Density of states for energy-dependent effective Hamiltonians

We provide two analytic expressions particularly useful for the evaluation of the density of states of multichannel interacting structures described by effective energy-dependent Hamiltonians. We show that the knowledge of the off-diagonal matrix elements of a properly defined Green's function, between the terminal sites of the system, is the main ingredient to obtain the total density of states. We have used our expressions to calculate the densities of states of ladder chains where each site of the chains may be connected to an external system. A couple of significant examples clarify the feasibility of these expressions.