Publicações

The Weyl-Wigner representations for canonical thermal equilibrium quantum states are obtained for the whole class of quadratic Hamiltonians through a Wick rotation of the Weyl-Wigner symbols of Heisenberg and metaplectic operators. The behavior of classical structures inherently associated to these unitaries is described under the Wick mapping, unveiling that a thermal equilibrium state is fully determined by a complex symplectic matrix, which sets all of its thermodynamical properties. The four categories of Hamiltonian dynamics (Parabolic, Elliptic, Hyperbolic, and Loxodromic) are analyzed. Semiclassical and high temperature approximations are derived and compared to the classical and/or quadratic behavior.

In this work we determine a lower bound to the mean value of the quantum potential for an arbitrary state. Furthermore, we derive a generalized uncertainty relation that is stronger than the Robertson-Schrödinger inequality and hence also stronger than the Heisenberg uncertainty principle. The mean value is then associated to the nonclassical part of the covariances of the momenta operator. This imposes a minimum bound for the nonclassical correlations of momenta and gives a physical characterization of the classical and semiclassical limits of quantum systems. The results obtained primarily for pure states are then generalized for density matrices describing mixed states.

We show how the dispersive regime of the Jaynes-Cummings model may serve as a valuable tool to the study of open quantum systems. We employ it in a bottom-up approach to build an environment that preserves qubit energy and induces varied coherence dynamics. We then present the derivation of a compact expression for the qubit coherence, applied here to the case of a finite number of thermally populated modes in the environment. We also discuss how the model parameters can be adjusted to facilitate the production of short-time monotonic decay (STMD) of the qubit coherence. Our results provide a broadly applicable platform for the investigation of energy-conserving open system dynamics which is fully within the grasp of current quantum technologies.