  By using nonequilibrium Green's functions and the equation of motion method,
we formulate a self-consistent field theory for the electron transport through
a single molecular junction (SMJ) coupled with a vibrational mode. We show that
the nonequilibrium dynamics of the phonons in strong electron-phonon coupling
regime can be taken into account appropriately in this self-consistent
perturbation theory, and the self-energy of phonons is connected with the
current fluctuations in the molecular junction. We calculate the
finite-frequency nonsymmetrized noise spectra and the ac conductance, which
reveal a wealth of inelastic electron tunneling characteristics on the
absorption and emission properties of this SMJ. In the presence of a finite
bias voltage and the electron tunneling current, the vibration mode of the
molecular junction is heated and driven to an unequilibrated state. The
influences of unequilibrated phonons on the current and the noise spectra are
investigated.
