Correlações intrínsecas em sistemas tipo-Dirac confinados por um campo magnético constante

Abstract

The Weyl-Wigner formalism in phase space is investigated in the context of Dirac spinors as qubits correlated by continuous degrees of freedom. The extension to relativistic equations connects quantum mechanical phenomena to quantifiers of the information stored in the Hilbert spaces of a confined Dirac particle. In particular, one focuses in linear entropy measures, calculated from the Wigner function for equal times. On the other hand, quantum information can be calculated by an entanglement measure, the quantum concurrence. In this context, to investigate the aspects of a quantum information theory, a fermion trapped by a magnetic field is considered. One finds that this entanglement measure is affected by interference in the configuration space, but not by linear combinations in phase space. Cat states can be obtained analytically as Gaussian superpositions dependent on a distance parameter in phase space. These states are followed by patterns of temporal evolution known as quantum revivals, as predicted for highly localized solutions. However, the unexpected feature is that the symmetry of cat states prevents them from following the usual dynamics. Namely, they exhibit fractional revivals with respect to their classical counterparts. Finally, statistical ensembles of Wigner-Dirac functions are also considered. A unique measure of quantum concurrence for mixed states is investigated. In this context, the partition function of the canonically distributed ensembles is also calculated. It is obtained from complex integration techniques, exhibiting distinct behavior for high and low temperatures. Respectively, a polynomial dependence on temperature and an expansion in terms of analytically continued Hurwitz functions are observed. Since this is the object that also describes the thermodynamics of confined Dirac-like systems in reduced spatial dimensions, our result establishes the formalism for calculating intrinsic correlations in systems that exhibit the same algebra as the Dirac equation in three spatial dimensions. In this context, we propose a method that can be applied to low energy systems, from electronic bands to bosonic systems.