Generation of maximally entangled states of qudits using twin photons

We report an experiment to generate maximally entangled states of D-dimensional quantum systems, qudits, by using transverse spatial correlations of two parametric down-converted photons. Apertures with D-slits in the arms of the twin fotons define the qudit space. By manipulating the pump beam correctly the twin photons will pass only by symmetrically opposite slits, generating entangled states between these differents paths. Experimental results for qudits with D=4 and D=8 are shown. We demonstrate that the generated states are entangled states.Comment: 04 pages, 04 figure

Quantized fields and gravitational particle creation in f(R) expanding universes

The problem of cosmological particle creation for a spatially flat, homogeneous and isotropic Universes is discussed in the context of f(R) theories of gravity. Different from cosmological models based on general relativity theory, it is found that a conformal invariant metric does not forbid the creation of massless particles during the early stages (radiation era) of the Universe.Comment: 14 pages, 2 figure

Born-Infeld magnetars: larger than classical toroidal magnetic fields and implications for gravitational-wave astronomy

Magnetars are neutron stars presenting bursts and outbursts of X- and soft-gamma rays that can be understood with the presence of very large magnetic fields. Thus, nonlinear electrodynamics should be taken into account for a more accurate description of such compact systems. We study that in the context of ideal magnetohydrodynamics and make a realization of our analysis to the case of the well-known Born-Infeld (BI) electromagnetism in order to come up with some of its astrophysical consequences. We focus here on toroidal magnetic fields as motivated by already known magnetars with low dipolar magnetic fields and their expected relevance in highly magnetized stars. We show that BI electrodynamics leads to larger toroidal magnetic fields when compared to Maxwell's electrodynamics. Hence, one should expect higher production of gravitational waves (GWs) and even more energetic giant flares from nonlinear stars. Given current constraints on BI's scale field, giant flare energetics and magnetic fields in magnetars, we also find that the maximum magnitude of magnetar ellipticities should be $10^{-6}-10^{-5}$. Besides, BI electrodynamics may lead to a maximum increase of order $10\%-20\%$ of the GW energy radiated from a magnetar when compared to Maxwell's, while much larger percentages may arise for other physically motivated scenarios. Thus, nonlinear theories of the electromagnetism might also be probed in the near future with the improvement of GW detectors.Comment: 8 pages, no figures, accepted for publication in The European Physical Journal C (EPJC

Parameterized Complexity of Equitable Coloring

A graph on $n$ vertices is equitably $k$-colorable if it is $k$-colorable and every color is used either $\left\lfloor n/k \right\rfloor$ or $\left\lceil n/k \right\rceil$ times. Such a problem appears to be considerably harder than vertex coloring, being $\mathsf{NP\text{-}Complete}$ even for cographs and interval graphs. In this work, we prove that it is $\mathsf{W[1]\text{-}Hard}$ for block graphs and for disjoint union of split graphs when parameterized by the number of colors; and $\mathsf{W[1]\text{-}Hard}$ for $K_{1,4}$-free interval graphs when parameterized by treewidth, number of colors and maximum degree, generalizing a result by Fellows et al. (2014) through a much simpler reduction. Using a previous result due to Dominique de Werra (1985), we establish a dichotomy for the complexity of equitable coloring of chordal graphs based on the size of the largest induced star. Finally, we show that \textsc{equitable coloring} is $\mathsf{FPT}$ when parameterized by the treewidth of the complement graph

From de Sitter to de Sitter: decaying vacuum models as a possible solution to the main cosmological problems

Decaying vacuum cosmological models evolving smoothly between two extreme (very early and late time) de Sitter phases are capable to solve or at least to alleviate some cosmological puzzles, among them: (i) the singularity, (ii) horizon, (iii) graceful-exit from inflation, and (iv) the baryogenesis problem. Our basic aim here is to discuss how the coincidence problem based on a large class of running vacuum cosmologies evolving from de Sitter to de Sitter can also be mollified. It is also argued that even the cosmological constant problem become less severe provided that the characteristic scales of the two limiting de Sitter manifolds are predicted from first principles.Comment: 7 pages, 2 figures, title changed, typos corrected, text and new references adde

Counterrotation in magnetocentrifugally driven jets and other winds

Rotation measurement in jets from T Tauri stars is a rather difficult task. Some jets seem to be rotating in a direction opposite to that of the underlying disk, although it is not yet clear if this affects the totality or part of the outflows. On the other hand, Ulysses data also suggest that the solar wind may rotate in two opposite ways between the northern and southern hemispheres. We show that this result is not as surprising as it may seem and that it emerges naturally from the ideal MHD equations. Specifically, counterrotating jets neither contradict the magnetocentrifugal driving of the flow nor prevent extraction of angular momentum from the disk. The demonstration of this result is shown by combining the ideal MHD equations for steady axisymmetric flows. Provided that the jet is decelerated below some given threshold beyond the Alfven surface, the flow will change its direction of rotation locally or globally. Counterrotation is also possible for only some layers of the outflow at specific altitudes along the jet axis. We conclude that the counterrotation of winds or jets with respect to the source, star or disk, is not in contradiction with the magnetocentrifugal driving paradigm. This phenomenon may affect part of the outflow, either in one hemisphere, or only in some of the outflow layers. From a time-dependent simulation, we illustrate this effect and show that it may not be permanent.Comment: To appear in ApJ