Efficient calculation of phonon dynamics through a low-rank solution of the Boltzmann equation
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866913673862184960 |
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| author | Malviya, Nikhil Ravichandran, Navaneetha K. |
| author_facet | Malviya, Nikhil Ravichandran, Navaneetha K. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00337 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Efficient calculation of phonon dynamics through a low-rank solution of the Boltzmann equation Malviya, Nikhil Ravichandran, Navaneetha K. Materials Science 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. |
| title | Efficient calculation of phonon dynamics through a low-rank solution of the Boltzmann equation |
| topic | Materials Science |
| url | https://arxiv.org/abs/2502.00337 |