  In this work, momentum-space decoherence using minimum and
nonminimum-uncertainty-product (stretched) Gaussian wave packets in the
framework of Caldeira-Leggett formalism and under the presence of a linear
potential is studied. As a dimensionless measure of decoherence, purity, a
quantity appearing in the definition of the {\it linear entropy}, is studied
taking into account the role of the stretching parameter. Special emphasis is
on the open dynamics of the well-known cat states and bosons and fermions
compared to distinguishable particles. For the cat state, while the stretching
parameter speeds up the decoherence, the external linear potential strength
does not affect the decoherence time; only the interference pattern is shifted.
Furthermore, the interference pattern is not observed for
minimum-uncertainty-product-Gaussian wave packets in the momentum space.
Concerning bosons and fermions, the question we have addressed is how the
symmetry of the wave functions of indistinguishable particles is manifested in
the decoherence process, which is understood here as the loss of being
indistinguishable due to the gradual emergence of classical statistics with
time. We have observed that the initial bunching and anti-bunching character of
bosons and fermions, respectively, in the momentum space are not preserved as a
function of the environmental parameters, temperature and damping constant.
However, fermionic distributions are slightly broader than the distinguishable
ones and these similar to the bosonic distributions. This general behavior
could be interpreted as a residual reminder of the symmetry of the wave
functions in the momentum space for this open dynamics.
