The Coupling Between Phason and Soft Modes Near the Smectic C* to Smectic a Phase Transition

Abstract

In condensed matter physics incommensurate phases can occur, if a symmetry of the underlying Hamiltonian is spontaneously broken more than once. The usual situation in incommensurate crystalline systems is that translational symmetry in one direction is broken twice due to the occurence of the periodical order of two different kinds of atoms or ions with different wavelengths. In a truly incommensurate phase the two wavelengths are incommensurate, there is no interaction energy between the two kinds of atoms and the relative motion is described by an acoustic-like excitation (phason). In a commensurate phase, where the ratio of the two wavelengths is rational, there is an interaction energy and the relative motion is optic-like (phason with gap). The transition between these two situations is the commensurate-incommensurate phase transition. In the following we will discuss incommensurate situations in liquid crystal systems and their similarities and differences compared to the usual crystalline phase.