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 cut-off is described in terms of an {\it incomplete} $\zeta$-function. The use of the Debye asymptotic expansion for Bessel functions allows to determine the dominant (volume, area, >...) terms in the Casimir energy. The possible interest of this kind of models for dielectric media (and its application to sonoluminescence) is also discussed.

7 pages, RevTeX. Version to appear in PRD (Introduction enlarged, references added)

References in corpus (3)

• Sonoluminescence as a QED vacuum effect. I: The Physical Scenario
• The Casimir Problem of Spherical Dielectrics: Quantum Statistical and Field Theoretical Approaches
• Sonoluminescence as a QED vacuum effect. II: Finite Volume Effects

Cited by in corpus (3)

• Effective Lagrangians for Scalar Fields and Finite Size Effects in Field Theory
• Divergencies in the Casimir energy for a medium with realistic ultraviolet behavior
• The covariant electromagnetic Casimir effect for real conducting spherical shells