Thermal conductivity of one- and two-dimensional lattices

Abstract

Numerical experiments were conducted to study the energy transfer through one- and two-dimensional nonlinear lattices, with various anharmonicities and diatomic mass ratios, when they are placed between two thermal reservoirs. The existence and dependence of normal thermal conductivity on the number of particles in the lattice (N<or=400) and the mass ratio is studied. In these lattices, an approximate transition is found to be related to the decay of a pulse travelling across the finite lattice. The threshold for the transition from infinite to normal thermal conductivity is also found to coincide with the value of these parameters for which the divergence of trajectories in every region of the phase space of the system becomes nonlinear with time, in an interval shorter than the time a pulse needs to travel through the lattice. It is also found that the thermal conductivity of the two-dimensional lattices that were examined differs from that of similar one-dimensional lattices only quantitatively and not qualitatively as predicted by Peierls' 'Umklapp' analysis.