  Several methods are proposed for the analysis, visualization and
interpretation of high-dimensional spin system trajectories produced by quantum
mechanical simulations. It is noted that expectation values of specific
observables in large spin systems often feature fast, complicated and
hard-to-interpret time dynamics and suggested that populations of carefully
selected subspaces of states are much easier to analyze and interpret. As an
illustration of the utility of the proposed methods, it is demonstrated that
the apparent "noisy" appearance of many optimal control pulses in NMR and EPR
spectroscopy is an illusion - the underlying spin dynamics is shown to be
smooth, orderly and very tightly controlled.
