Physical interpretation of the Wigner rotations and its implications for relativistic quantum information

We present a new treatment for the spin of a massive relativistic particle in the context of quantum information based on a physical interpretation of the Wigner rotations, obtaining different results in relation to the previous works. We are lead to the conclusions that it is not possible to define a reduced density matrix for the particle spin and that the Pauli-Lubanski (or similar) spin operators are not suitable to describe measurements where spin couples to an electromagnetic field in the measuring apparatus. These conclusions contradict the assumptions made by most of the previous papers on the subject. We also propose an experimental test of our formulation.Comment: 10 pages, 2 figures. Several changes were made on the text. One extra example was include

General Pattern Search Applied to the Optimization of the Shell and Tube Heat Exchanger

The literature has different implementations and results for the mono-objective and multiobjective optimization of the shell and tube heat exchanger (STHE), most of them using evolutionary computation. However, there is a gap to find the optimal solution of this problem through direct search methods (numerical optimization). So, this paper uses the Pattern Search algorithm of MATLAB toolbox applied to this case study

O conceito de etologia, com especial referência ao comportamento dos primatas: (comentário)

a evolução do estudo do comportamento animal ou etologia é interpretada como consequência da combinação de duas áreasde investigação: os estudos biológicos e naturalísticos e a pesquisa sobr aprendizagem animal. A etologia, como disciplina autônoma, fundamenta-se mais na sua abordagem e em seus métodos do que nos problemas que suscitam o comportamento animal

Energy and momentum entanglement in parametric downconversion

We present a simple treatment for the phenomenon of parametric downconversion considering the coherent scattering of one pump photon into a photon pair by a nonlinear crystal. The energy and momentum entanglement of the quantum state of the generated twin photons are seen as a consequence of the fundamental indistinguishability of the time and the position in which the photon pair is created inside the crystal. We also discuss some consequences of the system entanglement.Comment: 6 pages, 2 figures. v3: Minor changes on the text. Some references were include

The Asymptotics of Wilkinson's Iteration: Loss of Cubic Convergence

One of the most widely used methods for eigenvalue computation is the $QR$ iteration with Wilkinson's shift: here the shift $s$ is the eigenvalue of the bottom $2\times 2$ principal minor closest to the corner entry. It has been a long-standing conjecture that the rate of convergence of the algorithm is cubic. In contrast, we show that there exist matrices for which the rate of convergence is strictly quadratic. More precisely, let $T_X$ be the $3 \times 3$ matrix having only two nonzero entries $(T_X)_{12} = (T_X)_{21} = 1$ and let $T_L$ be the set of real, symmetric tridiagonal matrices with the same spectrum as $T_X$. There exists a neighborhood $U \subset T_L$ of $T_X$ which is invariant under Wilkinson's shift strategy with the following properties. For $T_0 \in U$, the sequence of iterates $(T_k)$ exhibits either strictly quadratic or strictly cubic convergence to zero of the entry $(T_k)_{23}$. In fact, quadratic convergence occurs exactly when $\lim T_k = T_X$. Let $X$ be the union of such quadratically convergent sequences $(T_k)$: the set $X$ has Hausdorff dimension 1 and is a union of disjoint arcs $X^\sigma$ meeting at $T_X$, where $\sigma$ ranges over a Cantor set.Comment: 20 pages, 8 figures. Some passages rewritten for clarit

Geometrically induced singular behavior of entanglement

We show that the geometry of the set of quantum states plays a crucial role in the behavior of entanglement in different physical systems. More specifically it is shown that singular points at the border of the set of unentangled states appear as singularities in the dynamics of entanglement of smoothly varying quantum states. We illustrate this result by implementing a photonic parametric down conversion experiment. Moreover, this effect is connected to recently discovered singularities in condensed matter models.Comment: v2: 4 pags, 4 figs. A discussion before the proof of Proposition 1 and tomographic results were included, Propostion 2 was removed and the references were fixe