  In the Letter by Nanette N. Jarenwattananon and Louis-S. Bouchard [PRL 114,
197601 (2015)] an NMR experiment on gases in the presence of a magnetic-field
gradient has been considered. As distinct from the traditional description of
molecular self-diffusion, the authors calculate the decoherence of the signal
taking into account the histories of molecular displacements. For this purpose
the generalized Langevin equation (GLE) is applied. We show that the use of
this equation is inappropriate. The calculations performed in the Letter are
not correct and do not lead to the reported revised expression for line
broadening that takes into account the autocorrelation effects in the diffusion
process. The surprising temperature behavior of the observed NMR signal is thus
not explained. In particular, the linewidth does not follow the power law f ~
T^(-1/2) at high temperatures.
  We give also Remarks on the Jarenwattananon and Bouchard Reply [Phys. Rev.
Lett. 117, 249702 (2016)].
