Close Approach during Hard Binary--Binary Scattering

We report on an extensive series of numerical experiments of binary--binary scattering, analysing the cross--section for close approach during interactions for a range of hard binary parameters of interest in globular cluster cores. We consider the implied rate for tidal interactions for different globular clusters and compare our results with previous, complementary estimates of stellar collision rates in globular clusters. We find that the collision rate for binary--binary encounters dominates in low density clusters if the binary fraction in the cluster is larger than $0.2$ for wide main--sequence binaries. In dense clusters binary--single interactions dominate the collision rate and the core binary fraction must be \ltorder 0.1 per decade in semi--major axis or too many collisions take place compared to observations. The rates are consistent if binaries with semi--major axes $\sim 100 AU$ are overabundant in low density clusters or if breakup and ejection substantially lowers the binary fraction in denser clusters. Given reasonable assumptions about fractions of binaries in the cores of low density clusters such as NGC~5053, we cannot account for all the observed blue stragglers by stellar collisions during binary encounters, suggesting a substantial fraction may be due to coalescence of tight primordial binaries.Comment: 13 pages including 13 ps figures. MNRAS in pres

The Optimal Single Copy Measurement for the Hidden Subgroup Problem

The optimization of measurements for the state distinction problem has recently been applied to the theory of quantum algorithms with considerable successes, including efficient new quantum algorithms for the non-abelian hidden subgroup problem. Previous work has identified the optimal single copy measurement for the hidden subgroup problem over abelian groups as well as for the non-abelian problem in the setting where the subgroups are restricted to be all conjugate to each other. Here we describe the optimal single copy measurement for the hidden subgroup problem when all of the subgroups of the group are given with equal a priori probability. The optimal measurement is seen to be a hybrid of the two previously discovered single copy optimal measurements for the hidden subgroup problem.Comment: 8 pages. Error in main proof fixe

Coherence-Preserving Quantum Bits

Real quantum systems couple to their environment and lose their intrinsic quantum nature through the process known as decoherence. Here we present a method for minimizing decoherence by making it energetically unfavorable. We present a Hamiltonian made up solely of two-body interactions between four two-level systems (qubits) which has a two-fold degenerate ground state. This degenerate ground state has the property that any decoherence process acting on an individual physical qubit must supply energy from the bath to the system. Quantum information can be encoded into the degeneracy of the ground state and such coherence-preserving qubits will then be robust to local decoherence at low bath temperatures. We show how this quantum information can be universally manipulated and indicate how this approach may be applied to a quantum dot quantum computer.Comment: 5 pages, 1 figur

Weak Gravitational Flexion

Flexion is the significant third-order weak gravitational lensing effect responsible for the weakly skewed and arc-like appearance of lensed galaxies. Here we demonstrate how flexion measurements can be used to measure galaxy halo density profiles and large-scale structure on non-linear scales, via galaxy-galaxy lensing, dark matter mapping and cosmic flexion correlation functions. We describe the origin of gravitational flexion, and discuss its four components, two of which are first described here. We also introduce an efficient complex formalism for all orders of lensing distortion. We proceed to examine the flexion predictions for galaxy-galaxy lensing, examining isothermal sphere and Navarro, Frenk & White (NFW) profiles and both circularly symmetric and elliptical cases. We show that in combination with shear we can precisely measure galaxy masses and NFW halo concentrations. We also show how flexion measurements can be used to reconstruct mass maps in 2-D projection on the sky, and in 3-D in combination with redshift data. Finally, we examine the predictions for cosmic flexion, including convergence-flexion cross-correlations, and find that the signal is an effective probe of structure on non-linear scales.Comment: 17 pages, including 12 figures, submitted to MNRA

The reduced cost of providing a nationally recognised service for familial hypercholesterolaemia

OBJECTIVE: Familial hypercholesterolaemia (FH) affects 1 in 500 people in the UK population and is associated with premature morbidity and mortality from coronary heart disease. In 2008, National Institute for Health and Care Excellence (NICE) recommended genetic testing of potential FH index cases and cascade testing of their relatives. Commissioners have been slow to respond although there is strong evidence of cost and clinical effectiveness. Our study quantifies the recent reduced cost of providing a FH service using generic atorvastatin and compares NICE costing estimates with three suggested alternative models of care (a specialist-led service, a dual model service where general practitioners (GPs) can access specialist advice, and a GP-led service).METHODS: Revision of existing 3?year costing template provided by NICE for FH services, and prediction of costs for running a programme over 10?years. Costs were modelled for the first population-based FH service in England which covers Southampton, Hampshire, Isle of Wight and Portsmouth (SHIP). Population 1.95 million.RESULTS: With expiry of the Lipitor (Pfizer atorvastatin) patent the cost of providing a 10-year FH service in SHIP reduces by 42.5% (£4.88 million on patent vs £2.80 million off patent). Further cost reductions are possible as a result of the reduced cost of DNA testing, more management in general practice, and lower referral rates to specialists. For instance a dual-care model with GP management of patients supported by specialist advice when required, costs £1.89 million.CONCLUSIONS: The three alternative models of care are now <50% of the cost of the original estimates undertaken by NICE

Finite automata for caching in matrix product algorithms

A diagram is introduced for visualizing matrix product states which makes transparent a connection between matrix product factorizations of states and operators, and complex weighted finite state automata. It is then shown how one can proceed in the opposite direction: writing an automaton that ``generates'' an operator gives one an immediate matrix product factorization of it. Matrix product factorizations have the advantage of reducing the cost of computing expectation values by facilitating caching of intermediate calculations. Thus our connection to complex weighted finite state automata yields insight into what allows for efficient caching in matrix product algorithms. Finally, these techniques are generalized to the case of multiple dimensions.Comment: 18 pages, 19 figures, LaTeX; numerous improvements have been made to the manuscript in response to referee feedbac

Few-body spin couplings and their implications for universal quantum computation

Electron spins in semiconductor quantum dots are promising candidates for the experimental realization of solid-state qubits. We analyze the dynamics of a system of three qubits arranged in a linear geometry and a system of four qubits arranged in a square geometry. Calculations are performed for several quantum dot confining potentials. In the three-qubit case, three-body effects are identified that have an important quantitative influence upon quantum computation. In the four-qubit case, the full Hamiltonian is found to include both three-body and four-body interactions that significantly influence the dynamics in physically relevant parameter regimes. We consider the implications of these results for the encoded universality paradigm applied to the four-electron qubit code; in particular, we consider what is required to circumvent the four-body effects in an encoded system (four spins per encoded qubit) by the appropriate tuning of experimental parameters.Comment: 1st version: 33 pages, 25 figures. Described at APS March Meeting in 2004 (P36.010) and 2005 (B17.00009). Most figures made uglier here to reduce file size. 2nd version: 19 pages, 9 figures. Much mathematical detail chopped away after hearing from journal referee; a few typos correcte

A double-helix neutron detector using micron-size B-10 powder

A double-helix electrode configuration is combined with a $^{10}$B powder coating technique to build large-area (9 in $\times$ 36 in) neutron detectors. The neutron detection efficiency for each of the four prototypes is comparable to a single 2-bar $^3$He drift tube of the same length (36 in). One unit has been operational continuously for 18 months and the change of efficiency is less than 1%. An analytic model for pulse heigh spectra is described and the predicted mean film thickness agrees with the experiment to within 30%. Further detector optimization is possible through film texture, power size, moderator box and gas. The estimated production cost per unit is less than 3k US\$ and the technology is thus suitable for deployment in large numbers

Probing the presence of a single or binary black hole in the globular cluster NGC 6752 with pulsar dynamics

The five millisecond pulsars that inhabit NGC 6752 display locations or accelerations that are quite unusual compared to all other pulsars known in globular clusters. In particular PSR-A, a binary pulsar, lives in the cluster halo, while PSR-B and PSR-E, located in the core, show remarkably high negative spin derivatives. This is suggestive that some uncommon dynamical process is at play in the cluster core that we attribute to the presence of a massive perturber. We here investigate whether a single intermediate-mass black hole, lying on the extrapolation of the Mass versus Sigma relation observed in galaxy spheroids, or a less massive binary consisting of two black holes could play the requested role. To this purpose we simulated binary-binary encounters involving PSR-A, its companion star, and the black hole(s). Various scenarios are discussed in detail. In our close 4-body encounters, a black hole-black hole binary may attract on a long-term stable orbit a millisecond pulsar. Timing measurements on the captured satellite-pulsar, member of a hierarchical triplet, could unambiguously unveil the presence of a black hole(s) in the core of a globular cluster.Comment: 13 pages, 8 figures, Accepted for publication in The Astrophysical Journa