Thermal conductivity in a chain of alternately free and bound particles

The thermal conductivity κ of a lattice of alternately free and harmonically bound particles placed between two temperature reservoirs is calculated for various chain lengths and dimensionless energy ε. It is found that Fourier's law is obeyed for all ε as long as the lattice is long enough. However, this length scale undergoes a transition from essentially an ε independence for ε<εc to a power-law dependence for ε>εc, meaning that larger lattices are needed to get normal thermal conductivity for large ε. This transition is seen to coincide with a change in scaling law for the maximum Lyapunov exponent λ. This behavior of λ 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.