Abstract
Unraveling general properties of renormalized phonons are of fundamental relevance to the heat transport in the regime of strong nonlinearity. In this work, we directly study the temperature and frequency dependent mean free path (MFP) of renormalized phonons with the newly developed numerical tuning fork method. The typical 1D nonlinear lattices such as Fermi–Pasta–Ulam β lattice and lattice are investigated in detail. Interestingly, it is found that the MFPs are inversely proportional to the frequencies of renormalized phonons rather than the square of phonon frequencies predicted by existing phonon scattering theory.
Highlights
Phonon is a basic concept in solid state physics describing the collective motions of lattice vibrations
It is found that the mean free path (MFP) are inversely proportional to the frequencies of renormalized phonons rather than the square of phonon frequencies predicted by existing phonon scattering theory
The renormalized phonons are discovered by different groups independently in various research areas ranging from lattice vibrations [1, 2], heat conduction [3], field thermalization [4] and nonlinear waves [5, 6]
Summary
Phonon is a basic concept in solid state physics describing the collective motions of lattice vibrations. The phenomenological effective phonon theory [7, 11,12,13, 16] is developed within the framework of renormalized phonons dedicated to the explanations of temperature dependence of thermal conductivities for nonlinear lattices. The effective phonon theory predicts the temperature dependent thermal conductivities k(T ) of 1D Fermi–Pasta–Ulam β (FPU-β) lattice are inversely proportional to temperature as k(T ) μ T-1 at low temperature region and proportional to the quartic root of temperature as k(T ) μ T1 4 at high temperature region [13, 16]. The temperature and frequency dependent MFPs of renormalized phonons will be calculated and compared with the conjecture for typical 1D FPU-β, H4 and f4 lattices. The good agreement between numerical results and the conjecture indicates that the MFP of renormalized phonons is inversely proportional to the renormalized phonons frequency and the nonlinearity strength, which is beyond the scope of any conventional perturbative phonon transport theory
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