Dynamics of helicoidal ferroelectric smectic-$\tilde{C}$ liquid crystals

The order-parameter fluctuation spectrum of a chiral system undergoing a helicoidal ferroelectric $\mathrm{s}\mathrm{m}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{c}-A\to \mathrm{s}\mathrm{m}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{c}-\tilde{C}$ phase transition is evaluated both above and below $T_c$. The transition is produced by a condensation of a coupled tilt-polarization soft mode. The "in-phase" amplitude fluctuations in the tilt and the polarization represent the soft mode of the low-temperature phase, whereas "in-phase" orientational fluctuations represent the Goldstone mode which is recovering the continuous symmetry group broken at $T_c$.