Efficient calculation of phonon dynamics through a low-rank solution of the Boltzmann equation

Exotic nondiffusive heat transfer regimes such as the second sound, where heat propagates as a damped wave at speeds comparable to those of mechanical disturbances, often occur at cryogenic temperatures (T) and nanosecond timescales in semiconductors. First-principles prediction of such rapid, low-T phonon dynamics requires finely-resolved temporal tracking of large, dense, and coupled linear phonon dynamical systems arising from the governing linearized Peierls-Boltzmann equation (LPBE). Here, we uncover a rigorous low-rank representation of these linear dynamical systems, derived from the spectral properties of the phonon collision matrix, that accelerates the first-principles prediction of phonon dynamics by a factor of over a million without compromising on the computational accuracy. By employing this low-rank representation of the LPBE, we predict strong amplification of the wave-like second sound regime upon isotopic enrichment in diamond - a finding that would have otherwise been computationally intractable using the conventional brute-force approaches. Our framework enables a rapid and accurate discovery of the conditions under which wave-like heat flow can be realized in common semiconductors.