Improved Callaway model for lattice thermal conductivity

In developing the phonon quasiparticle picture, Peierls discovered that, in a perfect crystal, without anharmonic umklapp ($U$) events, a current-carrying distribution can never relax to a zero-current distribution. Callaway introduced a simplified approximate model version of the Peierls-Boltzmann equation, retaining its ability to deal separately with normal ($N$) and $U$ events. This paper clarifies and improves the Callaway model, and shows that Callaway underestimated the suppression of $N$ processes in relaxing thermal current. The new result should improve computations of thermal conductivity from relaxation-time studies.