Classical Tensors and Quantum Entanglement I: Pure States

The geometrical description of a Hilbert space asociated with a quantum system considers a Hermitian tensor to describe the scalar inner product of vectors which are now described by vector fields. The real part of this tensor represents a flat Riemannian metric tensor while the imaginary part represents a symplectic two-form. The immersion of classical manifolds in the complex projective space associated with the Hilbert space allows to pull-back tensor fields related to previous ones, via the immersion map. This makes available, on these selected manifolds of states, methods of usual Riemannian and symplectic geometry. Here we consider these pulled-back tensor fields when the immersed submanifold contains separable states or entangled states. Geometrical tensors are shown to encode some properties of these states. These results are not unrelated with criteria already available in the literature. We explicitly deal with some of these relations.Comment: 16 pages, 1 figure, to appear in Int. J. Geom. Meth. Mod. Phy

SPORTS-RELATED ORO-FACIAL INJURIES: WHICH KIND OF MOUTHGUARD WILL BE THE MOST SUITABLE TO PLAY SAFE?

The risk of sports-related injuries is constantly present in various sporting activities, like box, rugby, tae-kwon-do, etc. Athletes should be informed of the best characteristics of a custom-made mouthguard in order to prevent oro-facial trauma. Materials used in the manufacture of mouthguards should satisfy a number of physical, mechanical and biological requirements. It is essential to differentiate the intra-oral devices available for the athletes to play safe. There are three main goals that should be taken into account, and that are provided by the authors’ modified occlusion outhguard (MOM): (i) the occlusal stability, by the contacts of the mouthguard with the antagonist teeth, (ii) the equilibrium of the masticatory muscles and (iii) the temporomandibular joint protection from excessive unbalanced forces

Classical Tensors and Quantum Entanglement II: Mixed States

Invariant operator-valued tensor fields on Lie groups are considered. These define classical tensor fields on Lie groups by evaluating them on a quantum state. This particular construction, applied on the local unitary group U(n)xU(n), may establish a method for the identification of entanglement monotone candidates by deriving invariant functions from tensors being by construction invariant under local unitary transformations. In particular, for n=2, we recover the purity and a concurrence related function (Wootters 1998) as a sum of inner products of symmetric and anti-symmetric parts of the considered tensor fields. Moreover, we identify a distinguished entanglement monotone candidate by using a non-linear realization of the Lie algebra of SU(2)xSU(2). The functional dependence between the latter quantity and the concurrence is illustrated for a subclass of mixed states parametrized by two variables.Comment: 23 pages, 4 figure

Marine Biodiversity and Ecosystem Health of Ilhas Selvagens, Portugal

In September 2015, National Geographic's Pristine Seas project, in conjunction with the Instituto Universitário-Portugal, The Waitt Institute, the University of Western Australia, and partners conducted a comprehensive assessment of the rarely surveyed Ilhas Selvagens to explore the marine environment, especially the poorly understood deep sea and open ocean areas, and quantify the biodiversity of the nearshore marine environment

Some applications of quasi-velocities in optimal control

In this paper we study optimal control problems for nonholonomic systems defined on Lie algebroids by using quasi-velocities. We consider both kinematic, i.e. systems whose cost functional depends only on position and velocities, and dynamic optimal control problems, i.e. systems whose cost functional depends also on accelerations. The formulation of the problem directly at the level of Lie algebroids turns out to be the correct framework to explain in detail similar results appeared recently (Maruskin and Bloch, 2007). We also provide several examples to illustrate our construction.Comment: Revtex 4.1, 20 pages. To appear in Int. J. Geom. Meth. Modern Physic

Enzymes as Feed Additive to Aid in Responses Against Eimeria Species in Coccidia-Vaccinated Broilers Fed Corn-Soybean Meal Diets with Different Protein Levels

This research aimed to evaluate the effects of adding a combination of exogenous enzymes to starter diets varying in protein content and fed to broilers vaccinated at day of hatch with live oocysts and then challenged with mixed Eimeria spp. Five hundred four 1-d-old male Cobb-500 chickens were distributed in 72 cages. The design consisted of 12 treatments. Three anticoccidial control programs [ionophore (IO), coccidian vaccine (COV), and coccidia-vaccine + enzymes (COV + EC)] were evaluated under 3 CP levels (19, 21, and 23%), and 3 unmedicated-uninfected (UU) negative controls were included for each one of the protein levels. All chickens except those in unmedicated-uninfected negative controls were infected at 17 d of age with a mixed oral inoculum of Eimeria acervulina, Eimeria maxima, and Eimeria tenella. Live performance, lesion scores, oocyst counts, and samples for gut microflora profiles were evaluated 7 d postinfection. Ileal digestibility of amino acids (IDAA) was determined 8 d postinfection. Microbial communities (MC) were analyzed by G + C%, microbial numbers were counted by flow cytometry, and IgA concentrations were measured by ELISA. The lowest CP diets had poorer (P ≤ 0.001) BW gain and feed conversion ratio in the preinfection period. Coccidia-vaccinated broilers had lower performance than the ones fed ionophore diets during pre- and postchallenge periods. Intestinal lesion scores were affected (P ≤ 0.05) by anticoccidial control programs, but responses changed according to gut section. Feed additives or vaccination had no effect (P ≥ 0.05) on IDAA, and diets with 23% CP had the lowest (P ≤ 0.001) IDAA. Coccidial infection had no effect on MC numbers in the ileum but reduced MC numbers in ceca and suppressed ileal IgA production. The COV + EC treatment modulated MC during mixed coccidiosis infection but did not significantly improve chicken performance. Results indicated that feed enzymes may be used to modulate the gut microflora of cocci-vaccinated broiler chickens

Quantum Error Correction with magnetic molecules

Quantum algorithms often assume independent spin qubits to produce trivial $|\uparrow\rangle=|0\rangle$, $|\downarrow\rangle=|1\rangle$ mappings. This can be unrealistic in many solid-state implementations with sizeable magnetic interactions. Here we show that the lower part of the spectrum of a molecule containing three exchange-coupled metal ions with $S=1/2$ and $I=1/2$ is equivalent to nine electron-nuclear qubits. We derive the relation between spin states and qubit states in reasonable parameter ranges for the rare earth $^{159}$Tb$^{3+}$ and for the transition metal Cu$^{2+}$, and study the possibility to implement Shor's Quantum Error Correction code on such a molecule. We also discuss recently developed molecular systems that could be adequate from an experimental point of view.Comment: 5 pages, 3 figures, 2 table