Low Temperature Properties of Glasses: Two Level Systems, Soft Modes, and Spectral Diffusion

A theoretical method that systematically finds tunneling systems in glasses and allows a microscopic justification of the standard tunneling model of Phillips and Anderson, Halperin and Varma is presented. The calculation shows that the major assumptions of the tunneling model are qualitatively correct; however, there are small deviations in the distribution functions of tunneling parameters that give rise to the T1+ε law for specific heat and the T2-α law for the thermal conductivity. The calculation also allows a quantitative estimate of the interaction of the two level systems with phonons (the deformation potential). The calculations confirm the weak coupling picture, in contrast with recent conjectures. The theory is then mapped onto all structural glasses via a Lennard-Jones model for the interaction between sub-units in the glass. These sub-units are molecular systems (e.g monomers in a polymer glass or tetrahedra in silicate glasses). From this mapping, we find that the tunneling parameters, and hence the thermal properties, of most structural glasses can be estimated semi-quantitatively from the microscopic parameters of the Hamiltonian. A further argument allows the connection between the tunneling parameters and the macroscopic experimental properties (sound velocity and density) to be drawn. The calculations also go smoothly into the "soft potential" model that explains the thermal behavior at higher temperatures (~10K), thus providing a universal model. From these calculations, the distribution of tunneling rates that give rise to spectral diffusion can be calculated and compared to recent experiments. These will be presented at the conference, along with calculations of the effect on the two level system distributions of introducing an impurity (i.e. chromophore) into the glass.