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Comment on "Motional Averaging of Nuclear Resonance in a Field Gradient"

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)].