Phonon-dressing effects on two-level systems in amorphous solids and their influence on the low-temperature specific heat

The effects of a phonon thermal bath on the energy spectrum of a two-level system (TLS) in an amorphous solid are studied in the weak-coupling limit. We use the Hamiltonian resolvent technique, which allows us to calculate the corrections to the eigenenergies and lifetimes. We find that the influence of the interaction of TLS's with phonons, though small, is not negligible, and as an example, a numerical calculation of the low-temperature specific heat of various amorphous solids is presented. The numerical results show that the present accuracy in the determination of the model parameters makes it very difficult to establish a comparison between a dressed TLS and a free TLS description.