Universal sound absorption in low-temperature glasses

Abstract

Phenomenologically assuming a sharp decrease of shear relaxation time for large wavevector $k>k_\xi$ density modes (where $k_\xi$ is of order of inverse of several interatomic distances $a$), I develop a general elasto-hydrodynamic theory describing the low-energy excitations of glassy and amorphous solids, which are responsible for anomalous specific heat and thermal conductivity. The theory explains the origin of collective two-level states and Boson peak. The ratio of the wavelength of the phonon, $\lambda$, to its mean free path, $l$, - universal property of sound absorption in glasses - is derived in this theory to be $\lambda/l=(2/3) (c_t/c_l)^2 (k_\xi a)^3$, where $c_t$ and $c_l$ are transverse and longitudinal sound velocities correspondingly.