  Gaussian state decoherence aspects due to interacting magnetic-like and
gravitational fields are quantified through the quantum fidelity and Shannon
entropy in the scope of the phase-space representation of elementary quantum
systems. For Gaussian Wigner functions describing harmonic oscillator states,
an interacting external field destroys the quantum fidelity and introduces a
quantum beating behavior. Likewise, it introduces harmonic profiles for free
particle systems. Some aspects of quantum decoherence for the quantum harmonic
oscillator and for the free particle limit are also quantified through the
Shannon entropy. For the gravitational quantum well, the effect of a
magnetic-like field on the quantum fidelity is suppressed by the linear term of
the gravitational potential. To conclude, one identifies a fine formal
connection of the quantum decoherence aspects discussed here with the
noncommutative quantum mechanics.
