Nonlinear vibrational dynamics and stability of quantum intrinsic localized modes in carbon nanotubes: Influence of harmonic and nonlinear coupling parameters

Carbon nanotubes are nanostructures renowned for their remarkable mechanical, electrical, and thermal properties, with their vibrational dynamics playing a central role in their stability and functionality. This article presents an in-depth modeling of the quantum vibrational dynamics of two-dimensional carbon nanotubes. By developing an anharmonic discrete Hamiltonian and then quantizing it using bosonic operators, a nonlinear two-dimensional Schrödinger equation is derived. This equation allows for the study of the formation, stability, and dynamics of quantum localized vibrational modes. The results show that the stability of these modes strongly depends on the parameters of linear and nonlinear coupling, particularly the local rigidity and anharmonic interactions. Modulating these parameters provides precise control over the localization, dissipation, and collisions of breathers, enabling manipulation of vibrational excitations at the nanometric scale. Analytical and numerical analyses also reveal the emergence of energy confinement phenomena and controlled dissipation. Furthermore, the numerical study of breather collisions highlights complex dynamics such as trapping, energy barriers, excitation, and the formation of energy wells which depend on the ratio between the local nonlinear parameter and the inter-site nonlinear parameter. This work provides a deeper understanding of nonlinear phenomena at the nanoscale, opening avenues for precise control of vibrational excitations in carbon nanotubes, with potential applications in energy management, nanoelectronics, and nanomechanics.