The frequency spectrum of rotobreathers with many degrees of freedom

Abstract

A rotobreather in a lattice of coupled particles with rotational degrees of freedom is a dynamical regime when one particle rotates and the other particles vibrate with amplitudes exponentially decaying with distance from the rotating particle. In addition to rotational, particles can have internal degrees of freedom. Here, the influence of internal degrees of freedom on the possible rotational frequencies of rotobreathers is discussed for two models: a chain of coupled elastic rotators and a molecular crystal of carbon nanotubes (CNTs). It is shown that additional degrees of freedom create forbidden frequency bands for rotobreathers. In the case of a CNT crystal, due to resonances with many internal degrees of freedom, the frequency spectrum of a rotobreather has a complex structure resembling a Cantor set.