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

Ehrenfest dynamics is purity non-preserving: a necessary ingredient for decoherence

We discuss the evolution of purity in mixed quantum/classical approaches to electronic nonadiabatic dynamics in the context of the Ehrenfest model. As it is impossible to exactly determine initial conditions for a realistic system, we choose to work in the statistical Ehrenfest formalism that we introduced in Ref. 1. From it, we develop a new framework to determine exactly the change in the purity of the quantum subsystem along the evolution of a statistical Ehrenfest system. In a simple case, we verify how and to which extent Ehrenfest statistical dynamics makes a system with more than one classical trajectory and an initial quantum pure state become a quantum mixed one. We prove this numerically showing how the evolution of purity depends on time, on the dimension of the quantum state space $D$, and on the number of classical trajectories $N$ of the initial distribution. The results in this work open new perspectives for studying decoherence with Ehrenfest dynamics.Comment: Revtex 4-1, 14 pages, 2 figures. Final published versio

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

Aspectos do controlo da qualidade da fluodesoxiglucose num laboratório de produção

Resumo do poster apresentado ao XII Congresso Nacional de Medicina Nuclear, 12-14 Novembro 2009, Mealhad

Hybrid Quantum-Classical Monte-Carlo Study of a Molecule-Based Magnet

Using a Monte Carlo (MC) method, we study an effective model for the Fe(II)Fe(III) bimetallic oxalates. Within a hybrid quantum-classical MC algorithm, the Heisenberg S=2 and $S'=5/2$ spins on the Fe(II) and Fe(III) sites are updated using a quantum MC loop while the Ising-like orbital angular momenta on the Fe(II) sites are updated using a single-spin classical MC flip. The effective field acting on the orbital angular momenta depends on the quantum state of the system. We find that the mean-field phase diagram for the model is surprisingly robust with respect to fluctuations. In particular, the region displaying two compensation points shifts and shrinks but remains finite.Comment: 8 pages, 7 figure