Chin. Phys. Lett.  2021, Vol. 38 Issue (4): 044401    DOI: 10.1088/0256-307X/38/4/044401
 FUNDAMENTAL AREAS OF PHENOMENOLOGY(INCLUDING APPLICATIONS) |
Approach to Phonon Relaxation Time and Mean Free Path in Nonlinear Lattices
Yue Liu  and Dahai He*
Department of Physics, Xiamen University, Xiamen 361005, China
Yue Liu  and Dahai He 2021 Chin. Phys. Lett. 38 044401
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Abstract Based on the self-consistent phonon theory, the spectral energy density is calculated by the canonical transformation and the Fourier transformation. Through fitting the spectral energy density by the Lorentzian profile, the phonon frequency as well as the phonon relaxation time is obtained in one-dimensional nonlinear lattices, which is validated in the Fermi–Pasta–Ulam-$\beta$ (FPU-$\beta$) and $\phi^{4}$ lattices at different temperatures. The phonon mean free path is then evaluated in terms of the phonon relaxation time and phonon group velocity. The results show that, in the FPU-$\beta$ lattice, the phonon mean free path as well as the phonon relaxation time displays divergent power-law behavior. The divergent exponent coincides well with that derived from the Peierls–Boltzmann theory at weak anharmonic nonlinearity. The value of the divergent exponent expects a power-law divergent heat conductivity with system size, which violates Fourier's law. For the $\phi^{4}$ lattice, both the phonon relaxation time and mean free path are finite, which ensures normal heat conduction.
Received: 19 December 2020      Published: 06 April 2021
 PACS: 63.20.Ry (Anharmonic lattice modes) 05.60.Cd (Classical transport) 63.20.D 66.70.
Fund: Supported by the National Natural Science Foundation of China (Grant Nos. 12075199 and 11675133).
 TRENDMD: URL: http://cpl.iphy.ac.cn/10.1088/0256-307X/38/4/044401       OR      http://cpl.iphy.ac.cn/Y2021/V38/I4/044401