Dissipation due to two-level systems in nano-mechanical devices

We analyze the dissipation of the frequency vibrations of nano-mechanical devices. We show that the coupling between flexural modes and two-level systems leads to sub-ohmic dissipation. The inverse quality factor of the low energy vibrations depends on temperature as $Q^{-1}(T)\approx Q_0+C{T}^{1\mathrm{/}3}$, providing a quantitative description of the experimental data.