OHMIC DISSIPATION OF TUNNELING IN DIELECTRIC GLASSES AT LOW-TEMPERATURE

An additional interaction term of a two-level tunnelling system with t he thermal lattice motion is derived, which is missed when expanding t he Hamiltonian in terms of the elastic distortion. As a consequence, t he bath spectral function comprises a part linear in frequency, beside s the well-known contribution proportional to omega3. Whereas the latt er is due to the derivative of the phonon field delu, the new term ari ses from coupling to the vibrational amplitude u itself. Since it requ ires an asymmetric atomic environment, this novel feature is intimatel y connected to the disordered configuration of atoms in amorphous soli ds; it leads to an Ohmic damping function which becomes predominant at very low temperature. The resulting linear variation of sound attenua tion with temperature possibly resolves a manifest discrepancy between predictions of the tunnelling model and attenuation data below 100 mi llikelvins.