Mode coupling and resonance-induced relaxation in carbon nanotubes

Understanding how vibrational modes relax in low-dimensional materials is central to thermal transport, mechanical coherence control, and the design of high-Q nanomechanical resonators. Here we investigate the intrinsic relaxation dynamics of armchair carbon nanotubes (CNTs) under single-mode excitation, using molecular dynamics (MD) simulations combined with Floquet stability analysis. By classifying all zone-center modes according to their azimuthal quantum number and inversion parity, we provide a symmetry-based description of the vibrational spectrum at the Brillouin-zone center. MD simulations then reveal the selection rules governing intermodal coupling and the early-time redistribution of vibrational energy, while the theory of bushes of normal modes shows that these rules originate from the residual symmetry of the initially excited mode and the associated invariant modal subspace. Crucially, we find that the actual relaxation of the excited mode is determined not by these selection rules but instead by the presence of multiwave resonances. Both three-wave and degenerate four-wave processes can produce exponential growth of specific daughter modes, triggering a pronounced decay of the excited mode, whereas in the absence of such resonances the excitation remains dynamically stable. By constructing monodromy matrices, we compute Floquet multipliers that accurately predict the rate of these resonance-induced instabilities, yielding relaxation times in quantitative agreement with simulation. These results provide a unified microscopic understanding of intrinsic relaxation in CNTs and suggest practical strategies for selecting vibrational modes with enhanced robustness, which offers deeper insight into designing nanoscale systems in which intermodal coupling plays a functional role.