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

Published online by Cambridge University Press:  14 February 2012

R. Fürth
R. Fürth
Affiliation:
Birkbeck College, University of London
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Synoposis

General 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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 67 , Issue 4 , 1967 , pp. 289 - 302
Copyright
Copyright © Royal Society of Edinburgh 1967

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References

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