Experimental Verification of a Universal Operator Growth Hypothesis

TL;DR

This paper uses F19 NMR data to experimentally verify a universal operator growth hypothesis, supporting its predictions and calculating growth parameters for different crystal orientations.

Contribution

It provides experimental validation for the universal growth hypothesis of Lanczos coefficients and discusses conditions for observing singularities in the data.

Findings

Strong support for the universal growth hypothesis.

Calculated growth parameter $oldsymbol{}$ for three crystal orientations.

Identified branch-point type singularity in the analytic continuation of FID.

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.