Why Phonon Scattering in Glasses is Universally Small at Low Temperatures

We present a novel view of the standard model of tunneling two level systems (TLSs) to explain the puzzling universal value of a quantity, $C\sim 3\times {10}^{-4}$, that characterizes phonon scattering in glasses below 1 K as reflected in thermal conductivity, ultrasonic attenuation, internal friction, and the change in sound velocity. Physical considerations lead to a broad distribution of phonon-TLS couplings that (1) exponentially renormalize tunneling matrix elements, and (2) reduce the TLS density of states through TLS-TLS interactions. We find good agreement between theory and experiment for a variety of individual glasses.