Percorrer por autor "Dias, N. C."
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- Boundaries and profiles in the Wigner formalismoPublication . Dias, N. C.; Prata, J. N.We consider a quantum device contained in an interval in the context of the Weyl–Wigner formalism. This approach was originally suggested by Frensley and is known to be plagued with several problems, such as non-physical and non-unique solutions. We show that some of these problems may be avoided if one writes the correct dynamical equation. This requires the (non-local) infuence of the potential outside of the device and the inclusion of singular boundary potentials. We also discuss the problem of imposing boundary conditions on the Wigner function that mimic the efect of the external environment. We argue that these conditions have to be chosen with extreme care, as they may otherwise lead to non-physical solutions
- Ordinary differential equations with singular coefficients: An intrinsic formulation with applications to the Euler-Bernoulli beam equation.Publication . Dias, N. C.; Jorge, C.; Prata, J. N.
- Partial Traces and the Geometry of Entanglement; Sufficient Conditions for the Separability of Gaussian States.Publication . Dias, N. C.; Gossan, M. de; Prata, J. N.The notion of partial trace of a density operator is essential for the understanding of the entanglement and separability properties of quantum states. In this paper, we investigate these notions putting an emphasis on the geometrical properties of the covariance ellipsoids of the reduced states. We thereafter focus on Gaussian states and we give new and easily numerically implementable sufficient conditions for the separability of all Gaussian states. Unlike the positive partial transposition criterion, none of these conditions is however necessary.
- Quantum mappings acting by coordinate transformations on Wigner distributionsPublication . Dias, N. C.; Prata, J. N
- Some topological properties of the sets of non-negative Wigner functionsPublication . Dias, N. C.The set of non-negative Wigner functions is a convex set which, in the finite dimensional case, is compact and equal to the convex hull of its extreme points. Thus, in finite dimensions, these particular (extreme) Wigner functions can be used to generate the entire set of non-negative Wigner functions. We show that the extreme Wigner functions can be identified by the properties of their null sets, and discuss the problem of constructing these states explicitly. As a by-product, we also elaborate on the properties of the interior and the boundary of the set of non-negative Wigner functions. Finally, if time permits, we will discuss the difficulties of extending some of these results to the infinite dimensional case.