Temperature-dependent thermal conductivities of one-dimensional nonlinear Klein-Gordon lattices with soft on-site potential

TL;DR

This study systematically investigates how temperature affects thermal conductivities in one-dimensional nonlinear Klein-Gordon lattices with soft on-site potentials, confirming theoretical predictions through numerical simulations.

Contribution

It demonstrates that the temperature dependence of thermal conductivity in soft-KG lattices can be explained by effective phonon theory, extending understanding from hard-KG lattices.

Findings

Renormalized phonons exist in soft-KG lattices.

Temperature dependence of phonon frequency matches classical field theory.

Thermal conductivities follow a power-law dependence consistent with theoretical predictions.

Abstract

The temperature-dependent thermal conductivities of one-dimensional nonlinear Klein-Gordon lattices with soft on-site potential (soft-KG) have been investigated systematically. Similar to the previously studied hard-KG lattices, the existence of renormalized phonons has also been confirmed in soft-KG lattices. In particular, the temperature-dependence of renormalized phonon frequency predicted by a classical field theory has been verified by detailed numerical simulations. However, the thermal conductivities of soft-KG lattices exhibit opposite trend in the temperature dependence in comparison with the hard-KG lattices. The interesting thing is that both the temperature-dependent thermal conductivities of soft- and hard-KG lattices can be interpreted in the same framework of effective phonon theory. According to the effective phonon theory, the exponents of the power-law dependence of the thermal conductivities as the function of temperature are only determined by the exponents of the soft or hard on-site potentials. These theoretical predictions have been consistently verified very well by extensive numerical simulations.