  Motivated by cosmological examples we study quantum field theoretical
tunnelling from an initial state where the "classical field", i.e. the vacuum
expectation value of the field operator is spatially homogeneous but performing
a time-dependent oscillation about a local minimum. In particular we estimate
both analytically and numerically the exponential contribution to the
tunnelling probability. We additionally show that after the tunnelling event,
the classical field solution - the so-called "bubble" - mediating the phase
transition can either grow or collapse. We present a simple analytical
criterium to distinguish between the two behaviours.
