The truncated Levy-flight process: Application to the random spin phase change in non-linear magnetic fields

Oleg Posnansky, Ruiwang Huang and N. Jon Shah

Physica A: Statistical Mechanics and its Applications, 2006, vol. 370, issue 2, 553-564

Abstract: In NMR experiments, self-diffusion of water molecules leads to a random spin phase distribution which is Gaussian in linear magnetic fields. The rate of convergence of the random phase distribution to the Gaussian distribution is very slow. Moreover, a small departure from linear magnetic fields results in significant changes in the spin phase distribution, especially in the central part, and the distribution can be described by Levy-flight process. However, the far-tails of the Levy-like distribution conserve information about the Gaussian prehistory and can validate the degree of non-linearity of the magnetic field. In this paper, the rate, α, of convergence to the Gaussian distribution is calculated for the case of the variation of the power of non-linearity of the magnetic field p and it is shown that α(p)∈(0,0.66] when p∈[1,∞).

Keywords: Levy-flight process; Random walk; NMR; Non-linear field; Crossover; Convergence rate; Monte-Carlo simulations (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:370:y:2006:i:2:p:553-564

DOI: 10.1016/j.physa.2006.03.062

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