  In this paper we study the time evolution of an observable in the interacting
fermion systems driven out of equilibrium. We present a method for solving the
Heisenberg equations of motion by constructing excitation operators which are
defined as the operators A satisfying [H,A]=\lambda A. It is demonstrated how
an excitation operator and its excitation energy \lambda can be calculated. By
an appropriate supposition of the form of A we turn the problem into the one of
diagonalizing a series of matrices whose dimension depends linearly on the size
of the system. We perform this method to calculate the evolution of the
creation operator in a toy model Hamiltonian which is inspired by the Hubbard
model and the nonequilibrium current through the single impurity Anderson
model. This method is beyond the traditional perturbation theory in
Keldysh-Green's function formalism, because the excitation energy \lambda is
modified by the interaction and it will appear in the exponent in the function
of time.
