Anti-Fermi-Pasta-Ulam energy recursion in diatomic lattices at low energy densities

We study the dynamics of one- and two-dimensional diatomic lattices with the interatomic Morse potentials for the initial conditions selected at the edge of the Brillouin zone of the dispersion spectrum, when only light atoms are excited with the staggered mode while all heavy atoms remain at rest (the so-called anti-Fermi-Pasta-Ulam problem). We demonstrate that modulational instability of such a nonlinear state may result in almost periodic temporal dynamics of the lattice with spatial localization and delocalization of energies. Such a recursion occurs many times with a very slow decay, especially for the initial states with low energy. The energy recursion results in the formation of highly localized, large-amplitude gap discrete breathers. For one-dimensional diatomic lattices, we describe the periodic energy recursion analytically for a simple model with the nearest-neighbor interaction and cubic anharmonicity.