Nonintegrability of the two-body problem in constant curvature spaces

We consider the reduced two-body problem with the Newton and the oscillator potentials on the sphere ${\bf S}^{2}$ and the hyperbolic plane ${\bf H}^{2}$. For both types of interaction we prove the nonexistence of an additional meromorphic integral for the complexified dynamic systems.Comment: 20 pages, typos correcte

The harmonic oscillator on Riemannian and Lorentzian configuration spaces of constant curvature

The harmonic oscillator as a distinguished dynamical system can be defined not only on the Euclidean plane but also on the sphere and on the hyperbolic plane, and more generally on any configuration space with constant curvature and with a metric of any signature, either Riemannian (definite positive) or Lorentzian (indefinite). In this paper we study the main properties of these `curved' harmonic oscillators simultaneously on any such configuration space, using a Cayley-Klein (CK) type approach, with two free parameters \ki, \kii which altogether correspond to the possible values for curvature and signature type: the generic Riemannian and Lorentzian spaces of constant curvature (sphere ${\bf S}^2$, hyperbolic plane ${\bf H}^2$, AntiDeSitter sphere {\bf AdS}^{\unomasuno} and DeSitter sphere {\bf dS}^{\unomasuno}) appear in this family, with the Euclidean and Minkowski spaces as flat limits. We solve the equations of motion for the `curved' harmonic oscillator and obtain explicit expressions for the orbits by using three different methods: first by direct integration, second by obtaining the general CK version of the Binet's equation and third, as a consequence of its superintegrable character. The orbits are conics with centre at the potential origin in any CK space, thereby extending this well known Euclidean property to any constant curvature configuration space. The final part of the article, that has a more geometric character, presents those results of the theory of conics on spaces of constant curvature which are pertinent.Comment: 29 pages, 6 figure

Two-dimensional periodic frustrated Ising models in a transverse field

We investigate the interplay of classical degeneracy and quantum dynamics in a range of periodic frustrated transverse field Ising systems at zero temperature. We find that such dynamics can lead to unusual ordered phases and phase transitions, or to a quantum spin liquid (cooperative paramagnetic) phase as in the triangular and kagome lattice antiferromagnets, respectively. For the latter, we further predict passage to a bond-ordered phase followed by a critical phase as the field is tilted. These systems also provide exact realizations of quantum dimer models introduced in studies of high temperature superconductivity.Comment: Revised introduction; numerical error in hexagonal section correcte

Power-law spin correlations in pyrochlore antiferromagnets

The ground state ensemble of the highly frustrated pyrochlore-lattice antiferromagnet can be mapped to a coarse-grained ``polarization'' field satisfying a zero-divergence condition From this it follows that the correlations of this field, as well as the actual spin correlations, decay with separation like a dipole-dipole interaction ($1/|R|^3$). Furthermore, a lattice version of the derivation gives an approximate formula for spin correlations, with several features that agree well with simulations and neutron-diffraction measurements of diffuse scattering, in particular the pinch-point (pseudo-dipolar) singularities at reciprocal lattice vectors. This system is compared to others in which constraints also imply diffraction singularities, and other possible applications of the coarse-grained polarization are discussed.Comment: 13 pp, revtex, two figure

Intraoperative hyperspectral label-free imaging: from system design to first-in-patient translation.

Despite advances in intraoperative surgical imaging, reliable discrimination of critical tissue during surgery remains challenging. As a result, decisions with potentially life-changing consequences for patients are still based on the surgeon's subjective visual assessment. Hyperspectral imaging (HSI) provides a promising solution for objective intraoperative tissue characterisation, with the advantages of being non-contact, non-ionising and non-invasive. However, while its potential to aid surgical decision-making has been investigated for a range of applications, to date no real-time intraoperative HSI (iHSI) system has been presented that follows critical design considerations to ensure a satisfactory integration into the surgical workflow. By establishing functional and technical requirements of an intraoperative system for surgery, we present an iHSI system design that allows for real-time wide-field HSI and responsive surgical guidance in a highly constrained operating theatre. Two systems exploiting state-of-the-art industrial HSI cameras, respectively using linescan and snapshot imaging technology, were designed and investigated by performing assessments against established design criteria and ex vivo tissue experiments. Finally, we report the use of our real-time iHSI system in a clinical feasibility case study as part of a spinal fusion surgery. Our results demonstrate seamless integration into existing surgical workflows

Exact results of the mixed-spin Ising model on a decorated square lattice with two different decorating spins of integer magnitudes

The mixed-spin Ising model on a decorated square lattice with two different decorating spins of the integer magnitudes S_B = 1 and S_C = 2 placed on horizontal and vertical bonds of the lattice, respectively, is examined within an exact analytical approach based on the generalized decoration-iteration mapping transformation. Besides the ground-state analysis, finite-temperature properties of the system are also investigated in detail. The most interesting numerical result to emerge from our study relates to a striking critical behaviour of the spontaneously ordered 'quasi-1D' spin system. It was found that this quite remarkable spontaneous order arises when one sub-lattice of the decorating spins (either S_B or S_C) tends towards their 'non-magnetic' spin state S = 0 and the system becomes disordered only upon further single-ion anisotropy strengthening. The effect of single-ion anisotropy upon the temperature dependence of the total and sub-lattice magnetization is also particularly investigated.Comment: 17 pages, 6 figure

Low-temperature properties of classical, geometrically frustrated antiferromagnets

We study the ground-state and low-energy properties of classical vector spin models with nearest-neighbour antiferromagnetic interactions on a class of geometrically frustrated lattices which includes the kagome and pyrochlore lattices. We explore the behaviour of these magnets that results from their large ground-state degeneracies, emphasising universal features and systematic differences between individual models. We investigate the circumstances under which thermal fluctuations select a particular subset of the ground states, and find that this happens only for the models with the smallest ground-state degeneracies. For the pyrochlore magnets, we give an explicit construction of all ground states, and show that they are not separated by internal energy barriers. We study the precessional spin dynamics of the Heisenberg pyrochlore antiferromagnet. There is no freezing transition or selection of preferred states. Instead, the relaxation time at low temperature, T, is of order hbar/(k_B T). We argue that this behaviour can also be expected in some other systems, including the Heisenberg model for the compound SrCr_8Ga_4O_{19}.Comment: to appear in Phys. Rev.

Association of Genetic Variants With Primary Open-Angle Glaucoma Among Individuals With African Ancestry.

Importance:Primary open-angle glaucoma presents with increased prevalence and a higher degree of clinical severity in populations of African ancestry compared with European or Asian ancestry. Despite this, individuals of African ancestry remain understudied in genomic research for blinding disorders. Objectives:To perform a genome-wide association study (GWAS) of African ancestry populations and evaluate potential mechanisms of pathogenesis for loci associated with primary open-angle glaucoma. Design, Settings, and Participants:A 2-stage GWAS with a discovery data set of 2320 individuals with primary open-angle glaucoma and 2121 control individuals without primary open-angle glaucoma. The validation stage included an additional 6937 affected individuals and 14 917 unaffected individuals using multicenter clinic- and population-based participant recruitment approaches. Study participants were recruited from Ghana, Nigeria, South Africa, the United States, Tanzania, Britain, Cameroon, Saudi Arabia, Brazil, the Democratic Republic of the Congo, Morocco, Peru, and Mali from 2003 to 2018. Individuals with primary open-angle glaucoma had open iridocorneal angles and displayed glaucomatous optic neuropathy with visual field defects. Elevated intraocular pressure was not included in the case definition. Control individuals had no elevated intraocular pressure and no signs of glaucoma. Exposures:Genetic variants associated with primary open-angle glaucoma. Main Outcomes and Measures:Presence of primary open-angle glaucoma. Genome-wide significance was defined as P < 5 × 10-8 in the discovery stage and in the meta-analysis of combined discovery and validation data. Results:A total of 2320 individuals with primary open-angle glaucoma (mean [interquartile range] age, 64.6 [56-74] years; 1055 [45.5%] women) and 2121 individuals without primary open-angle glaucoma (mean [interquartile range] age, 63.4 [55-71] years; 1025 [48.3%] women) were included in the discovery GWAS. The GWAS discovery meta-analysis demonstrated association of variants at amyloid-β A4 precursor protein-binding family B member 2 (APBB2; chromosome 4, rs59892895T>C) with primary open-angle glaucoma (odds ratio [OR], 1.32 [95% CI, 1.20-1.46]; P = 2 × 10-8). The association was validated in an analysis of an additional 6937 affected individuals and 14 917 unaffected individuals (OR, 1.15 [95% CI, 1.09-1.21]; P < .001). Each copy of the rs59892895*C risk allele was associated with increased risk of primary open-angle glaucoma when all data were included in a meta-analysis (OR, 1.19 [95% CI, 1.14-1.25]; P = 4 × 10-13). The rs59892895*C risk allele was present at appreciable frequency only in African ancestry populations. In contrast, the rs59892895*C risk allele had a frequency of less than 0.1% in individuals of European or Asian ancestry. Conclusions and Relevance:In this genome-wide association study, variants at the APBB2 locus demonstrated differential association with primary open-angle glaucoma by ancestry. If validated in additional populations this finding may have implications for risk assessment and therapeutic strategies