MODE-COUPLING THEORY FOR THE DYNAMICS OF TUNNELING SYSTEMS IN DIELECTRICS

A mode-coupling theory (MCT) is presented for the spin-boson model wit h a spectral density which accounts for a heat bath made up of lattice vibrations of a dielectric solid (superohmic dissipation). A usual de coupling approximation provides a set of non-linear integral equations which are solved both numerically by iteration on a computer and anal ytically by means of a frequency dependent ansatz for the memory funct ions. There is a transition to incoherent motion at a temperature T w here the bare two-level energy is equal to the damping rate, in contra diction to results obtained previously from a path integral formulatio n. The discrepancy arises since in the MCT the relevant self-energy fu nction does not exhibit a 1/z-pole at z=0. For tunnelling systems in d ielectrics this yields a new relaxation mechanism due to incoherent tu nnelling: the present results might require to modify some of the basi c assumptions of the standard tunnelling model for dielectric glasses.