Thermal Conduction in one dimensional $\Phi^4$ chains with colliding particles

Abstract

This work relaxes the assumption of point particles prevalent in the study of thermal transport characteristics in $\Phi^4$ chains. The particles of the modified chain, henceforth termed as the $\Phi^{4C}$ chain, can collide with each other. Collisions have been modelled by adding a short-ranged soft-sphere potential to the Hamiltonian of the $\Phi^4$ chain. The inclusion of soft-sphere potential drastically alters the thermal transport characteristics while still satisfying the Fourier's law: at low temperatures, the temperature profile has negligible boundary jumps in $\Phi^{4C}$ chains, thermal conductivity of $\Phi^{4C}$ chains is significantly smaller than $\Phi^4$ chains at low temperatures, at high temperatures, $\Phi^{4C}$ chains have a higher thermal conductivity than $\Phi^4$ chains, and unlike $\Phi^4$ chains, where thermal conductivity keeps decreasing upon increasing temperature, in $\Phi^{4C}$ chains thermal conductivity abruptly decreases first and then increases beyond an inversion temperature. Splitting the total heat current into the contributions of the harmonic and anharmonic inter-particle forces, reveals that the harmonic contributions decrease with increasing temperature. On the contrary, anharmonic contributions increase with rising temperature, and beyond the inversion temperature they overtake the harmonic contributions. Exploring the dynamics in Fourier space helps in identifying that the energy of the lowest modes redistribute to other modes much faster in $\Phi^{4C}$ chains due to collisions. The quicker redistribution of the energy to higher modes is the reason behind smaller thermal conductivity in $\Phi^{4C}$ chains at low temperatures. The proposed $\Phi^{4C}$ chains have the features of both momentum conserving as well as momentum non-conserving systems, and may become an important tool to study thermal transport in real-life systems.