Spin system trajectory analysis under optimal control pulses

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.