  Dynamical Casimir effect (DCE) and cosmological particle creation (CPC) share
the same underlying physical mechanism, that of parametric amplification of
vacuum fluctuations in the quantum field by an expanding universe or by a fast
moving boundary. Backreaction of cosmological particle creation at the Planck
time has been shown to play a significant role in the isotropization and
homogenization of the early universe. Understanding the backreaction effects of
quantum field processes in DCE is the goal of this work. We present analyses of
quantum field processes in two model systems: in 1+1D, a ring with
time-dependent radius, and in 3+1D, a symmetric rectangular conducting box with
one moving side. In both cases the time-dependence of the radius or the length
is determined solely by the backreaction of particle creation and related
effects, there is no external agent. We find that for 1+1D, the only quantum
field effect due to the trace anomaly tends to accelerate the contraction of
the ring over and above that due to the attractive force in the static Casimir
effect. For the rectangular box the expansion or contraction is slowed down
compared to that due to the static Casimir effect. Our findings comply with
what is known as the quantum Lenz law, found in cosmological backreaction
problems: the backreaction works in the direction of opposing further changes,
which means the suppression of particle creation and a slow down of the system
dynamics. In conclusion we suggest two related classes of problems of
theoretical significance for further investigations.
