Live soap: stability, order, and fluctuations in apolar active smectics.

We construct a hydrodynamic theory of noisy, apolar active smectics in bulk suspension or on a substrate. Unlike purely orientationally ordered active fluids, active apolar smectics can be dynamically stable in Stokesian bulk suspensions. Smectic order in these systems is quasilong ranged in dimension d=2 and long ranged in d=3. We predict reentrant Kosterlitz-Thouless melting to an active nematic in our simplest model in d=2, a nonzero second-sound speed parallel to the layers in bulk suspensions, and that there are no giant number fluctuations in either case. We also briefly discuss possible instabilities in these systems.