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

Optomechanical Backreaction of Quantum Field Processes in Dynamical Casimir Effect