Correlações no Espaço de Fase Quântico

We use the Wigner-Weyl formalism of quantum mechanics to study quantum correlations in phase space. We focus on the correlations between a state and all its possible translations in phase space. This treatment is done in both the quantum and the semiclassical regimes. It leads us to define the concept of blind spot: The points where the correlation is zero. We show that, for any dimension, those points are a characteristic of states without a definite point-reflection symmetry (also known as inversion symmetry). Superpositions of coherent states are specially analyzed; blind spots appear in the classical regions as the points of complete destructive interference pattern of plane waves. In fact, for triplets of coherent states they are arranged on an hexagonal lattice, which consists of two mutually orthogonal sub-lattices. In the Markovian limit, we show their extreme sensitivity to decoherence induced by an environment. Moreover, we evaluate the typical semiclassical distributions in phase space (i.e. the Wigner function and its symplectic Fourier transform) for Bohr-quantized energy states and we resolve their corresponding caustics (arisen by the short-wave approximation), in order to realize the presence of blind spots at semiclassical level. We also obtain a semiclassical approximation for the distribution moments in terms of the classical averages. These results are illustrated in a numerical study of Fock states. Finally, seeking for the blind spots in the case of general evolution, beyond translations, we study the quantum fidelity or Loschmidt echo semiclassically. We obtain an Initial-Value Representation for the fidelity, which generalizes and formalizes the Dephasing Representation (see Ref. [Van04]). Our results hold even for regular dynamics, for which the previous treatments are not suitable.