Discrete breathers in aperiodic diatomic FPU lattices with long range order

Abstract

This study presents various aspects of discrete breathers in diatomic FPU lattices with masses varying according to the aperiodic Fibonacci and Thue–Morse sequences. We investigate the existence of time-periodic breathers, starting from the anti-continuous limit and consider excitations of isolated light atoms, hence obtaining the domain of unique existence for these breathers. We also perform a linear stability analysis by studying the Floquet operator. The found exact solutions are used, slightly perturbed, as initial conditions for long-time simulations of the breathers. These breathers turn out to be robust. Finally we consider how initial excitations of two consecutive light atoms evolve. Depending on the properties of the phase space for the two-atom system at the anti-continuous limit, we obtain different behaviour of these excitations. Especially we find that the aperiodic lattices can support localized excitations with a continuous frequency distribution for the timescales we consider, while a periodic lattice is unable to. These excitations are referred to as chaotic breathers.