Casimir energy for a scalar field with a frequency dependent boundary condition

Abstract

We consider the vacuum energy for a scalar field subject to a frequency dependent boundary condition. The effect of a frequency cutoff is described in terms of an incomplete ζ function. The use of the Debye asymptotic expansion for Bessel functions allows us to determine the dominant (volume, area, ...) terms in the Casimir energy. The possible interest of this kind of model for dielectric media (and its application to sonoluminescence) is also discussed.