Why is sound absorption by tunneling defects the same in all glasses?
In plain words
In every glass tested, sound waves lose nearly the same small fraction of their energy per cycle at low temperature, within a factor of about twenty. The standard tunneling model fits this but gives no reason why the number should be universal.
Precise statement
Below $\sim 1\,\mathrm{K}$ amorphous solids show specific heat $C \sim T$, thermal conductivity $\kappa \sim T^{2}$ and an internal-friction plateau $Q^{-1} = (\pi/2) C_{\mathrm{tun}}$, with tunneling strength $C_{\mathrm{tun}} = P \gamma^{2}/(\rho v^{2})$ between $\sim 10^{-4}$ and $10^{-3}$ across chemically different glasses ($P$ = density of states of tunneling two-level systems, $\gamma$ = deformation potential, $\rho$ = mass density, $v$ = sound velocity); equivalently the phonon mean free path is $\sim 150$ wavelengths. Explain this universality, e.g. by interaction-induced renormalization of the defects (Yu and Leggett; Burin and Kagan) or by a generic soft-mode mechanism, and predict where it fails.
What would settle it
A theory deriving $C_{\mathrm{tun}} \sim 10^{-4} \text{ to } 10^{-3}$ from generic properties of glasses, confirmed by a predicted exception or by simulations that compute $P$ and $\gamma$ in several model glasses.
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See also
- Related Do tunneling two-level defects dephase conduction electrons at millikelvin temperatures?
- Related Origin of the boson peak in glasses
- Related Frequency law of sound damping in glasses below the boson peak
- Related What atoms tunnel in the two-level systems of amorphous silica?
- Related Can two-level systems be removed by making glasses more stable?
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