Thermal transport characteristics of Fermi-Pasta-Ulam chains undergoing soft-sphere type collisions

Abstract

We show numerically that including soft-sphere type collisions in the celebrated Fermi-Pasta-Ulam ($FPU$) chain completely alters the thermal transport characteristics. The resulting $FPU^C$ chains, while being momentum preserving, satisfy the Fourier's law and do not show anomalous thermal transport behavior. Collisions play a significant role in reducing the boundary jumps typically observed in $FPU$ chains. The thermal conductivity of the $FPU^C$ chains is significantly smaller than the $FPU$ chains at low temperatures due to the fast redistribution of energy from the lowest mode of vibrations to the higher modes. At high temperatures, however, the $FPU^C$ chains have larger thermal conductivity than the $FPU$ chains due to the large contributions to the heat flux because of the large-magnitude short-ranged anharmonic collision force.