Hydrodynamics of the incommensurate phases of smectics-EandHg3−δAsF6

We discuss the linearized hydrodynamic equations for the incommensurate phases of smectic-$E$ liquid crystals and of the mercury chain compound ${\mathrm{Hg}}_{3-\delta }\mathrm{As}{\mathrm{F}}_6$. In particular, we clarify the nature of the spontaneously broken continuous symmetries and point out their consequences for the number of hydrodynamic variables and thus for the number of propagating and diffusive normal modes. In addition, contact is made with a microscopic description by deriving Kubo relations for the transport parameters involved. A discussion of the crossover between propagating and diffusive modes due to finite interactions between the chains and the host lattice of ${\mathrm{Hg}}_{3-\delta }\mathrm{As}{\mathrm{F}}_6$ is also included.