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

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

Non-Hermitian Hamiltonians in Field Theory

This thesis is centred around the role of non-Hermitian Hamiltonians in Physics both at the quantum and classical levels. In our investigations of two-level models we demonstrate [1] the phenomenon of fast transitions developed in the PT -symmetric quantum brachistochrone problem may in fact be attributed to the non-Hermiticity of evolution operator used, rather than to its invariance under PT operation. Transition probabilities are calculated for Hamiltonians which explicitly violate PT -symmetry. When it comes to Hilbert spaces of infinite dimension, starting with non-Hermitian Hamiltonians expressed as linear and quadratic combinations of the generators of the su(1; 1) Lie algebra, we construct [2] Hermitian partners in the same similarity class. Alongside, metrics with respect to which the original Hamiltonians are Hermitian are also constructed, allowing to assign meaning to a large class of non-Hermitian Hamiltonians possessing real spectra. The finding of exact results to establish the physical acceptability of other non-Hermitian models may be pursued by other means, especially if the system of interest cannot be expressed in terms of Lie algebraic elements. We also employ [3] a representation of the canonical commutation relations for position and momentum operators in terms of real-valued functions and a noncommutative product rule of differential form. Besides exact solutions, we also compute in a perturbative fashion metrics and isospectral partners for systems of physical interest. Classically, our efforts were concentrated on integrable models presenting PT - symmetry. Because the latter can also establish the reality of energies in classical systems described by Hamiltonian functions, we search for new families of nonlinear differential equations for which the presence of hidden symmetries allows one to assemble exact solutions. We use [4] the Painleve test to check whether deformations of integrable systems preserve integrability. Moreover we compare [5] integrable deformed models, which are thus likely to possess soliton solutions, to a broader class of systems presenting compacton solutions. Finally we study [6] the pole structure of certain real valued nonlinear integrable systems and establish that they behave as interacting particles whose motion can be extended to the complex plane in a PT -symmetric way

The Mercedes water Cherenkov detector

The concept of a small, single-layer water Cherenkov detector,with three photomultiplier tubes (PMTs), placed at its bottom in a 120◦ star configuration (Mercedes Water Cherenkov Detector) is presented. The PMTs are placed near the lateral walls of the stations with an adjustable inclination and may be installed inside or outside the water volume. To illustrate the technical viability of this concept and obtain a first-order estimation of its cost, an engineering designwas elaborated. The sensitivity of these stations to low energy Extensive Air Shower (EAS) electrons, photons and muons is discussed, both in compact and sparse array configurations. It is shown that the analysis of the intensity and time patterns of the PMT signals, using machine learning techniques, enables the tagging of muons, achieving an excellent gamma/hadron discrimination for TeV showers. This concept minimises the station production and maintenance costs, allowing for a highly flexible and fast installation. Mercedes Water Cherenkov Detectors (WCDs) are thus well-suited for use in high-altitude large gamma-ray observatories covering an extended energy range from the low energies, closing the gap between satellite and ground-based measurements, to very high energy regions, beyond the PeV scale.Portuguese Foundation for Science and Technology PTDC/FISPAR/4300/2020 DL57/2016/cP1330/cT0002MEYS of the Czech Republic LTT 20002Fundacao Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio De Janeiro (FAPERJ) 211.342/2021Portuguese Foundation for Science and TechnologyEuropean Commission PRT/BD/151553/202

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

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