We study propagation of low-intensity light in a medium within a one-dimensional ͑1D͒ model electrodynamics. It is shown that the coupled theory for light and matter fields may be solved, in principle exactly, by means of stochastic simulations that account for both collective linewidths and line shifts, and for quantum statistical position correlations of the atoms. Such simulations require that one synthesize atomic positions that have correlation functions appropriate for the given type of atomic sample. We demonstrate how one may simulate both a Bose-Einstein condensate ͑BEC͒ and a zero-temperature noninteracting Fermi-Dirac gas. Results of simulations of light propagation in such quantum degenerate gases are compared with analytical density expansions obtained by adapting the approach of Morice, Castin, and Dalibard ͓Phys. Rev. A 51, 3896 ͑1995͔͒ to the 1D electrodynamics. A BEC exhibits an optical resonance that narrows and stays somewhat below the atomic resonance frequency as collective effects set in with increasing atom density. The first two terms in the analytical density expansion are in excellent agreement with numerical results for a condensate. While fermions display a similar narrowing and shift of the resonance with increasing density, already in the limit of very dilute gas the linewidth is only half of the resonance linewidth of an isolated atom. We attribute this to the regular spacing between the atoms, which is enforced by the Pauli exclusion principle. The analytical density expansion successfully predicts the narrowing, and also gives the next term in the density expansion of the optical response in semiquantitative agreement with numerical simulations.
SummaryIt this paper are developed 4 models for estimation of blood platelet survival. They are put forward not as completely realistic but as at least first order approximations which should at once provide a systematic basis for estimation of mean platelet survival and the standard error of the estimate ; they will at the same time circumvent the subjective element in analysing the data with the attendant biases, and also provide a unifying theory for the several different models which the various investigators have more or less explicitly used in the past. The models may perhaps be thought of as smoothing functions to iron out the high experimental error inherent in the study of platelet survival.An attempt has been made to construct the model on the basis of present knowledge of the economy of the platelet and the factors influencing its survival. Doubtless further knowledge in these fields will call for modification of the details. Nevertheless it is evident that with these relatively simple models it is possible to generate quite a wide range of patterns which appear to conform well to those found by those working on this subject.
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