  We calculate exactly the quantum mechanical, temporal Wigner quasiprobability
density for a single-mode, degenerate parametric amplifier for a system in the
Gaussian state, viz., a displaced-squeezed thermal state. The Wigner function
allows us to calculate the fluctuations in photon number and the quadrature
variance. We contrast the difference between the nonclassicality criteria,
which is independent of the displacement parameter $\alpha$, based on the
Glauber-Sudarshan quasiprobability distribution $P(\beta)$ and the
classical/nonclassical behavior of the Mandel $Q_{M}(\tau)$ parameter, which
depends strongly on $\alpha$. We find a phase transition as a function of
$\alpha$ such that at the critical point $\alpha_{c}$, $Q_{M}(\tau)$, as a
function of $\tau$, goes from strictly classical, for $|\alpha|< |\alpha_{c}|$,
to a mixed classical/nonclassical behavior, for $|\alpha|> |\alpha_{c}|$.
