Nonlinear dynamical Casimir effect at weak nonstationarity

We show that even small nonlinearities significantly affect particle production in the dynamical Casimir effect at large evolution times. To end, we derive effective Hamiltonian and resum leading loop corrections to flux a massless scalar field theory with time-dependent Dirichlet boundary conditions quartic self-interaction. perform resummation, assume deviations from equilibrium employ kind of rotating wave approximation. Besides that, consider quantum circuit analog effect, which is also essentially nonlinear. In both cases, contributions number created particles are comparable tree-level values.