Projected Density of Transitions for Heisenberg Models

The projected density of transitions (PDoT) is the interacting analogue of the projected or local density of states. The PDoT is proportional to the probability, averaged over all states of the system, that some disturbance (the projection) induces a transition with a specific energy. It is calculated in the same way as the density of states, but using Heisenberg's equation instead of Schr\"{o}dinger's equation. As an example we have applied it to the Heisenberg model for spin interactions of electrons on linear, square, and cubic lattices. One surprise in these calculations is what seems to be a consequence of the spin's rotational symmetry.