= Phonon mean free path
{title2=$\ell=v_g\tau$}
The <phonon mean free path> is the typical distance traveled by a <phonon> between the relevant scattering events. For heat transport, the relevant relaxation time must describe relaxation of heat current, not merely count all collisions. An isotropic kinetic estimate is $\kappa\simeq c_Vv_s\ell/3$, where $c_V$ is <heat capacity> per unit <volume>. Boundary-limited $\ell$ and the low-temperature <Debye model> give $\kappa\propto T^3$.
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