In one-dimensional lattice systems, I will present results on the dynamics of composite objects such as repulsively bound pairs, triplets and clusters.

One highlight is a dramatic series of dynamics-suppression effects near edges or geometric features, associated with fractal structures in the energy spectrum.

Versions of these phenomena appear in (1) the Bose-Hubbard model; (2) the spinless fermion model with nearest neighbor repulsion; (3) the XXZ spin chain; (4) the fermionic Hubbard chain.