Maps of Dynamic Regimes of Incommensurate Superstructures Described by the Lifshitz Invariant

Object of research: complex dynamical systems characterized by the existence of incommensurate superstructures; processes of origin of an incommensurate (IC) superstructure, its dynamics in sinusoidal, soliton and stochastic regimes, and in the field of surface energy. The aim of the work: to investigate the dynamics of an incommensurate superstructure from the magnitude of the long-range interaction and the anisotropic interaction, which is described by the Dzyaloshinskii invariant; under the influence of a mechanical and electric field, and in the field of surface energy; the effects of the transition from sinusoidal to solitonic and stochastic modes of an incommensurate superstructure. Results obtained. It has been established that the parameters T and K, which are responsible for the long-range and anisotropic interactions, respectively, in the first approximation well describe the behavior of the wave vector of IC modulation, and its modes. Maps of dynamic modes in coordinates, the value of the anisotropic interaction parameter, which is described by the Dzyaloshinskii invariant (K) and the value describing the long-range interaction (T), are obtained), testify to the complex processes of transformation of an incommensurable superstructure. These processes (appearance, change, and disappearance of periodicities) are determined by the spatial change in the phase and amplitude of the order parameter. It is shown that regardless of the symmetry of the thermodynamic potential (n), the dynamics of an incommensurable superstructure is determined by the change in the phase and amplitude of the order parameter. The influence of surface energy on an incommensurate superstructure in crystals of the family (N[CH3]4)2MeCl4 causes a change in the magnitude of the anisotropic interaction. It has been found that a decrease in the magnitude of anisotropic interaction in an incommensurate phase due to the influence of surface energy, in which there is a transition from a commensurate phase to a commensurate one, is associated with an increase in the contribution of spatial changes in the phase and amplitude of the order parameter. This leads to an increase in deformation structure, and therefore, in general, to an increase in the anisotropic interaction against the background of a decrease in the anisotropic interaction, which is described by the Dzialoshinskii invariant.