h2. Dynamics


{latex}
$s(t)=e^{-t/T_{2}}\int P(r)e^{-i\int^{t}_{0}\omega(r,t')dt'}dr$
{latex}

* 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 refucus 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)

frequency that an arbitrary location will see
{latex}
$\omega(t) = \gamma r \frac{\partial B_{z}}{\partial x} cos(\omega _{s} t + \phi)$
{latex}