Dynamics of an electric dipole moment in a stochastic electric field

The mean-field dynamics of an electric dipole moment in a deterministic and a fluctuating electric field is solved to obtain the average over fluctuations of the dipole moment and the angular momentum as a function of time for a Gaussian white-noise stochastic electric field. The components of the average electric dipole moment and the average angular momentum along the deterministic electric-field direction do not decay to zero, despite fluctuations in all three components of the electric field. This is in contrast to the decay of the average over fluctuations of a magnetic moment in a stochastic magnetic field with Gaussian white noise in all three components. The components of the average electric dipole moment and the average angular momentum perpendicular to the deterministic electric-field direction oscillate with time but decay to zero, and their variance grows with time.