Temperature and Frequency Dependent Mean Free Paths of Renormalized Phonons in Nonlinear Lattices

TL;DR

This study investigates how the mean free paths of renormalized phonons depend on temperature and frequency in nonlinear lattices, revealing an inverse proportionality to phonon frequency that challenges existing theories.

Contribution

It introduces a numerical tuning fork method to directly measure the temperature and frequency dependent mean free paths of renormalized phonons in nonlinear lattices.

Findings

Mean free paths are inversely proportional to phonon frequencies.

Results challenge the quadratic frequency dependence predicted by traditional phonon scattering theory.

Study focuses on FPU-β and φ^4 lattice models.

Abstract

In the regime of strong nonlinearity, the validity of conventional perturbation based phonon transport theories is questionable. In particular, the renormalized phonons instead of phonons are responsible for heat transport in nonlinear lattices. 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 $\beta$ (FPU-$\beta$) lattice and $\phi^4$ lattice are investigated in details. 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.