  Polarization in ferroelectrics, described by the Landau-Ginzburg Hamiltonian,
is considered, based on a multi-dimensional Fokker-Planck equation. This
formulation describes the time evolution of the probability distribution
function over the polarization field configurations in the presence of a time
dependent external field. The Fokker-Planck equation in a Fourier
representation is obtained, which can then be solved numerically for a finite
number of modes. Calculation results are presented for one and three modes.
These results show the hysteresis of the mean polarization as well as that of
the mean squared gradient of the polarization.
