  Long-scale dynamic fluctuation phenomena in freely suspended films is
analyzed. We consider isotropic films that, say, can be pulled from bulk
smectic A liquid crystals. The key feature of such objects is possibility of
bending deformations of the film. The bending (also known as flexular) mode
turns out to be anomalously weakly attenuated. In the harmonic approximation
there is no viscous-like damping of the bending mode, proportional to q^2 (q is
the wave vector of the mode), since it is forbidden by the rotational symmetry.
Therefore the bending mode is strongly affected by non-linear dynamic
fluctuation effects. We calculate the dominant fluctuation contributions to the
damping of the bending mode due to its coupling to the in-plane viscous mode,
that restores the viscous-like q^2 damping of the bending mode. Our
calculations are performed in the framework of the perturbation theory where
the coupling of the modes is assumed to be small, then the bending mode damping
is relatively weak. We discuss our results in the context of existing
experiments and numeric simulations of the freely suspended films and propose
possible experimental observations of our predictions.
