Static and Dynamic Casimir Effect Instabilities

The static Casimir effect concerns quantum electrodynamic induced Lamb shifts in the mode frequencies and thermal free energies of condensed matter systems. Sometimes, the condensed matter constitutes the boundaries of a vacuum region. The static frequency shift effects have been calculated in the one photon loop perturbation theory approximation. The dynamic Casimir effect concerns two photon radiation processes arising from time dependent frequency modulations again computed in the one photon loop approximation. Under certain conditions the one photon loop computation may become unstable and higher order terms must be invoked to achieve stable solutions. This stability calculation is discussed for a simple example dynamical Casimir effect system.