Universality for moving stripes: a hydrodynamic theory of polar active smectics.

We present a theory of moving stripes ("polar active smectics"), both with and without number conservation. The latter is described by a compact anisotropic Kardar-Parisi-Zhang equation, which implies smectic order is quasilong ranged in d=2 and long ranged in d=3. In d=2 the smectic disorders via a Kosterlitz-Thouless transition, which can be driven by either increasing the noise or varying certain nonlinearities.

Smectic-A to -C phase transition in isotropic disordered environments.

We study theoretically the smectic-A to -C phase transition in isotropic disordered environments. Surprisingly, we find that, as in the clean smectic-A to -C phase transition, smectic layer fluctuations do not affect the nature of the transition, in spite of the fact that they are much stronger in the presence of the disorder. As a result, we find that the universality class of the transition is that of the "random field XY model" (RFXY).