The effective Hamiltonian for the degenerate energy-eigenvalue problem in adiabatic perturbation theory is cast in a form that permits an expansion in Feynman diagrams. By means of a block representation a resummation of these diagrams is carried out such that in the adiabatic limit no...

We present a very brief and general proof that the series expansion for the effective constant of a heterogeneous medium can be expressed in irreducible cluster integrals only. The argument does not use details of the cluster expansion. On the other hand, for any given expansion it provides a...

The adiabatic perturbation formalism is used to derive several alternative expressions for the effective Hamiltonian of a discrete energy level. It is shown how in the nondegenerate case these expressions may be cast in the form of linked-cluster expansions. The connection between the energy...