  We consider a system of two cavities separated by a reflecting boundary of
finite mass that is free to move, and bounded to its equilibrium position by a
harmonic potential. This yields an effective mirror-field interaction, as well
as an effective interaction between the field modes mediated by the movable
boundary. Two massless scalar fields are defined in each cavity. We consider
the second-order interacting ground state of the system, that contains virtual
excitations of both mirror's degrees of freedom and of the scalar fields. We
investigate the correlation functions between field observables in the two
cavities, and find that the squared scalar fields in the two cavities, in the
interacting ground state, are anticorrelated. We discuss the dependence of the
correlation on the distance of the two points considered from the mirror's
average position and on its mass and oscillation angular frequency. These
results show a sort of communication between the two half-spaces separated by
the movable mirror, mediated by its position fluctuations. Observability of
this new phenomenon exploiting two- or many-body dispersion interactions
between polarizable bodies is discussed. The dependence on a cutoff frequency
introduced to regularize the frequency integrations, as well as the case of a
real conductor, are also discussed.
