Spatio-Temporal Correlations of Local Polarization in Ferroelectrics

Abstract

The spatio-temporal correlations of the local polarization in ferroelectrics is considered. Starting from the Landau-Ginzburg Hamiltonian, the kinetics of the system is reintroduced by the Langevin equation with additive white noise. The problem is transformed into a noise perturbed Fokker-Planck equation. A continuous path integral represents the formal solution of this Fokker-Planck equation and yields the time evolution of the probability distribution function over all the spatial configurations of the polarization. The spatio-temporal correlation function is evaluated in the Feynman diagram technique by solving the related Dyson equation. An approximate analytical solution for the Fourier transform of the correlation function is found in a case where the Landau-Ginzburg Hamiltonian includes a competitive interaction term. The competitive interaction yields the formation of spatially correlated regions (precursors) with opposite polarization.