Journal of Statistical Physics, Vol. 56, Nos. 3/4, 1989, p. 331-355.
In recent years tunneling centers have frequently been used to explain the unusual thermodynamic properties of disordered materials; in these approaches, however, the effect of the tunneling-phonon interaction is neglecte& The present study considers the archetype model of phonon-assisted tunneling, which is well known from other areas of tunneling physics (quantum diffusion, etc.). It is shown that the full thermodynamic information can be rigorously extracted from a single Green function. An extended factorization procedure beyond Hartree-Fock is introduced, which is checked by sum rules as well as by exact Goldberger-Adams expansions. The phonon-modulated internal energy and specific heat are calculated for different power-law coupling setups.