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A Generic Microscopic Theory for the Universality of TTLS Model Meissner-Berret Ratio in Low-Temperature Glasses

Tunneling-two-level-system (TTLS) model has successfully explained several low-temperature glass universal properties which do not exist in their crystalline counterparts. The coupling constants between longitudinal and transverse phonon strain fields and two-level-systems are denoted as $γ_l$ and $γ_t$. The ratio $γ_l/γ_t$ was observed to lie between $1.44$ and $1.84$ for 18 different kinds of glasses. Such universal property cannot be explained within TTLS model. In this paper by developing a microscopic generic coupled block model, we show that the ratio $γ_l/γ_t$ is proportinal to the ratio of sound velocity $c_l/c_t$. We prove that the universality of $γ_l/γ_t$ essentially comes from the mutual interaction between different glass blocks, independent of the microscopic structure and chemical compound of the amorphous materials. In the appendix we also give a detailed correction on the coefficient of non-elastic stress-stress interaction $Λ_{ijkl}^{(ss')}$ which was obtained by Joffrin and Levelut\cite{Joffrin1976}.