Phason dynamics in one-dimensional lattices

In quasicrystals, the phason degree of freedom and the inherent anharmonic potentials lead to complex dynamics, which cannot be described by the usual phonon modes of motion. We have constructed simple one-dimensional model systems, the dynamic Fibonacci chain, and approximants thereof. They allow us to study the dynamics of periodic and quasiperiodic structures with anharmonic double-well interactions both by analytical calculations and by molecular-dynamics simulations. We found soliton modes such as breathers and kink solitons and we were able to obtain closed analytical solutions for special cases, which are in good agreement with our simulations. Calculation of the specific heat shows an increase above the Dulong-Petit value, which is due to the anharmonicity of the potential and not caused by the phason degree of freedom.