Stretched Exponentials
Relaxonomy --> here
In between exponential [math]\displaystyle{ \exp(-\lambda t) }[/math] and gaussian [math]\displaystyle{ \exp[-(\sigma t)^2] }[/math] relaxation (and indeed extending beyond either) is the much-abused empirical "stretched exponential" function,
I don't much care for it. It will fit a wide variety of ZF-µSR relaxation functions, but what do the results mean? What do they tell us about the physics? There are cases where "root exponential" relaxation functions ([math]\displaystyle{ \beta = 1/2 }[/math]) suggest a rapidly fluctuating spin glass, but fit results with [math]\displaystyle{ \beta }[/math] all the way from 0.25 to 3 have been published without any hint of irony. Please don't resort to this.
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[math]\displaystyle{ G(t) = \exp[-(\Lambda t)^\beta] }[/math] for [math]\displaystyle{ \Lambda = 1 }[/math] and [math]\displaystyle{ \beta = 0.25, 0.5, 1, 2, 3 }[/math]. Only [math]\displaystyle{ \beta = 1, 2 }[/math] and sometimes [math]\displaystyle{ 0.5 }[/math] have familiar physical meanings. |
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