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Key role of asymmetric interactions in low-dimensional heat transport

We study the heat current autocorrelation function (HCAF) in one-dimensional, momentum-conserving lattices. In particular, we explore if there is any relation between the decaying characteristics of the HCAF and asymmetric interparticle interactions. The Lennard-Jones model is intensively investigated in view of its significance to applications. It is found that in wide ranges of parameters, the HCAF decays faster than power-law manners, and in some cases it decays even exponentially. Following the Green-Kubo formula, the fast decay of HCAF implies the convergence of heat conductivity, which is also corroborated by numerical simulations. In addition, with a comparison to the Fermi-Pasta-Ulam-$β$ model of symmetric interaction, the HCAF of the Fermi-Pasta-Ulam-$α$-$β$ model of asymmetric interaction is also investigated. Our study suggests that, in certain ranges of parameters, the decaying behavior of the HCAF is correlated to the asymmetry degree of interaction.