Thermal conductivity in a chain of alternately free and bound particles

The thermal conductivity kappa of a lattice of alternately free and harmonically bound particles placed between two temperature reservoirs is calculated for various chain lengths and dimensionless energy epsilon. It is found that Fourier's law is obeyed for all epsilon as long as the lattice is long enough. However, this length scale undergoes a transition from essentially an epsilon independence for epsilon<epsilon(c) to a power-law dependence for epsilon>epsilon(c), meaning that larger lattices are needed to get normal thermal conductivity for large epsilon. This transition is seen to coincide with a change in scaling law for the maximum Lyapunov exponent lambda. This behavior of lambda is known to correspond to a transition to total chaos, where all stable regions of phase space have vanished. It is surmised that this measure of the dynamics can be used as a probe of the Fourier law properties of other systems.