  We study the influence of quantum fluctuations on the phase, density, and
pair correlations in a trapped quasicondensate after a quench of the
interaction strength. To do so, we derive a description similar to the
stochastic Gross-Pitaevskii equation (SGPE) but keeping a fully quantum
description of the low-energy fields using the positive-P representation. This
allows us to treat both the quantum and thermal fluctuations together in an
integrated way. A plain SGPE only allows for thermal fluctuations. The approach
is applicable to such situations as finite temperature quantum quenches, but
not equilibrium calculations due to the time limitations inherent in positive-P
descriptions of interacting gases. One sees the appearance antibunching, the
generation of counter-propagating atom pairs, and increased phase fluctuations.
We show that the behavior can be estimated by adding the T=0 quantum
fluctuation contribution to the thermal fluctuations described by the plain
SGPE.
