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

Spin-phonon induced magnetic order in Kagome ice

We study the effects of lattice deformations on the Kagome spin ice, with Ising spins coupled by nearest neighbor exchange and long range dipolar interactions, in the presence of in-plane magnetic fields. We describe the lattice energy according to the Einstein model, where each site distortion is treated independently. Upon integration of lattice degrees of freedom, effective quadratic spin interactions arise. Classical MonteCarlo simulations are performed on the resulting model, retaining up to third neighbor interactions, under different directions of the magnetic field. We find that, as the effect of the deformation is increased, a rich plateau structure appears in the magnetization curves.Comment: 7 pages, 8 figure

A Strict Test of Stellar Evolution Models: The Absolute Dimensions of Massive Benchmark Eclipsing Binary V578 Mon

We determine the absolute dimensions of the eclipsing binary V578 Mon, a detached system of two early B-type stars (B0V + B1V, P$=$2.40848 d) in the star-forming region NGC 2244 of the Rosette Nebula. From the light curve analysis of 40 yr of photometry and the analysis of HERMES spectra, we find radii of $5.41\pm0.04$ Rsun and $4.29\pm 0.05$ Rsun, and temperatures of $30000\pm 500$~K and $25750\pm 435$ K respectively. We find that our disentangled component spectra for V578 Mon agree well previous spectral disentangling from the literature. We also reconfirm the previous spectroscopic orbit of V578 Mon finding that masses of $14.54\pm 0.08$ Msun and $10.29\pm 0.06$ Msun are fully compatible with the new analysis. We compare the absolute dimensions to the rotating models of the Geneva and Utrecht groups and the models of Granada group. We find all three sets of models marginally reproduce the absolute dimensions of both stars with a common age within uncertainty for gravity-effective temperature isochrones. However - there are some apparent age discrepancies for the corresponding mass-radius isochrones. Models with larger convective overshoot $>0.35$ worked best. Combined with our previously determined apsidal motion of $0.07089^{+0.00021}_{-0.00013}$ deg cycle$^{-1}$, we compute the internal structure constants (tidal Love number) for the newtonian and general relativistic contribution to the apsidal motion, $\log{k_2}=-1.975\pm0.017$ and $\log{k_2}=-3.412\pm0.018$ respectively. We find the relativistic contribution to the apsidal motion of be small $<4\%$. We find that the prediction of $\log{k_{\rm 2,theo}}=-2.005\pm0.025$ of the Granada models fully agrees with our observed $\log{k_2}$.Comment: accepted for publication in AJ 05/02/201

Optimal map of the modular structure of complex networks

Modular structure is pervasive in many complex networks of interactions observed in natural, social and technological sciences. Its study sheds light on the relation between the structure and function of complex systems. Generally speaking, modules are islands of highly connected nodes separated by a relatively small number of links. Every module can have contributions of links from any node in the network. The challenge is to disentangle these contributions to understand how the modular structure is built. The main problem is that the analysis of a certain partition into modules involves, in principle, as many data as number of modules times number of nodes. To confront this challenge, here we first define the contribution matrix, the mathematical object containing all the information about the partition of interest, and after, we use a Truncated Singular Value Decomposition to extract the best representation of this matrix in a plane. The analysis of this projection allow us to scrutinize the skeleton of the modular structure, revealing the structure of individual modules and their interrelations.Comment: 21 pages, 10 figure

Exceptional orthogonal polynomials and the Darboux transformation

We adapt the notion of the Darboux transformation to the context of polynomial Sturm-Liouville problems. As an application, we characterize the recently described $X_m$ Laguerre polynomials in terms of an isospectral Darboux transformation. We also show that the shape-invariance of these new polynomial families is a direct consequence of the permutability property of the Darboux-Crum transformation.Comment: corrected abstract, added references, minor correction

Misleading signatures of quantum chaos

The main signature of chaos in a quantum system is provided by spectral statistical analysis of the nearest neighbor spacing distribution and the spectral rigidity given by $\Delta_3(L)$. It is shown that some standard unfolding procedures, like local unfolding and Gaussian broadening, lead to a spurious increase of the spectral rigidity that spoils the $\Delta_3(L)$ relationship with the regular or chaotic motion of the system. This effect can also be misinterpreted as Berry's saturation.Comment: 4 pages, 5 figures, submitted to Physical Review

Quantum effects on Lagrangian points and displaced periodic orbits in the Earth-Moon system

Recent work in the literature has shown that the one-loop long distance quantum corrections to the Newtonian potential imply tiny but observable effects in the restricted three-body problem of celestial mechanics, i.e., at the Lagrangian libration points of stable equilibrium the planetoid is not exactly at equal distance from the two bodies of large mass, but the Newtonian values of its coordinates are changed by a few millimeters in the Earth-Moon system. First, we assess such a theoretical calculation by exploiting the full theory of the quintic equation, i.e., its reduction to Bring-Jerrard form and the resulting expression of roots in terms of generalized hypergeometric functions. By performing the numerical analysis of the exact formulas for the roots, we confirm and slightly improve the theoretical evaluation of quantum corrected coordinates of Lagrangian libration points of stable equilibrium. Second, we prove in detail that also for collinear Lagrangian points the quantum corrections are of the same order of magnitude in the Earth-Moon system. Third, we discuss the prospects to measure, with the help of laser ranging, the above departure from the equilateral triangle picture, which is a challenging task. On the other hand, a modern version of the planetoid is the solar sail, and much progress has been made, in recent years, on the displaced periodic orbits of solar sails at all libration points, both stable and unstable. The present paper investigates therefore, eventually, a restricted three-body problem involving Earth, Moon and a solar sail. By taking into account the one-loop quantum corrections to the Newtonian potential, displaced periodic orbits of the solar sail at libration points are again found to exist

A Note On R-Parity Violation and Fermion Masses

We consider a class of supersymmetric SU(3)\times SU(2)\times U(1) multihiggs models in which R-parity is violated through bilinear Higgs-lepton interactions. The required, due to R-parity violation, higgs-lepton rotations introduce an alternative way to generate the phenomenologically desirable fermion mass matrix structures independently of the equality of Yukawas, possibly imposed by superstring or other unification.Comment: 8 pages, uses LaTeX2

Bounds for the time to failure of hierarchical systems of fracture

For years limited Monte Carlo simulations have led to the suspicion that the time to failure of hierarchically organized load-transfer models of fracture is non-zero for sets of infinite size. This fact could have a profound significance in engineering practice and also in geophysics. Here, we develop an exact algebraic iterative method to compute the successive time intervals for individual breaking in systems of height $n$ in terms of the information calculated in the previous height $n-1$. As a byproduct of this method, rigorous lower and higher bounds for the time to failure of very large systems are easily obtained. The asymptotic behavior of the resulting lower bound leads to the evidence that the above mentioned suspicion is actually true.Comment: Final version. To appear in Phys. Rev. E, Feb 199