New superintegrable models with position-dependent mass from Bertrand's Theorem on curved spaces

A generalized version of Bertrand's theorem on spherically symmetric curved spaces is presented. This result is based on the classification of (3+1)-dimensional (Lorentzian) Bertrand spacetimes, that gives rise to two families of Hamiltonian systems defined on certain 3-dimensional (Riemannian) spaces. These two systems are shown to be either the Kepler or the oscillator potentials on the corresponding Bertrand spaces, and both of them are maximally superintegrable. Afterwards, the relationship between such Bertrand Hamiltonians and position-dependent mass systems is explicitly established. These results are illustrated through the example of a superintegrable (nonlinear) oscillator on a Bertrand-Darboux space, whose quantization and physical features are also briefly addressed.Comment: 13 pages; based in the contribution to the 28th International Colloquium on Group Theoretical Methods in Physics, Northumbria University (U.K.), 26-30th July 201

Geometric discretization of the Koenigs nets

We introduce the Koenigs lattice, which is a new integrable reduction of the quadrilateral lattice (discrete conjugate net) and provides natural integrable discrete analogue of the Koenigs net. We construct the Darboux-type transformations of the Koenigs lattice and we show permutability of superpositions of such transformations, thus proving integrability of the Koenigs lattice. We also investigate the geometry of the discrete Koenigs transformation. In particular we characterize the Koenigs transformation in terms of an involution determined by a congruence conjugate to the lattice.Comment: 17 pages, 2 figures; some spelling and typing errors correcte

N-dimensional sl(2)-coalgebra spaces with non-constant curvature

An infinite family of ND spaces endowed with sl(2)-coalgebra symmetry is introduced. For all these spaces the geodesic flow is superintegrable, and the explicit form of their common set of integrals is obtained from the underlying sl(2)-coalgebra structure. In particular, ND spherically symmetric spaces with Euclidean signature are shown to be sl(2)-coalgebra spaces. As a byproduct of this construction we present ND generalizations of the classical Darboux surfaces, thus obtaining remarkable superintegrable ND spaces with non-constant curvature.Comment: 11 pages. Comments and new references have been added; expressions for scalar curvatures have been corrected and simplifie

Nondegenerate 3D complex Euclidean superintegrable systems and algebraic varieties

A classical (or quantum) second order superintegrable system is an integrable n-dimensional Hamiltonian system with potential that admits 2n-1 functionally independent second order constants of the motion polynomial in the momenta, the maximum possible. Such systems have remarkable properties: multi-integrability and multi-separability, an algebra of higher order symmetries whose representation theory yields spectral information about the Schroedinger operator, deep connections with special functions and with QES systems. Here we announce a complete classification of nondegenerate (i.e., 4-parameter) potentials for complex Euclidean 3-space. We characterize the possible superintegrable systems as points on an algebraic variety in 10 variables subject to six quadratic polynomial constraints. The Euclidean group acts on the variety such that two points determine the same superintegrable system if and only if they lie on the same leaf of the foliation. There are exactly 10 nondegenerate potentials.Comment: 35 page

Altered Resting-State Functional Connectivity in Cortical Networks in Psychopathy

Psychopathy is a personality disorder characterized by callous antisocial behavior and criminal recidivism. Here we examine whether psychopathy is associated with alterations in functional connectivity in three large-scale cortical networks. Using fMRI in 142 adult male prison inmates, we computed resting-state functional connectivity using seeds from the default mode network, frontoparietal network, and cingulo-opercular network. To determine the specificity of our findings to these cortical networks, we also calculated functional connectivity using seeds from two comparison primary sensory networks: visual and auditory networks. Regression analyses related network connectivity to overall psychopathy scores and to subscores for the “factors” and “facets” of psychopathy: Factor 1, interpersonal/affective traits; Factor 2, lifestyle/antisocial traits; Facet 1, interpersonal; Facet 2, affective; Facet 3, lifestyle; Facet 4, antisocial. Overall psychopathy severity was associated with reduced functional connectivity between lateral parietal cortex and dorsal anterior cingulate cortex. The two factor scores exhibited contrasting relationships with functional connectivity: Factor 1 scores were associated with reduced functional connectivity in the three cortical networks, whereas Factor 2 scores were associated with heightened connectivity in the same networks. This dissociation was evident particularly in the functional connectivity between anterior insula and dorsal anterior cingulate cortex. The facet scores also demonstrated distinct patterns of connectivity. We found no associations between psychopathy scores and functional connectivity within visual or auditory networks. These findings provide novel evidence on the neural correlates of psychopathy and suggest that connectivity between cortical association hubs, such as the dorsal anterior cingulate cortex, may be a neurobiological marker of the disorder

On two superintegrable nonlinear oscillators in N dimensions

We consider the classical superintegrable Hamiltonian system given by $H=T+U={p^2}/{2(1+\lambda q^2)}+{{\omega}^2 q^2}/{2(1+\lambda q^2)}$, where U is known to be the "intrinsic" oscillator potential on the Darboux spaces of nonconstant curvature determined by the kinetic energy term T and parametrized by {\lambda}. We show that H is Stackel equivalent to the free Euclidean motion, a fact that directly provides a curved Fradkin tensor of constants of motion for H. Furthermore, we analyze in terms of {\lambda} the three different underlying manifolds whose geodesic motion is provided by T. As a consequence, we find that H comprises three different nonlinear physical models that, by constructing their radial effective potentials, are shown to be two different nonlinear oscillators and an infinite barrier potential. The quantization of these two oscillators and its connection with spherical confinement models is briefly discussed.Comment: 11 pages; based on the contribution to the Manolo Gadella Fest-60 years-in-pucelandia, "Recent advances in time-asymmetric quantum mechanics, quantization and related topics" hold in Valladolid (Spain), 14-16th july 201

Stable isotopes reveal trophic relationships and diet of consumers in temperate kelp forest and coral reef ecosystems

We explored the use of stable nitrogen (N) isotope analysis to assess trophic position of consumers in two marine ecosystems: the kelp forests of southern California and a coral atoll in the tropical Pacific. The delta N-15 values of consumers in both ecosystems increased from known herbivores (invertebrates and fish) to higher-level consumers (predatory invertebrates and fish). In the absence of data on trophic enrichment in N-15 for our study species, we used the oft-cited value of +3.4 parts per thousand increase in delta N-15 value per trophic level and estimates of the delta N-15 producer baseline value to estimate trophic position. The trophic position of consumers computed using N isotopes compared favorably to published observations of diet. Nitrogen isotope analysis revealed that some of our higher-level fish consumers from rocky reefs (i.e., some rockfish) were feeding largely on invertebrates rather than on fish, as is often assumed. Our analysis also suggests that higher-level consumers on coral reefs may consume more herbivorous prey (i.e., both fishes and invertebrates) than previously reported. Our data support the use of nitrogen isotope values to assess trophic position and, thus, their utility as one metric with which to explore the effects of short- and longer-term natural and human-induced changes on kelp forest and coral reef food webs

A ∼\sim15 kpc outflow cone piercing through the halo of the blue compact metal-poor galaxy SBS0335-052

Context: Outflows from low-mass star-forming galaxies are a fundamental ingredient for models of galaxy evolution and cosmology. Aims: The onset of kpc-scale ionised filaments in the halo of the metal-poor compact dwarf SBS 0335-052E was previously not linked to an outflow. We here we investigate whether these filaments provide evidence for an outflow. Methods: We obtained new VLT/MUSE WFM and deep NRAO/VLA B-configuration 21cm data of the galaxy. The MUSE data provide morphology, kinematics, and emission line ratios H$\beta$/H$\alpha$ and [\ion{O}{iii}]$\lambda5007$/H$\alpha$ of the low surface-brightness filaments, while the VLA data deliver morphology and kinematics of the neutral gas in and around the system. Both datasets are used in concert for comparisons between the ionised and the neutral phase. Results: We report the prolongation of a lacy filamentary ionised structure up to a projected distance of 16 kpc at $\mathrm{SB}_\mathrm{H\alpha} = 1.5\times10^{-18}$erg s$^{-1}$ cm$^{-2}$arcsec$^{-2}$. The filaments exhibit unusual low H$\alpha$/H$\beta \approx 2.4$ and low [\ion{O}{iii}]/H$\alpha \sim 0.4 - 0.6$ typical of diffuse ionised gas. They are spectrally narrow ($\sim 20$ km s$^{-1}$) and exhibit no velocity sub-structure. The filaments extend outwards of the elongated \ion{H}{I} halo. On small scales the $N_\mathrm{HI}$ peak is offset from the main star-forming sites. Morphology and kinematics of \ion{H}{I} and \ion{H}{II} reveal how star-formation driven feedback interacts differently with the ionised and the neutral phase. Conclusions: We reason that the filaments are a large scale manifestation of star-formation driven feedback, namely limb-brightened edges of a giant outflow cone that protrudes through the halo of this gas-rich system. A simple toy model of such a conical-structure is found to be commensurable with the observations.Comment: Accepted version in A&A after language editing. 22 pages, 24 figure