Abstract
We show that in the case of a dilute gas of neutral particles kinetic equations for autocorrelation functions such as
, can be obtained in a very simple manner by the use of the truncated BBGKY hierarchy. The resulting equations correspond to the low-density limit of the results of van Leeuwen and Yip. Moreover, the derivation does not make use of the Bogoliubov adiabatic approximation, and therefore includes non-Markovian effects which can be important in describing light scattering from gases and the collisional narrowing of atomic dipole radiation. The resulting equations in the long-wavelength limit correspond to the non-Markovian Boltzmann equation for the self-correlation part and the non-Markovian, linearized Boltzmann equation for the total autocorrelation function.
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This research was supported by the Advanced Research Projects Agency of the Department of Defense and was monitored by Army Research Office-Durham under Contract No. DA-31-124-ARO-D-139.
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Chappell, W.R. Kinetic equations for autocorrelation functions in dilute gases. J Stat Phys 2, 267–277 (1970). https://doi.org/10.1007/BF01030746
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DOI: https://doi.org/10.1007/BF01030746