Self-similarity and long-tailed distributions in the generation of thermal light
Rockower, Edward B.
MetadataShow full item record
Two counterintuitive phenomena are studied. ( 1) It is well known that a thermal electromagnetic field has a Bose-Einstein (geometric) distribution of photons within a coherence volume. This arises because of the photon clumping characteristic of a thermal Boson field. On the other hand, the distribution of the number of atoms emitting photons through spontaneous emission must be Poisson if emissions are truly independent. ( 2) The average time between atomic decays is finite, being just the inverse of the total decay rate of the atoms. However, it is shown that in a coherence volume or in a single mode of the resulting Gaussian electromagnetic field, the average photon interarrival time is infinite. Hence, on average, an infinite length of time must pass before (N) photons arrive in the field. These apparent paradoxes are discussed, showing how both arise from random interference of Boson fields. The infinite waiting time is seen to be one manifestation of a long-tailed distribution. Such distributions are increasingly important by virtue of their relation to self-similarity and fractals, e.g., strange attractors in the description of deterministic chaos; therefore, it is of interest to understand their counterintuitive properties and see how they arise naturally even in more traditional analyses.
Showing items related by title, author, creator and subject.
A simplified cell theory applied to the calculation of thermal neutron spectra in light water lattices MacVean, Charles Robert (Ithaca, New York; Cornell University, 1964-09);A simplified polyenergetic cell theory is formulated to determine spatially averaged energy dependent thermal fluxes in the moderator, cladding, and fuel regions within the unit cell of a reactor lattice. The derived ...
Liu, Kuang-Ming (Monterey, California: U.S. Naval Postgraduate School, 1961);The heat transfer and pressure drop of water flowing both upward and downward In an annulus were investigated. The data were obtained from a vertical narrow space annulus which was formed between 1.240 in. I. D. and ...
Trump, James C. (Monterey, California. Naval Postgraduate School, 1994-12);This thesis deals with analytical predictions and experimental determination of the modal frequencies and shapes associated with the arm portion of the Naval Postgraduate School's Flexible Spacecraft Simulator (FSS). A ...