Experimental Verification of a Universal Operator Growth Hypothesis

Abstract

F$^{19}$ nuclear magnetic resonance free induction decay (FID) data are used to verify the predictions of a universal growth hypothesis for the Lanczos coefficients proposed by Parker et al. Our results strongly support this hypothesis and permit to calculate values of the growth parameter $\alpha$ for three crystal orientations. For the magnetic field parallel the [100] crystal axis, we found $\alpha =3.161 \times 10^{4} sec^{-1}$. The special experimental conditions required for the observability of a singularity in the analytic continuation of the FID, which from the experimental data was found to be of branch-point type, are discussed.