Experimental approximation of the Jones polynomial with DQC1

We present experimental results approximating the Jones polynomial using 4 qubits in a liquid state nuclear magnetic resonance quantum information processor. This is the first experimental implementation of a complete problem for the deterministic quantum computation with one quantum bit model of quantum computation, which uses a single qubit accompanied by a register of completely random states. The Jones polynomial is a knot invariant that is important not only to knot theory, but also to statistical mechanics and quantum field theory. The implemented algorithm is a modification of the algorithm developed by Shor and Jordan suitable for implementation in NMR. These experimental results show that for the restricted case of knots whose braid representations have four strands and exactly three crossings, identifying distinct knots is possible 91% of the time.Comment: 5 figures. Version 2 changes: published version, minor errors corrected, slight changes to improve readabilit

Relativity and the low energy nd Ay puzzle

We solve the Faddeev equation in an exactly Poincare invariant formulation of the three-nucleon problem. The dynamical input is a relativistic nucleon-nucleon interaction that is exactly on-shell equivalent to the high precision CDBonn NN interaction. S-matrix cluster properties dictate how the two-body dynamics is embedded in the three-nucleon mass operator. We find that for neutron laboratory energies above 20 MeV relativistic effects on Ay are negligible. For energies below 20 MeV dynamical effects lower the nucleon analyzing power maximum slightly by 2% and Wigner rotations lower it further up to 10 % increasing thus disagreement between data and theory. This indicates that three-nucleon forces must provide an even larger increase of the Ay maximum than expected up to now.Comment: 29 pages, 2 ps figure

First Order Relativistic Three-Body Scattering

Relativistic Faddeev equations for three-body scattering at arbitrary energies are formulated in momentum space and in first order in the two-body transition-operator directly solved in terms of momentum vectors without employing a partial wave decomposition. Relativistic invariance is incorporated within the framework of Poincare invariant quantum mechanics, and presented in some detail. Based on a Malfliet-Tjon type interaction, observables for elastic and break-up scattering are calculated up to projectile energies of 1 GeV. The influence of kinematic and dynamic relativistic effects on those observables is systematically studied. Approximations to the two-body interaction embedded in the three-particle space are compared to the exact treatment.Comment: 26 pages, 13 figure

Evaluating inland valley agro-ecosystems in Ghana using a multi-scale characterization approach

As part of measures for improving the productive capacities of inland valley systems for rice-based cropping systems, a published multi-scale characterization approach was used in Ghana to assess the constraints and variables which must be understood before agronomic interventions are made. Macro, reconnaissance, semidetailed and detailed levels of characterization at their respective scales were used. Between 1996 and 1999, Geographical Information System (GIS) and transect studies were carried out, after which the extent of variability in the biotic and abiotic characteristics of two agro-ecologies were identified. Ten agro-ecological units were identified for Ghana based on map overlays and cluster analysis. The method allowed for the selection of Mankran and Jolo-Kwaha watersheds representing the equatorial and savanna agro-ecologies, respectively. Socio-economic parameters (markets, population density and suchlike) were recognized as the essential variables, which should be considered alongside lithology, climate, hydrology and others, for the choice of valleys for development interventions for crop production. At the detailed level of characterization, hydrological and soil characteristics underscored the need to properly understand the watershed-level and valleyspecific constraints before meaningful rice-based research and cropping systems are developed.En tant que partie de mesures pour améliorer les capacités productives de systémes de vallée de l\'intérieur pour les systèmes de culture basés sur le riz, une approche de caractérisation multiéchelle publiée était employée au Ghana en vue d\'estimer les contraintes et les variables qu\'il faut comprendre avant que les interventions agronomiques soient faites. Les niveaux macro, reconnaissance, semi-détaillé et détaillé de caractérisation à leurs échelles respectives étaient utilisés. Entre 1996 et 1999, l\'étude transversale et du Système Informationnel Géographique (SIG) étaient faites à la suite de quelle l\'étendue de variabilité de caractéristiques biotiques et abiotiques de deux agro-écologies étaient identifiées. Dix unités agro-écologiques étaient identifiées pour le Ghana basé sur l\'analyse de revêtements et de rassemblement sur la carte. La méthode permettait la sélection de lignes de partage des eaux de Mankran et de Jolo-Kwaha représentant respectivement les agroécologies équatoriales et savanes. Les paramètres socioéconomiques (les marchés, la densité de population, etc.) étaient reconnus comme les variables essentielles, qui devraient être considéré à côté de la lithologie, le climat, la hydrologie, etc.; pour le choix de vallées pour les interventions de développement pour la production des cultures. Au niveau détaillé de caractérisation, les caractéristiques de hydrologie et de sol soulignent la nécessité de comprendre vraiment les contraintes de niveaux de lignes de partage des eaux et les contraintes spécifiques à certaines vallées avant que la recherche et les systèmes de culture utiles basés sur le riz soient développés. Ghana Journal of Agricultural Science Vol. 40 (2) 2008: pp. 141-15

Quantitative Relativistic Effects in the Three-Nucleon Problem

The quantitative impact of the requirement of relativistic invariance in the three-nucleon problem is examined within the framework of Poincar\'e invariant quantum mechanics. In the case of the bound state, and for a wide variety of model implementations and reasonable interactions, most of the quantitative effects come from kinematic factors that can easily be incorporated within a non-relativistic momentum-space three-body code.Comment: 15 pages, 15 figure

Continuous pumping and control of mesoscopic superposition state in a lossy QED cavity

Here we consider the continuous pumping of a dissipative QED cavity and derive the time-dependent density operator of the cavity field prepared initially as a superposition of mesoscopic coherent states. The control of the coherence of this superposition is analyzed considering the injection of a beam of two-level Rydberg atoms through the cavity. Our treatment is compared to other approaches.Comment: 15 pages, 6 PostScript figures, To appear in Phys. Rev.

Basis States for Relativistic, Dynamically-Entangled Particles

In several recent papers on entanglement in relativistic quantum systems and relativistic Bell's inequalities, relativistic Bell-type two-particle states have been constructed in analogy to non-relativistic states. These constructions do not have the form suggested by relativistic invariance of the dynamics. Two relativistic formulations of Bell-type states are shown for massive particles, one using the standard Wigner spin basis and one using the helicity basis. The construction hinges on the use of Clebsch-Gordan coefficients of the Poincar\'e group to reduce the direct product of two unitary irreducible representations (UIRs) into a direct sum of UIRs.Comment: 19 pages, three tables, revte