Solid state spin systems are excellent platforms on which to study coherent dynamics 
of large quantum systems.  In addition to exploring questions of control and decoherence, 
these systems allow us to perform a number of large-scale analog quantum simulations.  
Using solid state NMR we have been able to characterize many-spin dynamics in the 
cubic spin lattice of calcium fluoride and the quasi-one-dimensional system fluorapatite.  
Of particular interest are experiments that use multiple-pulse coherent averaging 
techniques to implement an effective double quantum (DQ) Hamiltonian.  In one 
dimension the DQ Hamiltonian is analytically solvable in the limit of nearest-neighbor 
couplings, and is related by a similarity transformation to the isotropic XY Hamiltonian.  
An important feature of the dynamics in one dimension is that magnetization is transported 
down the chain at a constant velocity, in contrast to the diffusive transport observed 
under the dipolar Hamiltonian in three-dimensional systems.  After reviewing our 
experimental results I will go on to discuss how this work can be extended to directly 
measure the velocity of spin transport, and to study the effects of decoherence on the 
spin dynamics.