Bargmann invariants and off-diagonal geometric phases for multi-level quantum systems -- a unitary group approach

We investigate the geometric phases and the Bargmann invariants associated with a multi-level quantum systems. In particular, we show that a full set of `gauge-invariant' objects for an $n$-level system consists of $n$ geometric phases and ${1/2}(n-1)(n-2)$ algebraically independent 4-vertex Bargmann invariants. In the process of establishing this result we develop a canonical form for U(n) matrices which is useful in its own right. We show that the recently discovered `off-diagonal' geometric phases [N. Manini and F. Pistolesi, Phys. Rev. Lett. 8, 3067 (2000)] can be completely analysed in terms of the basic building blocks developed in this work. This result liberates the off-diagonal phases from the assumption of adiabaticity used in arriving at them.Comment: 13 pages, latex, no figure

Near-inertial wave scattering by random flows

The impact of a turbulent flow on wind-driven oceanic near-inertial waves is examined using a linearised shallow-water model of the mixed layer. Modelling the flow as a homogeneous and stationary random process with spatial scales comparable to the wavelengths, we derive a transport (or kinetic) equation governing wave-energy transfers in both physical and spectral spaces. This equation describes the scattering of the waves by the flow which results in a redistribution of energy between waves with the same frequency (or, equivalently, with the same wavenumber) and, for isotropic flows, in the isotropisation of the wave field. The time scales for the scattering and isotropisation are obtained explicitly and found to be of the order of tens of days for typical oceanic parameters. The predictions inferred from the transport equation are confirmed by a series of numerical simulations. Two situations in which near-inertial waves are strongly influenced by flow scattering are investigated through dedicated nonlinear shallow-water simulations. In the first, a wavepacket propagating equatorwards as a result from the $\beta$-effect is shown to be slowed down and dispersed both zonally and meridionally by scattering. In the second, waves generated by moving cyclones are shown to be strongly disturbed by scattering, leading again to an increased dispersion.Comment: Accepted for publication in Phys. Rev. Fluid

An optical fiber hydrogen sensor using a palladium-coated ball lens

A self-referenced optical fiber refractometer using a ball lens as a sensor head has been developed and characterized. A 350-μm ball lens created at the tip of a single mode fiber has been coated with a 40-nm optically thin layer of palladium that reacts with hydrogen to form a hydride, which has a lower reflectivity than pure palladium. Optical reflectance measurements from the tip of the ball lens were performed to determine the hydrogen response. The change in reflectivity is proportional to the hydrogen concentration in the range 0% to 1% hydrogen in air with a detection limit down to 10 ppm (1σ) in air. This technique offers a simple sensor head arrangement, with a larger sampling area (~40 times) than a typical single-mode fiber core. A statistical image analysis of a palladium film, with cracks created by accelerated failure, confirms that the anticipated sensor area for a ball lens sensor head has a more predictable reflectivity than that of a bare fiber core

Take it or leave it: prefrontal control in recreational cocaine users.

Though stimulant drugs such as cocaine are considered highly addictive, some individuals report recreational use over long periods without developing dependence. Difficulties in response inhibition have been hypothesized to contribute to dependence, but previous studies investigating response inhibition in recreational cocaine users have reported conflicting results. Performance on a stop-signal task was examined in 24 recreational cocaine users and 32 healthy non-drug using control participants matched for age, gender and verbal intelligence during functional magnetic resonance imaging scanning. The two groups were further matched on traumatic childhood histories and the absence of family histories of addiction. Results revealed that recreational cocaine users did not significantly differ from controls on any index of task performance, including response execution and stop-signal reaction time, with the latter averaging 198 ms in both groups. Functional magnetic resonance imaging analyses indicated that, compared with controls, stopping in the recreational users was associated with increased activation in the pre-supplementary motor area but not the right inferior frontal cortex. Thus, findings imply intact response inhibition abilities in recreational cocaine users, though the distinct pattern of accompanying activation suggests increased recruitment of brain areas implicated in response inhibition. This increased recruitment could be attributed to compensatory mechanisms that enable preserved cognitive control in this group, possibly relating to their hypothetical resilience to stimulant drug dependence. Such overactivation, alternatively, may be attributable to prolonged cocaine use leading to neuroplastic adaptations.This work was funded by a Medical Research Council (MRC) research grant to KDE, ETB and TWR (G0701497) and was conducted within the Behavioural and Clinical Neuroscience Institute, University of Cambridge, UK, which is supported by a joint award from the MRC and the Wellcome Trust; Both KDE and PSJ were supported by the MRC, SM was supported by a Wellcome Trust grant (089589/Z/09/Z) awarded to TW Robbins.This is the final version of the article. It first appeared from NPG via http://dx.doi.org/10.1038/tp.2015.8

Polyhedral Analysis using Parametric Objectives

The abstract domain of polyhedra lies at the heart of many program analysis techniques. However, its operations can be expensive, precluding their application to polyhedra that involve many variables. This paper describes a new approach to computing polyhedral domain operations. The core of this approach is an algorithm to calculate variable elimination (projection) based on parametric linear programming. The algorithm enumerates only non-redundant inequalities of the projection space, hence permits anytime approximation of the output

Chemiluminescence from the reaction of tin(II) with tris(2,2\u27-bipyridyl)ruthenium(III)

Unlike many other metal and metalloid ions, tin(II) elicits intense, analytically useful chemiluminescence upon reaction with tris(2,2΄-bipyridyl)ruthenium(III) in acidic aqueous solution. This finding provides new insight into the nature of this widely used reagent and has enabled the first direct, selective determination of a metal ion with tris(2,2΄-bipyridyl)ruthenium(III)

Augmented reality meeting table: a novel multi-user interface for architectural design

Immersive virtual environments have received widespread attention as providing possible replacements for the media and systems that designers traditionally use, as well as, more generally, in providing support for collaborative work. Relatively little attention has been given to date however to the problem of how to merge immersive virtual environments into real world work settings, and so to add to the media at the disposal of the designer and the design team, rather than to replace it. In this paper we report on a research project in which optical see-through augmented reality displays have been developed together with prototype decision support software for architectural and urban design. We suggest that a critical characteristic of multi user augmented reality is its ability to generate visualisations from a first person perspective in which the scale of rendition of the design model follows many of the conventions that designers are used to. Different scales of model appear to allow designers to focus on different aspects of the design under consideration. Augmenting the scene with simulations of pedestrian movement appears to assist both in scale recognition, and in moving from a first person to a third person understanding of the design. This research project is funded by the European Commission IST program (IST-2000-28559)