Intrinsic domain-wall pinning and spatial chaos in continuum models of one-dimensionally incommensurate systems

In the class of one-dimensional continuum models in which the incommensurate state arises from a term -(d{η}/dx)² in the free-energy density, the commensurate-incommensurate transition is first order, and the free energy as a function of domain-wall spacing can have a relative minimum which is not the global minimum. The pinning of the walls (relative to one another) which results is severe in this class of models, and occurs in both the commensurate and incommensurate states. A subclass of these models allows an additional type of incommensurate state, the rippled commensurate state; spatial chaos is found at the transition between the two types of incommensurate states.