Phonon damping in one-dimensional lattices with asymmetric interactions

The symmetry of interparticle interaction plays an important role in determining the energy transport and diffusion behavior of one-dimensional (1D) lattices, not only in the process of hydrodynamics but also in the process of kinetics. In this paper, we study the relaxation properties of phonons in 1D lattices with asymmetric and symmetric interparticle interactions, exemplified by the famous Fermi-Pasta-Ulam-Tsingou model. Asymmetric interparticle interactions (AIIs) lead to larger damping rates of phonons as compared to symmetric ones in the low-temperature limit, and the difference gradually vanishes when the temperature increases. Moreover, in lattices with AIIs, the dependence of the damping rate Γ of phonons still follows a power-law on the wave number q, i.e., Γ ∼ qγ for small q. In particular, at low temperatures, AIIs result in γ ≈ 1, which is out of the predictions of 3/2 ≤ γ ≤ 2 from various theories. Our results provide insights into understanding the anomalous heat conduction observed in 1D chains and ultra-low phonon heat conduction found in certain solids.