Heat conduction and energy diffusion in momentum-conserving 1D full lattice ding-a-ling model

TL;DR

This study investigates a full lattice ding-a-ling model conserving momentum, revealing that it exhibits anomalous heat conduction and superdiffusive energy transport across different potential types, with no normal conduction observed.

Contribution

It introduces a new full lattice ding-a-ling model conserving momentum and analyzes its heat conduction and energy diffusion properties.

Findings

Superdiffusive energy diffusion in symmetric potentials.

Anomalous heat conduction in asymmetric potentials.

No evidence of normal heat conduction in the model.

Abstract

The ding-a-ling model is a kind of half lattice and half hard-point-gas (HPG) model. The original ding-a-ling model proposed by Casati {\it et.al} does not conserve total momentum and has been found to exhibit normal heat conduction behavior. Recently, a modified ding-a-ling model which conserves total momentum has been studied and normal heat conduction has also been claimed. In this work, we propose a full lattice ding-a-ling model without hard point collisions where total momentum is also conserved. We investigate the heat conduction and energy diffusion of this full lattice ding-a-ling model with three different nonlinear inter-particle potential forms. For symmetrical potential lattices, the thermal conductivities diverges with lattice length and their energy diffusions are superdiffusive signaturing anomalous heat conduction. For asymmetrical potential lattices, although the thermal conductivity seems to converge as the length increases, the energy diffusion is definitely deviating from normal diffusion behavior indicating anomalous heat conduction as well. No normal heat conduction behavior can be found for the full lattice ding-a-ling model.