces based on finite fields. To do so we regard the set of all the discrete phase spaces as a symplectic vector space over the finite field. Auxiliary results include a derivation of the conjugacy classes of ${\rm ESL}(2, \mathbb{F}_N)$.Comment: Latex, 19page

On the dynamic tensile strength of Zirconium

Despite its fundamental nature, the process of dynamic tensile failure (spall) is poorly understood. Spall initiation via cracks, voids, etc, before subsequent coalesce, is known to be highly microstructure-dependant. In particular, the availability of slip planes and other methods of plastic deformation controls the onset (or lack thereof) of spall. While studies have been undertaken into the spall response of BCC and FCC materials, less attention has paid to the spall response of highly anisotropic HCP materials. Here the dynamic behaviour of zirconium is investigated via plate-impact experiments, with the aim of building on an ongoing in-house body of work investigating these highly complex materials. In particular, in this paper the effect of impact stress on spall in a commercially sourced Zr rod is considered, with apparent strain-rate softening highlighted

Patient and public involvement and engagement: Practice case study with reflections and learnings from a small rural district general hospital

The notion of patient and public involvement and engagement (PPIE) in research has been around for some time, and it is considered essential to ensure high-quality relevant research that is shared and that will make a difference. This case study of practice aims to share the PPIE practice from Dorset County Hospital NHS Foundation Trust, a small rural district general hospital. It describes the process of recruiting patients and members of the public as research volunteers, as well as the plethora of engagement and involvement activities with which they have been involved to date. This is followed by a reflection on the process and an overview of plans for the future, highlighting key challenges as well as learnings. A dedicated role to support/oversee PPIE activities is recommended to coordinate large groups of research volunteers, as well as to monitor the important impact of their input, which is considerable. Increasing diversity and access to under-served groups, and embedding the research volunteer role within the wider clinical research team, are also highlighted as fundamental challenges, as well as opportunities to make the most from this valuable resource. The case study of practice puts forward a recommendation to all research departments to embed PPIE in all of the work that they do

Mutually unbiased bases: tomography of spin states and star-product scheme

Mutually unbiased bases (MUBs) are considered within the framework of a generic star-product scheme. We rederive that a full set of MUBs is adequate for a spin tomography, i.e. knowledge of all probabilities to find a system in each MUB-state is enough for a state reconstruction. Extending the ideas of the tomographic-probability representation and the star-product scheme to MUB-tomography, dequantizer and quantizer operators for MUB-symbols of spin states and operators are introduced, ordinary and dual star-product kernels are found. Since MUB-projectors are to obey specific rules of the star-product scheme, we reveal the Lie algebraic structure of MUB-projectors and derive new relations on triple- and four-products of MUB-projectors. Example of qubits is considered in detail. MUB-tomography by means of Stern-Gerlach apparatus is discussed.Comment: 11 pages, 1 table, partially presented at the 17th Central European Workshop on Quantum Optics (CEWQO'2010), June 6-11, 2010, St. Andrews, Scotland, U

Husimi Transform of an Operator Product

It is shown that the series derived by Mizrahi, giving the Husimi transform (or covariant symbol) of an operator product, is absolutely convergent for a large class of operators. In particular, the generalized Liouville equation, describing the time evolution of the Husimi function, is absolutely convergent for a large class of Hamiltonians. By contrast, the series derived by Groenewold, giving the Weyl transform of an operator product, is often only asymptotic, or even undefined. The result is used to derive an alternative way of expressing expectation values in terms of the Husimi function. The advantage of this formula is that it applies in many of the cases where the anti-Husimi transform (or contravariant symbol) is so highly singular that it fails to exist as a tempered distribution.Comment: AMS-Latex, 13 page

On analytical solutions of f(R) modified gravity theories in FLRW cosmologies

A novel analytical method for f(R) modified theories without matter in Friedmann-Lemaitre-Robertson-Walker spacetimes is introduced. The equation of motion for the scale factor in terms of cosmic time is reduced to the equation for the evolution of the Ricci scalar R with the Hubble parameter H. The solution of equation of motion for actions of the form of power law in Ricci scalar R, is presented with a detailed elaboration of the action quadratic in R. The reverse use of the introduced method is exemplified in finding functional forms f(R) which lead to specified scale factor functions. The analytical solutions are corroborated by numerical calculations with excellent agreement. Possible further applications to the phases of inflationary expansion and late-time acceleration as well as f(R) theories with radiation are outlined.Comment: 16 pages, 6 figures. v2: minor changes, references added. v3: minor changes, more references added. v4: version to appear in IJMPD. v5: DOI and journal reference adde

Racetrack FFAG muon decay ring for nuSTORM with triplet focusing

The neutrino beam produced from muons decaying in a storage ring would be an ideal tool for precise neutrino cross section measurements and the search for sterile neutrinos due to its precisely known flavour content and spectrum. In the proposed nuSTORM facility, pions would be directly injected into a racetrack storage ring, where the circulating muon beam would be captured. In this paper we show that a muon decay ring based on a racetrack scaling FFAG (Fixed Field Alternating Gradient) with triplet focusing structures is a very promising option with potential advantages over the FODO based solution. We discuss the ring concept, machine parameters, linear optics design, beam dynamics and the injection system

Finite-precision measurement does not nullify the Kochen-Specker theorem

It is proven that any hidden variable theory of the type proposed by Meyer [Phys. Rev. Lett. {\bf 83}, 3751 (1999)], Kent [{\em ibid.} {\bf 83}, 3755 (1999)], and Clifton and Kent [Proc. R. Soc. London, Ser. A {\bf 456}, 2101 (2000)] leads to experimentally testable predictions that are in contradiction with those of quantum mechanics. Therefore, it is argued that the existence of dense Kochen-Specker-colorable sets must not be interpreted as a nullification of the physical impact of the Kochen-Specker theorem once the finite precision of real measurements is taken into account.Comment: REVTeX4, 5 page