Space and time dependent polarization fluctuations in dielectric media

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Abstract
Molecular dipole moments in a dielectric medium are statistically correlated over large distances. In this paper we derive an expression for the correlation function of two molecular dipoles at different times and at different points in space in the limit of large separation. The result is obtained by means of a purely macroscopic treatment. For the case of equal times our results agree with those obtained by Nienhuis and Deutch from a microscopic theory of a fluid of rigid dipoles; in particular we see the same dependence on the shape of the dielectric sample and on the nature of its surroundings. The methods used in deriving the expression for the dipole correlation function may also be used to calculate the fluctuations in the higher electric multipole moments of small spherical regions in a dielectric sample. A number of results of this type are presented.