Long time tails in Brownian motion 
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*Rings, D., et al. Theory of hot Brownian motion. Soft Matter 7.7 (2011): 3441-3452, doi:10.1039/C0SM00854K.


In this paper the author has mentioned that vorticity diffusion is disregarded due to it's finite time scale. Is the time scale of vorticity diffusion too large when compared to particle motion or is it in the opposite way? Please explain the meaning of the statement.
Thank You in Advance
 A: I believe that they are assuming that the vorticity diffusion decays faster than the timescale for the particle motion, and in fact they say so in the opening section of a later paper: EPL 96 60009 (2011).
It is not completely self evident that this assumption is justified, since the vorticity diffusion is responsible for the long-time tail in the particle velocity correlation function, which decays algebraically in time. It goes like $t^{-3/2}$ in 3D and like $t^{-1}$ in 2D. You can find more details on this if you look up "long time tails" in the literature. In other words, this contribution to the particle motion does not actually have a well-defined timescale: if you try to write it as $A (t/\tau)^{-3/2}$ there is actually no way of separating the amplitude $A$ from the apparent timescale $\tau$, in the combination $A\tau^{3/2}$. By contrast, for example, with an exponential decay $A\exp(-t/\tau)$ you can separately identify the amplitude $A$ and the timescale $\tau$. So it is hard to justify that this effect of vortex diffusion is "fast" compared with the particle motion.
Nonetheless, perhaps there is some other justification for the assumption that they can neglect the effects of vortex diffusion. It allows them to simplify the way they handle the Langevin equation.
