  We propose a scheme for extending the model Hamiltonian method developed
originally for studying the equilibrium properties of complex perovskite
systems to include Langevin dynamics. The extension is based on Zwanzig's
treatment of nonlinear generalized Langevin's equations. The parameters
entering the equations of motion are to be determined by mapping from
first-principles calculations, as in the original model Hamiltonian method. The
scheme makes possible, in principle, the study of the dynamics and kinetics of
structural transformations inaccessible to the original model Hamiltonian
method. Moreover, we show that the equilibrium properties are governed by an
effective Hamiltonian which differs from that used in previous work by a term
which captures the coherent part of the previously ignored dynamical
interaction with the omitted degrees of freedom. We describe how the additional
information required for the Langevin equations can be obtained by a minor
extension of the previous mapping.
