  We consider models in which two sets of matched two-level systems are coupled
to a common oscillator in the case where the oscillator energy is small
relative to the two-level transition energies. Since the two sets of two-level
systems are coupled indirectly through the oscillator, excitation transfer from
one set of two-level systems to the other is possible. In addition, the
excitation energy from the two-level systems may be exchanged with the
oscillator coherently, even though the oscillator energy may be orders of
magnitude smaller than the two-level system transition energy. In the lossless
case, we demonstrate these effects numerically, and also use an approximate
diagonalization to show that these effects are expected from the model
Hamiltonian.
  We augment the model to include loss effects, and show that loss enhances the
excitation transfer effect by breaking the severe cancelation between different
paths that occurs in the lossless case. We describe a simple approximate model
wavefunction appropriate when the loss increases rapidly with energy. Within
this model approximation, we present numerical and analytical results for
excitation transfer and energy transfer rates, showing that they are greatly
increased.
  Our study of these models is motivated in part by claims of excess heat
production in electrochemical experiments in heavy water. We examine the
question of whether the rates associated with this kind of model are
sufficiently large to be relevant to the experimental claims. We find that
consistency is possible given recent experimental results showing strong
screening effects in low energy deuteron-deuteron fusion experiments in metals.
