Dynamics
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$s(t)=e^{-t/T_{2}}\int P(r)e^{-i\int^
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_
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\omega(r,t')dt'}dr$
- Coherent - when ω is not a function of r (There are no interesting dynamics)
- Stationary - when ω is not a function of time (the system can be refocused by a π pulse for any time)
- Incoherent - stationary and not coherent, explicitly ω is a function of r (interesting question is the distribution of ω(r)
- Decoherent - when ω is a function of time and r, and the t dependence is stochastic/Marchovian (interesting dynamics: distribution of ω(r), spectral density of ω(r)
- Periodic - ω is a simple function of time (interesting dynamics: distribution of ω(r) at the characteristic frequency)
<PIC>
Frequency that an arbitrary location will see
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$\omega(t) = \gamma r \frac{\partial B_{z}}
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cos(\omega _
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t + \phi)$