  The influence of spacetime foam on a broad class of bosonic fields with
arbitrary numbers of particles in the low energy regime is investigated. Based
on recently formulated general description of open quantum gravitational
systems, we analyse the propagation of scalar, electromagnetic, and
gravitational waves on both long and short time scales with respect to their
mean frequencies. For the long time propagation, the Markov approximation is
employed that neglects the effects of initial conditions of these waves. In
this case, despite intuitively expected decoherence and dissipation from the
noisy spacetime, we show that such phenomena turn out to be completely
suppressed for scalar bosons, photons, and gravitons, which are coupled to
gravity but otherwise free. The short time effects are then recovered through
the transient non-Markovian evolution. Focusing on scalar bosons in initially
incoherent states, we find that the resulting quantum dissipation depend
strongly on the distribution of the particle momentum states. We further
identify a hitherto undiscovered collective anti-dissipation mechanism for a
large number of particles. The surprising new effect tends to "bundle"
identical particles within a sharply distributed momentum states having a width
inversely proportional to the particle number due to the thermal fluctuations,
or its square root due to the vacuum fluctuations of spacetime.
