Brownian motion of atomic systems: Fokker-Planck limit of the transport equation

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Abstract
A comparison is made between the Fokker-Planck equation (FPE) and the transport equation (TE) solutions of the problem of the collisional relaxation of an atomic or molecular system undergoing Brownian motion. It is shown that, for times ≲ (inverse collision rate), the FPE does not provide an appropriate approximation to the TE if the velocity bandwidth of the initially prepared sample is less than the root-mean-square change in velocity per collision. Possible experimental verification of the theory using laser-pump sources to provide narrow initial-velocity distributions is discussed.