R. Golestanian et M. Kardar, PATH-INTEGRAL APPROACH TO THE DYNAMIC CASIMIR EFFECT WITH FLUCTUATINGBOUNDARIES, Physical review. A, 58(3), 1998, pp. 1713-1722
A path-integral formulation is developed for the dynamic Casimir effec
t. It allows us to study small deformations in space and time of the p
erfectly reflecting (conducting) boundaries of a cavity. The mechanica
l response of the intervening vacuum is calculated to linear order in
the frequency-wave-vector plane, using which a plethora of interesting
phenomena can be studied. For a single corrugated plate we find a cor
rection to mass at low frequencies and an effective shear viscosity at
high frequencies that are both anisotropic. The anisotropy is set by
the wave vector of the corrugation. For two plates, the mass renormali
zation is modified by a function of the ratio between thr: separation
of the plates and the wavelength of corrugations. The dissipation rate
is not modified for frequencies below the lowest optical mode of the
cavity and there is a resonant dissipation for all frequencies greater
than that. In this regime, a divergence in the response function impl
ies that such high-frequency deformation modes of the cavity cannot be
excited by any macroscopic external forces. This phenomenon is intima
tely related to resonant particle creation. For particular examples of
two corrugated plates that are stationary, or moving uniformly in the
lateral directions, Josephson-like effects are observed. For capillar
y waves on the surface of mercury a renormalization to surface tension
and sound velocity is obtained.