XXIII.—Autocorrelation in Black Body Radiation and in Density Fluctuation Waves in Liquids

Abstract

SynoposisGeneral formulae are derived from first principles for the temporal and spatial autocorrelation functions of stochastic parameters which are defined in terms of superposed, uncorrelated waves with known spectral density distribution. These formulae are first used for obtaining expressions for the autocorrelation functions of the components of the electromagnetic field strength and the electromagnetic energy density in black body radiation fields. The general theory is further applied to compression waves in liquids, and expressions are derived for the temporal and spatial autocorrelation of thermal density fluctuations in liquids, in particular near their critical point. Finally the spectrum of the fluctuations in the total radiation emitted by a thermal source, owing to the fluctuations in the energy supply to the source, is obtained from the appropriate Langevin equation, and the temporal autocorrelation function of the radiation intensity due to this cause is derived from the spectrum.