Heat conduction in a chain of dissociating particles: Effect of dimensionality

The paper considers heat conduction in a model chain of composite particles with hard core and elastic external shell. Such model mimics three main features of realistic interatomic potentials--hard repulsive core, quasilinear behavior in a ground state, and possibility of dissociation. It has become clear recently that this latter feature has crucial effect on convergence of the heat conduction coefficient in thermodynamic limit. We demonstrate that in one-dimensional chain of elastic particles with hard core the heat conduction coefficient also converges, as one could expect. Then we explore effect of dimensionality on the heat transport in this model. For this sake, longitudinal and transversal motions of the particles are allowed in a long narrow channel. With varying width of the channel, we observe sharp transition from "one-dimensional" to "two-dimensional" behavior. Namely, the heat conduction coefficient drops by about order of magnitude for relatively small widening of the channel. This transition is not unique for the considered system. Similar phenomenon of transition to quasi-1D behavior with growth of aspect ratio of the channel is observed also in a gas of densely packed hard (billiard) particles, both for two- and three-dimensional cases. It is the case despite the fact that the character of transition in these two systems is not similar, due to different convergence properties of the heat conductivity. In the billiard model, the divergence pattern of the heat conduction coefficient smoothly changes from logarithmic to power-like law with increase of the length.