Energy Trapping in Loaded String Models with Long- and Short-Range Couplings

This note illustrates the possibility in simple loaded string models of trapping most of the system energy in a single degree of freedom for very long times, demonstrating in particular that the robustness of the trapping is enhanced by increasing the `connectance' of the system, i.e., the extent to which many degrees of freedom are coupled directly by the interaction Hamiltonian, and/or the strength of the couplings.