Dynamical Casimir effect in nonlinear vibrating cavities

Nonlinear terms in the equations of motion can induce secularly growing loop corrections to correlation functions. Recently such were shown affect particle production by a nonuniformly moving ideal mirror. We extend this conclusion cases vibrating cavity and single semitransparent These models provide natural IR UV scales allow more accurate study behavior. In both we confirm that two-loop correction Keldysh propagator quadratically grows with time. This growth indicates breakdown semiclassical approximation emphasizes bulk nonlinearities dynamical Casimir effect cannot be neglected for large evolution times.