PT-symmetry in quasi-integrable models

We reinforce the observations of almost stable scattering in nonintegrable models and show that $\mathcal{PT}$-symmetry can be used as a guiding principle to select relevant systems also when it comes to integrability properties. We show that the presence of unbroken $\mathcal{PT}$-symmetry in classical field theories produces quasi-integrable excitations with asymptotically conserved charges

Weber-like interactions and energy conservation

Velocity dependent forces varying as $k(\hat{r}/r)(1 - \mu \dot{r}^2 + \gamma r \ddot{r})$ (such as Weber force), here called Weber-like forces, are examined from the point of view of energy conservation and it is proved that they are conservative if and only if $\gamma=2\mu$. As a consequence, it is shown that gravitational theories employing Weber-like forces cannot be conservative and also yield both the precession of the perihelion of Mercury as well as the gravitational deflection of light.Comment: latex, 11 pages, no figure

On the Integrability and Chaos of an N=2 Maxwell-Chern-Simons-Higgs Mechanical Model

We apply different integrability analysis procedures to a reduced (spatially homogeneous) mechanical system derived from an off-shell non-minimally coupled N=2 Maxwell-Chern-Simons-Higgs model that presents BPS topological vortex excitations, numerically obtained with an ansatz adopted in a special - critical coupling - parametric regime. As a counterpart of the regularity associated to the static soliton-like solution, we investigate the possibility of chaotic dynamics in the evolution of the spatially homogeneous reduced system, descendant from the full N=2 model under consideration. The originally rich content of symmetries and interactions, N=2 susy and non-minimal coupling, singles out the proposed model as an interesting framework for the investigation of the role played by (super-)symmetries and parametric domains in the triggering/control of chaotic behavior in gauge systems. After writing down effective Lagrangian and Hamiltonian functions, and establishing the corresponding canonical Hamilton equations, we apply global integrability Noether point symmetries and Painleveproperty criteria to both the general and the critical coupling regimes. As a non-integrable character is detected by the pair of analytical criteria applied, we perform suitable numerical simulations, as we seek for chaotic patterns in the system evolution. Finally, we present some Comments on the results and perspectives for further investigations and forthcoming communications.Comment: 18 pages, 5 figure

Impurity and boundary effects in one and two-dimensional inhomogeneous Heisenberg antiferromagnets

We calculate the ground-state energy of one and two-dimensional spatially inhomogeneous antiferromagnetic Heisenberg models for spins 1/2, 1, 3/2 and 2. Our calculations become possible as a consequence of the recent formulation of density-functional theory for Heisenberg models. The method is similar to spin-density-functional theory, but employs a local-density-type approximation designed specifically for the Heisenberg model, allowing us to explore parameter regimes that are hard to access by traditional methods, and to consider complications that are important specifically for nanomagnetic devices, such as the effects of impurities, finite-size, and boundary geometry, in chains, ladders, and higher-dimensional systems.Comment: 4 pages, 4 figures, accepted by Phys. Rev.

Major shifts at the range edge of marine forests: the combined effects of climate changes and limited dispersal

Global climate change is likely to constrain low latitude range edges across many taxa and habitats. Such is the case for NE Atlantic marine macroalgal forests, important ecosystems whose main structuring species is the annual kelp Saccorhiza polyschides. We coupled ecological niche modelling with simulations of potential dispersal and delayed development stages to infer the major forces shaping range edges and to predict their dynamics. Models indicated that the southern limit is set by high winter temperatures above the physiological tolerance of overwintering microscopic stages and reduced upwelling during recruitment. The best range predictions were achieved assuming low spatial dispersal (5 km) and delayed stages up to two years (temporal dispersal). Reconstructing distributions through time indicated losses of similar to 30% from 1986 to 2014, restricting S. polyschides to upwelling regions at the southern edge. Future predictions further restrict populations to a unique refugium in northwestern Iberia. Losses were dependent on the emissions scenario, with the most drastic one shifting similar to 38% of the current distribution by 2100. Such distributional changes might not be rescued by dispersal in space or time (as shown for the recent past) and are expected to drive major biodiversity loss and changes in ecosystem functioning.Electricity of Portugal (Fundo EDP para a Biodiversidade); FCT - Portuguese Science Foundation [PTDC/MAR-EST/6053/2014, EXTANT-EXCL/AAG-GLO/0661/2012, SFRH/BPD/111003/2015

The Pauli equation with complex boundary conditions

We consider one-dimensional Pauli Hamiltonians in a bounded interval with possibly non-self-adjoint Robin-type boundary conditions. We study the influence of the spin-magnetic interaction on the interplay between the type of boundary conditions and the spectrum. A special attention is paid to PT-symmetric boundary conditions with the physical choice of the time-reversal operator T.Comment: 16 pages, 4 figure

Restoring observed classical behavior of the carbon nanotube field emission enhancement factor from the electronic structure

Experimental Fowler-Nordheim plots taken from orthodoxly behaving carbon nanotube (CNT) field electron emitters are known to be linear. This shows that, for such emitters, there exists a characteristic field enhancement factor (FEF) that is constant for a range of applied voltages and applied macroscopic fields $F_\text{M}$. A constant FEF of this kind can be evaluated for classical CNT emitter models by finite-element and other methods, but (apparently contrary to experiment) several past quantum-mechanical (QM) CNT calculations find FEF-values that vary with $F_\text{M}$. A common feature of most such calculations is that they focus only on deriving the CNT real-charge distributions. Here we report on calculations that use density functional theory (DFT) to derive real-charge distributions, and then use these to generate the related induced-charge distributions and related fields and FEFs. We have analysed three carbon nanostructures involving CNT-like nanoprotrusions of various lengths, and have also simulated geometrically equivalent classical emitter models, using finite-element methods. We find that when the DFT-generated local induced FEFs (LIFEFs) are used, the resulting values are effectively independent of macroscopic field, and behave in the same qualitative manner as the classical FEF-values. Further, there is fair to good quantitative agreement between a characteristic FEF determined classically and the equivalent characteristic LIFEF generated via DFT approaches. Although many issues of detail remain to be explored, this appears to be a significant step forwards in linking classical and QM theories of CNT electrostatics. It also shows clearly that, for ideal CNTs, the known experimental constancy of the FEF value for a range of macroscopic fields can also be found in appropriately developed QM theory.Comment: A slightly revised version has been published - citation below - under a title different from that originally used. The new title is: "Restoring observed classical behavior of the carbon nanotube field emission enhancement factor from the electronic structure

Experimental Observation of Quantum Correlations in Modular Variables

We experimentally detect entanglement in modular position and momentum variables of photon pairs which have passed through $D$-slit apertures. We first employ an entanglement criteria recently proposed in [Phys. Rev. Lett. {\bf 106}, 210501 (2011)], using variances of the modular variables. We then propose an entanglement witness for modular variables based on the Shannon entropy, and test it experimentally. Finally, we derive criteria for Einstein-Podolsky-Rosen-Steering correlations using variances and entropy functions. In both cases, the entropic criteria are more successful at identifying quantum correlations in our data.Comment: 7 pages, 4 figures, comments welcom