Thermal conductivity in one-dimensional quasi-periodic Toda lattices

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Abstract
The authors investigate the thermal conductivity in one-dimensional quasi-periodic Toda lattice by means of the molecular dynamics technique. The lattice consists of two kinds of atom with different masses which are arranged according to the Fibonacci sequence. The temperature profile exhibits exponential behaviour as does the diatomic Toda lattice presented in their previous paper. The thermal conductivity is evaluated by separating the ballistically propagating part from the total heat flow. Heat conduction in the Toda lattice with quasi-periodic mass distribution in found to obey Fourier's law. The resultant thermal conductivity is inversely proportional to local temperature and the magnitude is reduced remarkably in comparison with that of the diatomic Toda lattice.