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 $FP{U}^C$ 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 $FP{U}^C$ 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 $FP{U}^C$ 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.

References in corpus (7)

• Finite thermal conductivity in 1d lattices
• Momentum conservation implies anomalous energy transport in 1d classical lattices
• Bulk Properties of Anharmonic Chains in Strong Thermal Gradients: Non-Equilibrium ${\varphi }^4$ Theory
• 1D momentum-conserving systems: the conundrum of anomalous versus normal heat transport
• Fourier law in a momentum-conserving chain
• Non-Equilibrium Steady States and Transport in the Classical Lattice ${\varphi }^4$ Theory
• Thermal Conduction in one dimensional ${\Phi }^4$ chains with colliding particles