Inverse Laplace Transformation Analysis of Stretched Exponential Relaxation
| Autor: | C. Chaffey, H. Choi, Nicholas Curro, I. Vinograd |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Physics
Nuclear and High Energy Physics Strongly Correlated Electrons (cond-mat.str-el) Biophysics Spin–lattice relaxation FOS: Physical sciences Inverse Laplace transform Condensed Matter Physics 01 natural sciences Biochemistry Noise (electronics) 010305 fluids & plasmas Exponential function Condensed Matter - Strongly Correlated Electrons Distribution (mathematics) 0103 physical sciences Exponent Relaxation (physics) Statistical physics 010306 general physics Spin-½ |
| Popis: | We investigate the effectiveness of the Inverse Laplace Transform (ILT) analysis method to extract the distribution of relaxation rates from nuclear magnetic resonance data with stretched exponential relaxation. Stretched-relaxation is a hallmark of a distribution of relaxation rates, and an analytical expression exists for this distribution for the case of a spin-1/2 nucleus. We compare this theoretical distribution with those extracted via the ILT method for several values of the stretching exponent and at different levels of experimental noise. The ILT accurately captures the distributions for $\beta \lesssim 0.7$, and for signal to noise ratios greater than $\sim 40$; however the ILT distributions tend to introduce artificial oscillatory components. We further use the ILT approach to analyze stretched relaxation for spin $I>1/2$ and find that the distributions are accurately captured by the theoretical expression for $I=1/2$. Our results provide a solid foundation to interpret distributions of relaxation rates for general spin $I$ in terms of stretched exponential fits. Comment: 10 pages, 10 figures |
| Databáze: | OpenAIRE |
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