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The 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 mo- mentum 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 elec- tric 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.