Fluctuations and dissipation for a mirror in vacuum

Marc-Thierry Jaekel, Serge Reynaud

Published 2001-01-16Version 1

A mirror in the vacuum is submitted to a radiation pressure exerted by scattered fields. It is known that the resulting mean force is zero for a motionless mirror, but not for a mirror moving with a non-uniform acceleration. We show here that this force results from a motional modification of the field scattering while being associated with the fluctuations of the radiation pressure on a motionless mirror. We consider the case of a scalar field in a two-dimensional spacetime and characterize the scattering upon the mirror by frequency dependent transmissivity and reflectivity functions obeying unitarity, causality and high frequency transparency conditions. We derive causal expressions for dissipation and fluctuations and exhibit their relation for any stationary input. We recover the known damping force at the limit of a perfect mirror in vacuum. Finally, we interpret the force as a mechanical signature of the squeezing effect associated with the mirror's motion.