The frequency spectrum of rotobreathers with many degrees of freedom

¹ N. N. Semenov Federal Research Center for Chemical Physics of RAS (FRCCP RAS) - Moscow 119991, Russia
² Plekhanov Russian University of Economics - Moscow 117997, Russia
³ Institute of Mathematics with Computing Centre, UFRC of RAS - Ufa 450008, Russia
⁴ Institute of Molecule and Crystal Physics, Ufa Federal Research Centre of RAS - Ufa 450054, Russia

^(a) dmitriev.sergey.v@gmail.com (corresponding author)

Received: 11 September 2021
Accepted: 2 February 2022

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.